21. Syrakos, A; Varchanis, S; Dimakopoulos, Y; Goulas, A; Tsamopoulos, J

A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods Journal Article

In: Physics of Fluids, 29 (12), 2017, ISSN: 10706631, (cited By 10).

Abstract | Links | BibTeX | Tags:

@article{Syrakos2017,

title = {A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods},

author = {A Syrakos and S Varchanis and Y Dimakopoulos and A Goulas and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85040116407&doi=10.1063%2f1.4997682&partnerID=40&md5=30bbdac5477647015c5a49654fbf22d6},

doi = {10.1063/1.4997682},

issn = {10706631},

year = {2017},

date = {2017-01-01},

journal = {Physics of Fluids},

volume = {29},

number = {12},

abstract = {Finite volume methods (FVMs) constitute a popular class of methods for the numerical simulation of fluid flows. Among the various components of these methods, the discretisation of the gradient operator has received less attention despite its fundamental importance with regards to the accuracy of the FVM. The most popular gradient schemes are the divergence theorem (DT) (or Green-Gauss) scheme and the least-squares (LS) scheme. Both are widely believed to be second-order accurate, but the present study shows that in fact the common variant of the DT gradient is second-order accurate only on structured meshes whereas it is zeroth-order accurate on general unstructured meshes, and the LS gradient is second-order and first-order accurate, respectively. This is explained through a theoretical analysis and is confirmed by numerical tests. The schemes are then used within a FVM to solve a simple diffusion equation on unstructured grids generated by several methods; the results reveal that the zeroth-order accuracy of the DT gradient is inherited by the FVM as a whole, and the discretisation error does not decrease with grid refinement. On the other hand, use of the LS gradient leads to second-order accurate results, as does the use of alternative, consistent, DT gradient schemes, including a new iterative scheme that makes the common DT gradient consistent at almost no extra cost. The numerical tests are performed using both an in-house code and the popular public domain partial differential equation solver OpenFOAM. © 2017 Author(s).},

note = {cited By 10},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

Finite volume methods (FVMs) constitute a popular class of methods for the numerical simulation of fluid flows. Among the various components of these methods, the discretisation of the gradient operator has received less attention despite its fundamental importance with regards to the accuracy of the FVM. The most popular gradient schemes are the divergence theorem (DT) (or Green-Gauss) scheme and the least-squares (LS) scheme. Both are widely believed to be second-order accurate, but the present study shows that in fact the common variant of the DT gradient is second-order accurate only on structured meshes whereas it is zeroth-order accurate on general unstructured meshes, and the LS gradient is second-order and first-order accurate, respectively. This is explained through a theoretical analysis and is confirmed by numerical tests. The schemes are then used within a FVM to solve a simple diffusion equation on unstructured grids generated by several methods; the results reveal that the zeroth-order accuracy of the DT gradient is inherited by the FVM as a whole, and the discretisation error does not decrease with grid refinement. On the other hand, use of the LS gradient leads to second-order accurate results, as does the use of alternative, consistent, DT gradient schemes, including a new iterative scheme that makes the common DT gradient consistent at almost no extra cost. The numerical tests are performed using both an in-house code and the popular public domain partial differential equation solver OpenFOAM. © 2017 Author(s).22. Martino, E; Koilias, G; Athanasiou, M; Katsaounis, A; Dimakopoulos, Y; Tsamopoulos, J; Vayenas, C G

Experimental investigation and mathematical modeling of triode PEM fuel cells Journal Article

In: Electrochimica Acta, 248 , pp. 518-533, 2017, ISSN: 00134686, (cited By 2).

Abstract | Links | BibTeX | Tags: CO poisoning, Nafion membrane, Nernst-Planck equation, PEM fuel cell, Triode operation

@article{Martino2017518,

title = {Experimental investigation and mathematical modeling of triode PEM fuel cells},

author = {E Martino and G Koilias and M Athanasiou and A Katsaounis and Y Dimakopoulos and J Tsamopoulos and C G Vayenas},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85026742264&doi=10.1016%2fj.electacta.2017.07.168&partnerID=40&md5=4b8badef07890142c099e644ee1cb167},

doi = {10.1016/j.electacta.2017.07.168},

issn = {00134686},

year = {2017},

date = {2017-01-01},

journal = {Electrochimica Acta},

volume = {248},

pages = {518-533},

abstract = {The triode operation of humidified PEM fuel cells has been investigated both with pure H2 and with CO poisoned H2 feed over commercial Vulcan supported Pt(30%)-Ru(15%) anodes. It was found that triode operation, which involves the use of a third, auxiliary, electrode, leads to up to 400% power output increase with the same CO poisoned H2 gas feed. At low current densities, the power increase is accompanied by an increase in overall thermodynamic efficiency. A mathematical model, based on Kirchhoff's laws, has been developed which is in reasonably good agreement with the experimental results. In order to gain some additional insight into the mechanism of triode operation, the model has been also extended to describe the potential distribution inside the Nafion membrane via the numerical solution of the Nernst-Planck equation. Both model and experiment have shown the critical role of minimizing the auxiliary-anode or auxiliary-cathode resistance, and this has led to improved comb-shaped anode or cathode electrode geometries. © 2017},

note = {cited By 2},

keywords = {CO poisoning, Nafion membrane, Nernst-Planck equation, PEM fuel cell, Triode operation},

pubstate = {published},

tppubtype = {article}

}

The triode operation of humidified PEM fuel cells has been investigated both with pure H2 and with CO poisoned H2 feed over commercial Vulcan supported Pt(30%)-Ru(15%) anodes. It was found that triode operation, which involves the use of a third, auxiliary, electrode, leads to up to 400% power output increase with the same CO poisoned H2 gas feed. At low current densities, the power increase is accompanied by an increase in overall thermodynamic efficiency. A mathematical model, based on Kirchhoff's laws, has been developed which is in reasonably good agreement with the experimental results. In order to gain some additional insight into the mechanism of triode operation, the model has been also extended to describe the potential distribution inside the Nafion membrane via the numerical solution of the Nernst-Planck equation. Both model and experiment have shown the critical role of minimizing the auxiliary-anode or auxiliary-cathode resistance, and this has led to improved comb-shaped anode or cathode electrode geometries. © 201723. Fraggedakis, D; Papaioannou, J; Dimakopoulos, Y; Tsamopoulos, J

Discretization of three-dimensional free surface flows and moving boundary problems via elliptic grid methods based on variational principles Journal Article

In: Journal of Computational Physics, 344 , pp. 127-150, 2017, ISSN: 00219991, (cited By 6).

Abstract | Links | BibTeX | Tags: Contact angle models, Elliptic-grid generation, Free-surface flows, Mesh generation, Moving boundary problems, Moving contact line

@article{Fraggedakis2017127,

title = {Discretization of three-dimensional free surface flows and moving boundary problems via elliptic grid methods based on variational principles},

author = {D Fraggedakis and J Papaioannou and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85019087162&doi=10.1016%2fj.jcp.2017.04.060&partnerID=40&md5=91d7c6640649372c3fda59baa7e8497f},

doi = {10.1016/j.jcp.2017.04.060},

issn = {00219991},

year = {2017},

date = {2017-01-01},

journal = {Journal of Computational Physics},

volume = {344},

pages = {127-150},

abstract = {A new boundary-fitted technique to describe free surface and moving boundary problems is presented. We have extended the 2D elliptic grid generator developed by Dimakopoulos and Tsamopoulos (2003) [19] and further advanced by Chatzidai et al. (2009) [18] to 3D geometries. The set of equations arises from the fulfillment of the variational principles established by Brackbill and Saltzman (1982) [21], and refined by Christodoulou and Scriven (1992) [22]. These account for both smoothness and orthogonality of the grid lines of tessellated physical domains. The elliptic-grid equations are accompanied by new boundary constraints and conditions which are based either on the equidistribution of the nodes on boundary surfaces or on the existing 2D quasi-elliptic grid methodologies. The capabilities of the proposed algorithm are first demonstrated in tests with analytically described complex surfaces. The sequence in which these tests are presented is chosen to help the reader build up experience on the best choice of the elliptic grid parameters. Subsequently, the mesh equations are coupled with the Navier–Stokes equations, in order to reveal the full potential of the proposed methodology in free surface flows. More specifically, the problem of gas assisted injection in ducts of circular and square cross-sections is examined, where the fluid domain experiences extreme deformations. Finally, the flow-mesh solver is used to calculate the equilibrium shapes of static menisci in capillary tubes. © 2017 Elsevier Inc.},

note = {cited By 6},

keywords = {Contact angle models, Elliptic-grid generation, Free-surface flows, Mesh generation, Moving boundary problems, Moving contact line},

pubstate = {published},

tppubtype = {article}

}

A new boundary-fitted technique to describe free surface and moving boundary problems is presented. We have extended the 2D elliptic grid generator developed by Dimakopoulos and Tsamopoulos (2003) [19] and further advanced by Chatzidai et al. (2009) [18] to 3D geometries. The set of equations arises from the fulfillment of the variational principles established by Brackbill and Saltzman (1982) [21], and refined by Christodoulou and Scriven (1992) [22]. These account for both smoothness and orthogonality of the grid lines of tessellated physical domains. The elliptic-grid equations are accompanied by new boundary constraints and conditions which are based either on the equidistribution of the nodes on boundary surfaces or on the existing 2D quasi-elliptic grid methodologies. The capabilities of the proposed algorithm are first demonstrated in tests with analytically described complex surfaces. The sequence in which these tests are presented is chosen to help the reader build up experience on the best choice of the elliptic grid parameters. Subsequently, the mesh equations are coupled with the Navier–Stokes equations, in order to reveal the full potential of the proposed methodology in free surface flows. More specifically, the problem of gas assisted injection in ducts of circular and square cross-sections is examined, where the fluid domain experiences extreme deformations. Finally, the flow-mesh solver is used to calculate the equilibrium shapes of static menisci in capillary tubes. © 2017 Elsevier Inc.24. Pettas, D; Karapetsas, G; Dimakopoulos, Y; Tsamopoulos, J

On the degree of wetting of a slit by a liquid film flowing along an inclined plane Journal Article

In: Journal of Fluid Mechanics, 820 , pp. 5-41, 2017, ISSN: 00221120, (cited By 4).

Abstract | Links | BibTeX | Tags: coating, microfluidics, thin films

@article{Pettas20175,

title = {On the degree of wetting of a slit by a liquid film flowing along an inclined plane},

author = {D Pettas and G Karapetsas and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85018251137&doi=10.1017%2fjfm.2017.190&partnerID=40&md5=0326c1722b5184752e6664f1f164bac6},

doi = {10.1017/jfm.2017.190},

issn = {00221120},

year = {2017},

date = {2017-01-01},

journal = {Journal of Fluid Mechanics},

volume = {820},

pages = {5-41},

abstract = {Liquid film flow along an inclined plane featuring a slit, normal to the main direction of flow, creates a second gas-liquid interface connecting the two side walls of the slit. This inner interface forms two three-phase contact lines and supports a widely varying amount of liquid under different physical and geometrical conditions. The exact liquid configuration is determined by employing the Galerkin/finite element method to solve the two-dimensional Navier-Stokes equations at steady state. The interplay of inertia, viscous, gravity and capillary forces along with the substrate wettability and orientation with respect to gravity and the width of the slit determine the extent of liquid penetration and free-surface deformation. Finite wetting lengths are predicted in hydrophilic and hydrophobic substrates for inclination angles more or less than the vertical, respectively. Multiple steady solutions, connected by turning points forming a hysteresis loop, are revealed by pseudo-Arclength continuation. Under these conditions, small changes in certain parameter values leads to an abrupt change in the wetting length and the deformation amplitude of the outer film surface. In hydrophilic substrates the wetting lengths exhibit a local minimum for small values of the Reynolds number and a very small range of Bond numbers; when inertia increases, they exhibit the hysteresis loop with the second limit point in a very short range of Weber numbers. Simple force balances determine the proper rescaling in each case, so that critical points in families of solutions for different liquids or contact angles collapse. The flow inside the slit is quite slow in general because of viscous dissipation and includes counter-rotating vortices often resembling those reported by Moffatt (J. Fluid Mech., vol.Â 18, 1964, pp.Â 1-18). In hydrophobic substrates, the wetting lengths decrease monotonically until the first limit point of the hysteresis loop, which occurs in a limited range of Bond numbers when the Kapitza number is less than 300 and in a limited range of Weber numbers otherwise. Here additional solution families are possible as well, where one or both contact points (Cassie state) coincide with the slit corners. © 2017 Cambridge University PressÂ.},

note = {cited By 4},

keywords = {coating, microfluidics, thin films},

pubstate = {published},

tppubtype = {article}

}

Liquid film flow along an inclined plane featuring a slit, normal to the main direction of flow, creates a second gas-liquid interface connecting the two side walls of the slit. This inner interface forms two three-phase contact lines and supports a widely varying amount of liquid under different physical and geometrical conditions. The exact liquid configuration is determined by employing the Galerkin/finite element method to solve the two-dimensional Navier-Stokes equations at steady state. The interplay of inertia, viscous, gravity and capillary forces along with the substrate wettability and orientation with respect to gravity and the width of the slit determine the extent of liquid penetration and free-surface deformation. Finite wetting lengths are predicted in hydrophilic and hydrophobic substrates for inclination angles more or less than the vertical, respectively. Multiple steady solutions, connected by turning points forming a hysteresis loop, are revealed by pseudo-Arclength continuation. Under these conditions, small changes in certain parameter values leads to an abrupt change in the wetting length and the deformation amplitude of the outer film surface. In hydrophilic substrates the wetting lengths exhibit a local minimum for small values of the Reynolds number and a very small range of Bond numbers; when inertia increases, they exhibit the hysteresis loop with the second limit point in a very short range of Weber numbers. Simple force balances determine the proper rescaling in each case, so that critical points in families of solutions for different liquids or contact angles collapse. The flow inside the slit is quite slow in general because of viscous dissipation and includes counter-rotating vortices often resembling those reported by Moffatt (J. Fluid Mech., vol.Â 18, 1964, pp.Â 1-18). In hydrophobic substrates, the wetting lengths decrease monotonically until the first limit point of the hysteresis loop, which occurs in a limited range of Bond numbers when the Kapitza number is less than 300 and in a limited range of Weber numbers otherwise. Here additional solution families are possible as well, where one or both contact points (Cassie state) coincide with the slit corners. © 2017 Cambridge University PressÂ.25. Mitsoulis, E; Tsamopoulos, J

Numerical simulations of complex yield-stress fluid flows Journal Article

In: Rheologica Acta, 56 (3), pp. 231-258, 2017, ISSN: 00354511, (cited By 36).

Abstract | Links | BibTeX | Tags: Bingham plastics, Elastoviscoplastic fluids, Herschel-Bulkley fluids, Simulations, unyielded regions, Viscoplastic fluids, Viscoplastic models, Yield stress, Yielded

@article{Mitsoulis2017231,

title = {Numerical simulations of complex yield-stress fluid flows},

author = {E Mitsoulis and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85001022076&doi=10.1007%2fs00397-016-0981-0&partnerID=40&md5=78c8b6500b006f7b3ca82c4182414f3f},

doi = {10.1007/s00397-016-0981-0},

issn = {00354511},

year = {2017},

date = {2017-01-01},

journal = {Rheologica Acta},

volume = {56},

number = {3},

pages = {231-258},

abstract = {Viscoplasticity is characterized by a yield stress, below which the materials will not deform and above which they will deform and flow according to different constitutive relations. Viscoplastic models include the Bingham plastic, the Herschel-Bulkley model and the Casson model. All of these ideal models are discontinuous. Analytical solutions exist for such models in simple flows. For general flow fields, it is necessary to develop numerical techniques to track down yielded/unyielded regions. This can be avoided by introducing into the models a regularization parameter, which facilitates the solution process and produces virtually the same results as the ideal models by the right choice of its value. This work reviews several benchmark problems of viscoplastic flows, such as entry and exit flows from dies, flows around a sphere and a bubble and squeeze flows. Examples are also given for typical processing flows of viscoplastic materials, where the extent and shape of the yielded/unyielded regions are clearly shown. The above-mentioned viscoplastic models leave undetermined the stress and elastic deformation in the solid region. Moreover, deviations have been reported between predictions with these models and experiments for flows around particles using Carbopol, one of the very often used and heretofore widely accepted as a simple “viscoplastic” fluid. These have been partially remedied in very recent studies using the elastoviscoplastic models proposed by Saramito. © 2016, Springer-Verlag Berlin Heidelberg.},

note = {cited By 36},

keywords = {Bingham plastics, Elastoviscoplastic fluids, Herschel-Bulkley fluids, Simulations, unyielded regions, Viscoplastic fluids, Viscoplastic models, Yield stress, Yielded},

pubstate = {published},

tppubtype = {article}

}

Viscoplasticity is characterized by a yield stress, below which the materials will not deform and above which they will deform and flow according to different constitutive relations. Viscoplastic models include the Bingham plastic, the Herschel-Bulkley model and the Casson model. All of these ideal models are discontinuous. Analytical solutions exist for such models in simple flows. For general flow fields, it is necessary to develop numerical techniques to track down yielded/unyielded regions. This can be avoided by introducing into the models a regularization parameter, which facilitates the solution process and produces virtually the same results as the ideal models by the right choice of its value. This work reviews several benchmark problems of viscoplastic flows, such as entry and exit flows from dies, flows around a sphere and a bubble and squeeze flows. Examples are also given for typical processing flows of viscoplastic materials, where the extent and shape of the yielded/unyielded regions are clearly shown. The above-mentioned viscoplastic models leave undetermined the stress and elastic deformation in the solid region. Moreover, deviations have been reported between predictions with these models and experiments for flows around particles using Carbopol, one of the very often used and heretofore widely accepted as a simple “viscoplastic” fluid. These have been partially remedied in very recent studies using the elastoviscoplastic models proposed by Saramito. © 2016, Springer-Verlag Berlin Heidelberg.26. Karapetsas, G; Lampropoulos, N K; Dimakopoulos, Y; Tsamopoulos, J

Transient flow of gravity-driven viscous films over 3D patterned substrates: conditions leading to Wenzel, Cassie and intermediate states Journal Article

In: Microfluidics and Nanofluidics, 21 (2), 2017, ISSN: 16134982, (cited By 7).

Abstract | Links | BibTeX | Tags: Air entrapment, Cassie, coating, flow over topography, thin films, Wenzel

@article{Karapetsas2017,

title = {Transient flow of gravity-driven viscous films over 3D patterned substrates: conditions leading to Wenzel, Cassie and intermediate states},

author = {G Karapetsas and N K Lampropoulos and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85011409941&doi=10.1007%2fs10404-017-1853-3&partnerID=40&md5=f30a51ff54c05ec4e52780cac2476db1},

doi = {10.1007/s10404-017-1853-3},

issn = {16134982},

year = {2017},

date = {2017-01-01},

journal = {Microfluidics and Nanofluidics},

volume = {21},

number = {2},

abstract = {We examine the transient film flow under the action of gravity over solid substrates with three-dimensional topographical features. Our focus is placed on the coating of a periodic array of rectangular cuboid trenches. The Navier–Stokes equations are solved using the volume-of-fluid method, fully taking into account the flow in both the liquid and gas phases. Using this scheme, we are able to determine the different wetting patterns that may arise depending on parameters such as the various geometrical characteristics of the trench, the lateral distance between them, the substrate wettability and the liquid viscosity. We present flow maps that describe the conditions under which the liquid film may successfully coat the patterned substrate, resulting in the so-called Wenzel state, or air may become entrapped inside the topography of the substrate. In the latter case, we describe in detail the position and shape of the air inclusions, how they are formed and the conditions under which coating can approach the ideal Cassie–Baxter state. We investigate in detail the effect of the sidewalls, typically ignored when considering the case of ideal 2D trenches (i.e., trenches extending to infinity in the lateral direction), through the enhancement of the viscous resistance inside the trench and the effect of capillarity in the case of narrow trenches. We also examine the coating behavior for a wide range of liquids and show that successful coating is favored for liquids with moderate viscosities. Finally, we perform simulations for the coating of two successive trenches in the flow direction and show that in the case of 3D trenches, the differences between the coating of the first and subsequent trenches are not significant. © 2017, Springer-Verlag Berlin Heidelberg.},

note = {cited By 7},

keywords = {Air entrapment, Cassie, coating, flow over topography, thin films, Wenzel},

pubstate = {published},

tppubtype = {article}

}

We examine the transient film flow under the action of gravity over solid substrates with three-dimensional topographical features. Our focus is placed on the coating of a periodic array of rectangular cuboid trenches. The Navier–Stokes equations are solved using the volume-of-fluid method, fully taking into account the flow in both the liquid and gas phases. Using this scheme, we are able to determine the different wetting patterns that may arise depending on parameters such as the various geometrical characteristics of the trench, the lateral distance between them, the substrate wettability and the liquid viscosity. We present flow maps that describe the conditions under which the liquid film may successfully coat the patterned substrate, resulting in the so-called Wenzel state, or air may become entrapped inside the topography of the substrate. In the latter case, we describe in detail the position and shape of the air inclusions, how they are formed and the conditions under which coating can approach the ideal Cassie–Baxter state. We investigate in detail the effect of the sidewalls, typically ignored when considering the case of ideal 2D trenches (i.e., trenches extending to infinity in the lateral direction), through the enhancement of the viscous resistance inside the trench and the effect of capillarity in the case of narrow trenches. We also examine the coating behavior for a wide range of liquids and show that successful coating is favored for liquids with moderate viscosities. Finally, we perform simulations for the coating of two successive trenches in the flow direction and show that in the case of 3D trenches, the differences between the coating of the first and subsequent trenches are not significant. © 2017, Springer-Verlag Berlin Heidelberg.27. Beris, A N; Tsamopoulos, J A; Armstrong, R C; Brown, R A

Creeping motion of a sphere through a Bingham plastic. Journal Article

In: J. FLUID MECH., 158 , Sep. 1985, p.219-244. , 2017, ISSN: 00221120, (cited By 8).

Abstract | Links | BibTeX | Tags:

@article{Beris2017,

title = {Creeping motion of a sphere through a Bingham plastic.},

author = {A N Beris and J A Tsamopoulos and R C Armstrong and R A Brown},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-18544411999&partnerID=40&md5=664f94613d5109f2af9f9a92835c3a0d},

issn = {00221120},

year = {2017},

date = {2017-01-01},

journal = {J. FLUID MECH.},

volume = {158 , Sep. 1985, p.219-244.},

abstract = {A solid sphere falling through a Bingham plastic moves in a small envelope of fluid with shape that depends on the yield stress. A finite element/Newton method is presented for solving the free boundary problem composed of the velocity and pressure fields and the yield surfaces for creeping flow. Besides the outer surface, solid occurs as caps at the front and back of the sphere because of the stagnation points in the flow. The accuracy of solutions is ascertained by mesh refinement and by calculation of the integrals corresponding to the maximum and minimum variational principles for the problem. Large differences from the Newtonian values in the flow pattern around the sphere and in the drag coefficient are predicted, depending on the dimensionlesss value of the critical yield stress below which the material acts as a solid. The computed flow fields differ appreciably from Stokes' solution. The sphere will fall only when critical yield stress is below 0.143. For yield stresses near this value, a plastic boundary layer forms next to the sphere. Boundary layer scalings give the correct forms of the dependence of the drag coefficient and mass transfer coefficient on yield stress for values near the critical one. The Stokes limit of zero yield stress is singular in the sense that for any small value of optical yield stress there is a region of the flow away from the sphere where the plastic portion of the viscosity is at least as important as the Newtonian part. Calculations for the approach of the flow field to the Stokes result are in good agreement with the scalings derived from the matched asymptotic expansion valid in this limit. (A)},

note = {cited By 8},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

A solid sphere falling through a Bingham plastic moves in a small envelope of fluid with shape that depends on the yield stress. A finite element/Newton method is presented for solving the free boundary problem composed of the velocity and pressure fields and the yield surfaces for creeping flow. Besides the outer surface, solid occurs as caps at the front and back of the sphere because of the stagnation points in the flow. The accuracy of solutions is ascertained by mesh refinement and by calculation of the integrals corresponding to the maximum and minimum variational principles for the problem. Large differences from the Newtonian values in the flow pattern around the sphere and in the drag coefficient are predicted, depending on the dimensionlesss value of the critical yield stress below which the material acts as a solid. The computed flow fields differ appreciably from Stokes' solution. The sphere will fall only when critical yield stress is below 0.143. For yield stresses near this value, a plastic boundary layer forms next to the sphere. Boundary layer scalings give the correct forms of the dependence of the drag coefficient and mass transfer coefficient on yield stress for values near the critical one. The Stokes limit of zero yield stress is singular in the sense that for any small value of optical yield stress there is a region of the flow away from the sphere where the plastic portion of the viscosity is at least as important as the Newtonian part. Calculations for the approach of the flow field to the Stokes result are in good agreement with the scalings derived from the matched asymptotic expansion valid in this limit. (A)28. Fraggedakis, D; Dimakopoulos, Y; Tsamopoulos, J

Yielding the yield stress analysis: A thorough comparison of recently proposed elasto-visco-plastic (EVP) fluid models Journal Article

In: Journal of Non-Newtonian Fluid Mechanics, 238 , pp. 170-188, 2016, ISSN: 03770257, (cited By 12).

Abstract | Links | BibTeX | Tags: elasto-visco-plastic, EVP, falling sphere, LAOS, Viscometric

@article{Fraggedakis2016170,

title = {Yielding the yield stress analysis: A thorough comparison of recently proposed elasto-visco-plastic (EVP) fluid models},

author = {D Fraggedakis and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84999836120&doi=10.1016%2fj.jnnfm.2016.11.007&partnerID=40&md5=bc94ab444300e53cd26ce592cbced071},

doi = {10.1016/j.jnnfm.2016.11.007},

issn = {03770257},

year = {2016},

date = {2016-01-01},

journal = {Journal of Non-Newtonian Fluid Mechanics},

volume = {238},

pages = {170-188},

abstract = {We examine and compare five constitutive models, which have been recently proposed to describe the behavior of elasto-visco-plastic fluids. The comparison is performed in simple rheometric flows, i.e. simple-shear, uniaxial elongation and large amplitude oscillatory tests and in the complex flow generated by a falling spherical particle. The first set of three models do not explicitly include shear-thinning. These are the ones proposed by Saramito (2007), Park and Liu (2010) and Belblidia et al. (2011). The first one has been derived under a thermodynamic framework, while the other two have been based on viscosity regularization methods. When spatial and temporal inhomogeneity are not present in the flow field, the models generally produce acceptable predictions, except for: (a) the BWW in predicting the primary normal stress under small shear rate and under small strain in the LAOStrain test, (b) all models in predicting different parts of the spectra of G′ and G″, although the predictions of the SRM can be corrected when kinematic hardening is accounted for and (c) the P&L model in LAOStress because of nonexistence or multiplicity of solutions. In the complex flow, the predictions of each model are compared with the experimental data of Holenberg et al. (2012) under non shear-thinning conditions and the predictions of the SRM model are clearly superior. The second set of models have been proposed by Saramito (2009) to explicitly account for shear thinning either by extending the Herschel–Bulkley model to include elastic effects, SRM-HB, or by introducing a PTT-type term in the constitutive model, SRM-PTT. Both these models provide acceptable results in the rheometric tests. In the falling sphere test, their predictions are compared with the experimental results by Putz et al. (2008) for the settling of a particle under conditions that the Carbopol solution exhibits shear-thinning. Here the SRM-HB is found to be superior. © 2016},

note = {cited By 12},

keywords = {elasto-visco-plastic, EVP, falling sphere, LAOS, Viscometric},

pubstate = {published},

tppubtype = {article}

}

We examine and compare five constitutive models, which have been recently proposed to describe the behavior of elasto-visco-plastic fluids. The comparison is performed in simple rheometric flows, i.e. simple-shear, uniaxial elongation and large amplitude oscillatory tests and in the complex flow generated by a falling spherical particle. The first set of three models do not explicitly include shear-thinning. These are the ones proposed by Saramito (2007), Park and Liu (2010) and Belblidia et al. (2011). The first one has been derived under a thermodynamic framework, while the other two have been based on viscosity regularization methods. When spatial and temporal inhomogeneity are not present in the flow field, the models generally produce acceptable predictions, except for: (a) the BWW in predicting the primary normal stress under small shear rate and under small strain in the LAOStrain test, (b) all models in predicting different parts of the spectra of G′ and G″, although the predictions of the SRM can be corrected when kinematic hardening is accounted for and (c) the P&L model in LAOStress because of nonexistence or multiplicity of solutions. In the complex flow, the predictions of each model are compared with the experimental data of Holenberg et al. (2012) under non shear-thinning conditions and the predictions of the SRM model are clearly superior. The second set of models have been proposed by Saramito (2009) to explicitly account for shear thinning either by extending the Herschel–Bulkley model to include elastic effects, SRM-HB, or by introducing a PTT-type term in the constitutive model, SRM-PTT. Both these models provide acceptable results in the rheometric tests. In the falling sphere test, their predictions are compared with the experimental results by Putz et al. (2008) for the settling of a particle under conditions that the Carbopol solution exhibits shear-thinning. Here the SRM-HB is found to be superior. © 201629. Fraggedakis, D; Dimakopoulos, Y; Tsamopoulos, J

Yielding the yield stress analysis: A thorough comparison of recently proposed elasto-visco-plastic (EVP) fluid models Journal Article

In: Journal of Non-Newtonian Fluid Mechanics, 236 , pp. 104-122, 2016, ISSN: 03770257, (cited By 17).

Abstract | Links | BibTeX | Tags: elasto-visco-plastic, EVP, falling sphere, LAOS, Viscometric

@article{Fraggedakis2016104,

title = {Yielding the yield stress analysis: A thorough comparison of recently proposed elasto-visco-plastic (EVP) fluid models},

author = {D Fraggedakis and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84986893199&doi=10.1016%2fj.jnnfm.2016.09.001&partnerID=40&md5=e42bb4e2b966ac1f1eb985155ad207ce},

doi = {10.1016/j.jnnfm.2016.09.001},

issn = {03770257},

year = {2016},

date = {2016-01-01},

journal = {Journal of Non-Newtonian Fluid Mechanics},

volume = {236},

pages = {104-122},

abstract = {We examine and compare five constitutive models, which have been recently proposed to describe the behavior of elasto-visco-plastic fluids. The comparison is performed in simple rheometric flows, i.e. simple-shear, uniaxial elongation and large amplitude oscillatory tests and in the complex flow generated by a falling spherical particle. The first set of three models do not explicitly include shear-thinning. These are the ones proposed by Saramito [21], Park & Liu [27] and Belblidia et al. [28]. The first one has been derived under a thermodynamic framework, while the other two have been based on viscosity regularization methods. When spatial and temporal inhomogeneity are not present in the flow field, the models generally produce acceptable predictions, except for: (a) the BWW in predicting the primary normal stress under small shear rate and under small strain in the LAOStrain test, (b) all models in predicting different parts of the spectra of G′ and G″, although the predictions of the SRM can be corrected when kinematic hardening is accounted for and (c) the P&L model in LAOStress because of nonexistence or multiplicity of solutions. In the complex flow, the predictions of each model are compared with the experimental data of Holenberg et al. [34] under non shear-thinning conditions and the predictions of the SRM model are clearly superior. The second set of models have been proposed by Saramito [22] to explicitly account for shear thinning either by extending the Herschel–Bulkley model to include elastic effects, SRM-HB, or by introducing a PTT-type term in the constitutive model, SRM-PTT. Both these models provide acceptable results in the rheometric tests. In the falling sphere test, their predictions are compared with the experimental results by Putz et al. [15] for the settling of a particle under conditions that the Carbopol solution exhibits shear-thinning. Here the SRM-HB is found to be superior. © 2016 Elsevier B.V.},

note = {cited By 17},

keywords = {elasto-visco-plastic, EVP, falling sphere, LAOS, Viscometric},

pubstate = {published},

tppubtype = {article}

}

We examine and compare five constitutive models, which have been recently proposed to describe the behavior of elasto-visco-plastic fluids. The comparison is performed in simple rheometric flows, i.e. simple-shear, uniaxial elongation and large amplitude oscillatory tests and in the complex flow generated by a falling spherical particle. The first set of three models do not explicitly include shear-thinning. These are the ones proposed by Saramito [21], Park & Liu [27] and Belblidia et al. [28]. The first one has been derived under a thermodynamic framework, while the other two have been based on viscosity regularization methods. When spatial and temporal inhomogeneity are not present in the flow field, the models generally produce acceptable predictions, except for: (a) the BWW in predicting the primary normal stress under small shear rate and under small strain in the LAOStrain test, (b) all models in predicting different parts of the spectra of G′ and G″, although the predictions of the SRM can be corrected when kinematic hardening is accounted for and (c) the P&L model in LAOStress because of nonexistence or multiplicity of solutions. In the complex flow, the predictions of each model are compared with the experimental data of Holenberg et al. [34] under non shear-thinning conditions and the predictions of the SRM model are clearly superior. The second set of models have been proposed by Saramito [22] to explicitly account for shear thinning either by extending the Herschel–Bulkley model to include elastic effects, SRM-HB, or by introducing a PTT-type term in the constitutive model, SRM-PTT. Both these models provide acceptable results in the rheometric tests. In the falling sphere test, their predictions are compared with the experimental results by Putz et al. [15] for the settling of a particle under conditions that the Carbopol solution exhibits shear-thinning. Here the SRM-HB is found to be superior. © 2016 Elsevier B.V.30. Pavlidis, M; Karapetsas, G; Dimakopoulos, Y; Tsamopoulos, J

Steady viscoelastic film flow over 2D Topography: II. The effect of capillarity, inertia and substrate geometry Journal Article

In: Journal of Non-Newtonian Fluid Mechanics, 234 , pp. 201-214, 2016, ISSN: 03770257, (cited By 9).

Abstract | Links | BibTeX | Tags: Film, flow with inertia, PTT model, topography, Viscoelastic

@article{Pavlidis2016201,

title = {Steady viscoelastic film flow over 2D Topography: II. The effect of capillarity, inertia and substrate geometry},

author = {M Pavlidis and G Karapetsas and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84978175741&doi=10.1016%2fj.jnnfm.2016.06.011&partnerID=40&md5=2bc2260dbcbb2b50e02a27f773dda1f6},

doi = {10.1016/j.jnnfm.2016.06.011},

issn = {03770257},

year = {2016},

date = {2016-01-01},

journal = {Journal of Non-Newtonian Fluid Mechanics},

volume = {234},

pages = {201-214},

abstract = {We examine the two-dimensional, steady flow of a viscoelastic film under the action of gravity over a substrate with periodic topographical features. We account for the rheology of the viscoelastic material using the exponential Phan–Thien and Tanner (PTT) constitutive model. The conservation equations are solved via the mixed finite element method combined with a quasi-elliptic grid generation scheme, while the viscoelastic stresses are discretized using the EVSS-G/SUPG method. Our scheme allows the computation of accurate steady-state solutions up to high values of Deborah, Reynolds and capillary numbers. We perform a thorough parametric analysis to investigate the effect of the elastic, capillary and inertia forces on the flow characteristics. Our results indicate that surface tension and elasticity affect the film closer to the location with abrupt changes of the substrate topography; the sizes of the capillary ridge before a step down and of the depression before a step up are increased and move upstream as fluid elasticity or interfacial tension increase. It is shown that under creeping flow conditions the length scale of the capillary ridge increases with De following a power law of ¼, which can also be predicted by simple scaling arguments. Inertia has a more global effect on the film affecting larger portions of it, while in its presence the length scale of the capillary features is not affected significantly by the material elasticity. Moreover, it is shown that similarly to the case of Newtonian liquids, high inertia causes the formation of a ridge just after the step up. We also explore the effect of the geometrical characteristics of the substrate as well as its inclination angle and it is shown that the interface shape becomes more deformed as the topography appears wider, deeper or it approaches the vertical plane. © 2016},

note = {cited By 9},

keywords = {Film, flow with inertia, PTT model, topography, Viscoelastic},

pubstate = {published},

tppubtype = {article}

}

We examine the two-dimensional, steady flow of a viscoelastic film under the action of gravity over a substrate with periodic topographical features. We account for the rheology of the viscoelastic material using the exponential Phan–Thien and Tanner (PTT) constitutive model. The conservation equations are solved via the mixed finite element method combined with a quasi-elliptic grid generation scheme, while the viscoelastic stresses are discretized using the EVSS-G/SUPG method. Our scheme allows the computation of accurate steady-state solutions up to high values of Deborah, Reynolds and capillary numbers. We perform a thorough parametric analysis to investigate the effect of the elastic, capillary and inertia forces on the flow characteristics. Our results indicate that surface tension and elasticity affect the film closer to the location with abrupt changes of the substrate topography; the sizes of the capillary ridge before a step down and of the depression before a step up are increased and move upstream as fluid elasticity or interfacial tension increase. It is shown that under creeping flow conditions the length scale of the capillary ridge increases with De following a power law of ¼, which can also be predicted by simple scaling arguments. Inertia has a more global effect on the film affecting larger portions of it, while in its presence the length scale of the capillary features is not affected significantly by the material elasticity. Moreover, it is shown that similarly to the case of Newtonian liquids, high inertia causes the formation of a ridge just after the step up. We also explore the effect of the geometrical characteristics of the substrate as well as its inclination angle and it is shown that the interface shape becomes more deformed as the topography appears wider, deeper or it approaches the vertical plane. © 201631. Syrakos, A; Dimakopoulos, Y; Georgiou, G C; Tsamopoulos, J

Viscoplastic flow in an extrusion damper Journal Article

In: Journal of Non-Newtonian Fluid Mechanics, 232 , pp. 102-124, 2016, ISSN: 03770257, (cited By 7).

Abstract | Links | BibTeX | Tags:

@article{Syrakos2016102,

title = {Viscoplastic flow in an extrusion damper},

author = {A Syrakos and Y Dimakopoulos and G C Georgiou and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84963959942&doi=10.1016%2fj.jnnfm.2016.02.011&partnerID=40&md5=8c56c0fdf73c1a5ff58bbf97139cdc93},

doi = {10.1016/j.jnnfm.2016.02.011},

issn = {03770257},

year = {2016},

date = {2016-01-01},

journal = {Journal of Non-Newtonian Fluid Mechanics},

volume = {232},

pages = {102-124},

abstract = {Numerical simulations of the flow in an extrusion damper are performed using a finite volume method. The damper is assumed to consist of a shaft, with or without a spherical bulge, oscillating axially in a containing cylinder filled with a viscoplastic material of Bingham type. The response of the damper to a forced sinusoidal displacement is studied. In the bulgeless case the configuration is the annular analogue of the well-known lid-driven cavity problem, but with a sinusoidal rather than constant lid velocity. Navier slip is applied to the shaft surface in order to bound the reaction force to finite values. Starting from a base case, several problem parameters are varied in turn in order to study the effects of viscoplasticity, slip, damper geometry and oscillation frequency to the damper response. The results show that, compared to Newtonian flow, viscoplasticity causes the damper force to be less sensitive to the shaft velocity; this is often a desirable damper property. The bulge increases the required force on the damper mainly by generating a pressure difference across itself; the latter is larger the smaller the gap between the bulge and the casing is. At high yield stresses or slip coefficients the amount of energy dissipation that occurs due to sliding friction at the shaft-fluid interface is seen to increase significantly. At low frequencies the flow is in quasi steady state, dominated by viscoplastic forces, while at higher frequencies the fluid kinetic energy storage and release also come into the energy balance, introducing hysteresis effects. © 2016 Elsevier B.V.},

note = {cited By 7},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

Numerical simulations of the flow in an extrusion damper are performed using a finite volume method. The damper is assumed to consist of a shaft, with or without a spherical bulge, oscillating axially in a containing cylinder filled with a viscoplastic material of Bingham type. The response of the damper to a forced sinusoidal displacement is studied. In the bulgeless case the configuration is the annular analogue of the well-known lid-driven cavity problem, but with a sinusoidal rather than constant lid velocity. Navier slip is applied to the shaft surface in order to bound the reaction force to finite values. Starting from a base case, several problem parameters are varied in turn in order to study the effects of viscoplasticity, slip, damper geometry and oscillation frequency to the damper response. The results show that, compared to Newtonian flow, viscoplasticity causes the damper force to be less sensitive to the shaft velocity; this is often a desirable damper property. The bulge increases the required force on the damper mainly by generating a pressure difference across itself; the latter is larger the smaller the gap between the bulge and the casing is. At high yield stresses or slip coefficients the amount of energy dissipation that occurs due to sliding friction at the shaft-fluid interface is seen to increase significantly. At low frequencies the flow is in quasi steady state, dominated by viscoplastic forces, while at higher frequencies the fluid kinetic energy storage and release also come into the energy balance, introducing hysteresis effects. © 2016 Elsevier B.V.32. Lampropoulos, N K; Dimakopoulos, Y; Tsamopoulos, J

Transient flow of gravity-driven viscous films over substrates with rectangular topographical features Journal Article

In: Microfluidics and Nanofluidics, 20 (3), pp. 1-24, 2016, ISSN: 16134982, (cited By 7).

Abstract | Links | BibTeX | Tags: Air entrapment, Cassie-Baxter state, Wenzel

@article{Lampropoulos20161,

title = {Transient flow of gravity-driven viscous films over substrates with rectangular topographical features},

author = {N K Lampropoulos and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84959369218&doi=10.1007%2fs10404-016-1716-3&partnerID=40&md5=ef6048a1426431eb04e3b7bc364b3c50},

doi = {10.1007/s10404-016-1716-3},

issn = {16134982},

year = {2016},

date = {2016-01-01},

journal = {Microfluidics and Nanofluidics},

volume = {20},

number = {3},

pages = {1-24},

abstract = {We study the transient, two-dimensional film flow over solid substrates with variable topography, a flow that has practical applications in microelectronics and microfluidics. The problem we address here is the advancing of a thin liquid film over square-shaped trenches with different depths and widths, under the influence of the gravitational force. We use the volume-of-fluid method to obtain completely different wetting patterns depending on the dimensions of the topography, the capillary and Reynolds numbers, and the contact angle. On one hand, we predict continuous coating, i.e., the formation of the Wenzel state, in which a thin liquid film covers the entire trench, while steady flow is established upstream and downstream this topographical feature. This is the desirable pattern, when perfect coating is sought, as in the manufacturing of microelectronic devices. Under different conditions, we predict that the film almost completely bypasses the trench, entrapping air inside it, i.e., forming the Cassie state. The coating quality is clearly poor in this case, but this pattern reduces the drag on the film, and therefore, it is desirable in the operation of super-hydrophobic surfaces for microfluidic applications. Between these two extreme configurations, we uncover a large variety of patterns, in which the film partially wets the trench forming an air inclusion all along its bottom or its upstream or downstream inner corners or the film may break up periodically. We produce comprehensive flow maps covering a wide range of relevant parameter values. © 2016, Springer-Verlag Berlin Heidelberg.},

note = {cited By 7},

keywords = {Air entrapment, Cassie-Baxter state, Wenzel},

pubstate = {published},

tppubtype = {article}

}

We study the transient, two-dimensional film flow over solid substrates with variable topography, a flow that has practical applications in microelectronics and microfluidics. The problem we address here is the advancing of a thin liquid film over square-shaped trenches with different depths and widths, under the influence of the gravitational force. We use the volume-of-fluid method to obtain completely different wetting patterns depending on the dimensions of the topography, the capillary and Reynolds numbers, and the contact angle. On one hand, we predict continuous coating, i.e., the formation of the Wenzel state, in which a thin liquid film covers the entire trench, while steady flow is established upstream and downstream this topographical feature. This is the desirable pattern, when perfect coating is sought, as in the manufacturing of microelectronic devices. Under different conditions, we predict that the film almost completely bypasses the trench, entrapping air inside it, i.e., forming the Cassie state. The coating quality is clearly poor in this case, but this pattern reduces the drag on the film, and therefore, it is desirable in the operation of super-hydrophobic surfaces for microfluidic applications. Between these two extreme configurations, we uncover a large variety of patterns, in which the film partially wets the trench forming an air inclusion all along its bottom or its upstream or downstream inner corners or the film may break up periodically. We produce comprehensive flow maps covering a wide range of relevant parameter values. © 2016, Springer-Verlag Berlin Heidelberg.33. Tsouka, S; Dimakopoulos, Y; Tsamopoulos, J

Stress-gradient induced migration of polymers in thin films flowing over smoothly corrugated surfaces Journal Article

In: Journal of Non-Newtonian Fluid Mechanics, 228 , pp. 79-95, 2016, ISSN: 03770257, (cited By 5).

Abstract | Links | BibTeX | Tags: Film, finitte element, stress-induced migration, topography, Viscoelastic

@article{Tsouka201679,

title = {Stress-gradient induced migration of polymers in thin films flowing over smoothly corrugated surfaces},

author = {S Tsouka and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84954563601&doi=10.1016%2fj.jnnfm.2015.12.011&partnerID=40&md5=aa2116b992108188a06bb85e0e3c4e46},

doi = {10.1016/j.jnnfm.2015.12.011},

issn = {03770257},

year = {2016},

date = {2016-01-01},

journal = {Journal of Non-Newtonian Fluid Mechanics},

volume = {228},

pages = {79-95},

abstract = {We consider the two dimensional, steady flow of a dilute polymer solution over a solid substrate with periodic topography under the action of a body force. We examine how the distribution of polymer is affected by flow conditions, physical properties and substrate geometry and how it affects the dynamics of the free-surface. The Mavrantzas-Beris two-fluid Hamiltonian model is used in order to account for polymer migration due to stress gradients. The model is solved via the mixed finite element method combined with a quasi-elliptic grid generation technique. Results for polymer concentration, stress and velocity fields are presented as a function of the non-dimensional parameters of the problem. The basic phenomena that appear in the case of polymer migration in undulating channels (Tsouka et al., 2014), also appear in free surface flows. Increasing the elastic stresses, increases migration of macromolecules towards the free surface, developing a polymer-depleted layer especially over the substrate maxima, which finally gives rise to äpparent" slip. Increasing the cavity steepness also enhances migration and the thickness of the depletion layer and induces strong variation in the stresses away from the substrate wall, especially in low polymer concentrations. All these phenomena cannot be captured by the homogenous Oldroyd-B model. The evaluation of the Stokes number shows that flow resistance decreases as elasticity increases, increases monotonically up to an asymptote with the capillary number, and exhibits a non-monotonic dependence on the Reynolds number. Moderate inertial effects can give rise to large deformations of the free surface, developing waves with complex shapes. If we use a similarly modified ePTT model, we observe that its inherent shear-thinning is enhanced by the stress induced migration and tends to reduce the gradients on both polymeric stresses and polymer concentration along the film. © 2016 Elsevier B.V.},

note = {cited By 5},

keywords = {Film, finitte element, stress-induced migration, topography, Viscoelastic},

pubstate = {published},

tppubtype = {article}

}

We consider the two dimensional, steady flow of a dilute polymer solution over a solid substrate with periodic topography under the action of a body force. We examine how the distribution of polymer is affected by flow conditions, physical properties and substrate geometry and how it affects the dynamics of the free-surface. The Mavrantzas-Beris two-fluid Hamiltonian model is used in order to account for polymer migration due to stress gradients. The model is solved via the mixed finite element method combined with a quasi-elliptic grid generation technique. Results for polymer concentration, stress and velocity fields are presented as a function of the non-dimensional parameters of the problem. The basic phenomena that appear in the case of polymer migration in undulating channels (Tsouka et al., 2014), also appear in free surface flows. Increasing the elastic stresses, increases migration of macromolecules towards the free surface, developing a polymer-depleted layer especially over the substrate maxima, which finally gives rise to äpparent" slip. Increasing the cavity steepness also enhances migration and the thickness of the depletion layer and induces strong variation in the stresses away from the substrate wall, especially in low polymer concentrations. All these phenomena cannot be captured by the homogenous Oldroyd-B model. The evaluation of the Stokes number shows that flow resistance decreases as elasticity increases, increases monotonically up to an asymptote with the capillary number, and exhibits a non-monotonic dependence on the Reynolds number. Moderate inertial effects can give rise to large deformations of the free surface, developing waves with complex shapes. If we use a similarly modified ePTT model, we observe that its inherent shear-thinning is enhanced by the stress induced migration and tends to reduce the gradients on both polymeric stresses and polymer concentration along the film. © 2016 Elsevier B.V.34. Fraggedakis, D; Pavlidis, M; Dimakopoulos, Y; Tsamopoulos, J

On the velocity discontinuity at a critical volume of a bubble rising in a viscoelastic fluid Journal Article

In: Journal of Fluid Mechanics, 789 , pp. 310-346, 2016, ISSN: 00221120, (cited By 31).

Abstract | Links | BibTeX | Tags: bubbles, drops, free surface, interfacial flows, non-Newtonian flows

@article{Fraggedakis2016310,

title = {On the velocity discontinuity at a critical volume of a bubble rising in a viscoelastic fluid},

author = {D Fraggedakis and M Pavlidis and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84954500253&doi=10.1017%2fjfm.2015.740&partnerID=40&md5=c2b49680bd59b9b7015498cf1615ca98},

doi = {10.1017/jfm.2015.740},

issn = {00221120},

year = {2016},

date = {2016-01-01},

journal = {Journal of Fluid Mechanics},

volume = {789},

pages = {310-346},

abstract = {We examine the abrupt increase in the rise velocity of an isolated bubble in a viscoelastic fluid occurring at a critical value of its volume, under creeping flow conditions. This 'velocity discontinuity', in most experiments involving shear-thinning fluids, has been somehow associated with the change of the shape of the bubble to an inverted teardrop with a tip at its pole and/or the formation of the 'negative wake' structure behind it. The interconnection of these phenomena is not fully understood yet, making the mechanism of the 'velocity jump' unclear. By means of steady-state analysis, we study the impact of the increase of bubble volume on its steady rise velocity and, with the aid of pseudo arclength continuation, we are able to predict the stationary solutions, even lying in the discontinuous area in the diagrams of velocity versus bubble volume. The critical area of missing experimental results is attributed to a hysteresis loop. The use of a boundary-fitted finite element mesh and the open-boundary condition are essential for, respectively, the correct prediction of the sharply deformed bubble shapes caused by the large extensional stresses at the rear pole of the bubble and the accurate application of boundary conditions far from the bubble. The change of shape of the rear pole into a tip favours the formation of an intense shear layer, which facilitates the bubble translation. At a critical volume, the shear strain developed at the front region of the bubble sharply decreases the shear viscosity. This change results in a decrease of the resistance to fluid displacement, allowing the developed shear stresses to act more effectively on bubble motion. These coupled effects are the reason for the abrupt increase of the rise velocity. The flow field for stationary solutions after the velocity jump changes drastically and intense recirculation downstream of the bubble is developed. Our predictions are in quantitative agreement with published experimental results by Pilz & Brenn (J. Non-Newtonian Fluid Mech., vol. 145, 2007, pp. 124-138) on the velocity jump in fluids with well-characterized rheology. Additionally, we predict shapes of larger bubbles when both inertia and elasticity are present and obtain qualitative agreement with experiments by Astarita & Apuzzo. © 2016 Cambridge University Press.},

note = {cited By 31},

keywords = {bubbles, drops, free surface, interfacial flows, non-Newtonian flows},

pubstate = {published},

tppubtype = {article}

}

We examine the abrupt increase in the rise velocity of an isolated bubble in a viscoelastic fluid occurring at a critical value of its volume, under creeping flow conditions. This 'velocity discontinuity', in most experiments involving shear-thinning fluids, has been somehow associated with the change of the shape of the bubble to an inverted teardrop with a tip at its pole and/or the formation of the 'negative wake' structure behind it. The interconnection of these phenomena is not fully understood yet, making the mechanism of the 'velocity jump' unclear. By means of steady-state analysis, we study the impact of the increase of bubble volume on its steady rise velocity and, with the aid of pseudo arclength continuation, we are able to predict the stationary solutions, even lying in the discontinuous area in the diagrams of velocity versus bubble volume. The critical area of missing experimental results is attributed to a hysteresis loop. The use of a boundary-fitted finite element mesh and the open-boundary condition are essential for, respectively, the correct prediction of the sharply deformed bubble shapes caused by the large extensional stresses at the rear pole of the bubble and the accurate application of boundary conditions far from the bubble. The change of shape of the rear pole into a tip favours the formation of an intense shear layer, which facilitates the bubble translation. At a critical volume, the shear strain developed at the front region of the bubble sharply decreases the shear viscosity. This change results in a decrease of the resistance to fluid displacement, allowing the developed shear stresses to act more effectively on bubble motion. These coupled effects are the reason for the abrupt increase of the rise velocity. The flow field for stationary solutions after the velocity jump changes drastically and intense recirculation downstream of the bubble is developed. Our predictions are in quantitative agreement with published experimental results by Pilz & Brenn (J. Non-Newtonian Fluid Mech., vol. 145, 2007, pp. 124-138) on the velocity jump in fluids with well-characterized rheology. Additionally, we predict shapes of larger bubbles when both inertia and elasticity are present and obtain qualitative agreement with experiments by Astarita & Apuzzo. © 2016 Cambridge University Press.35. Fraggedakis, D; Dimakopoulos, Y; Tsamopoulos, J

In: Soft Matter, 12 (24), pp. 5378-5401, 2016, ISSN: 1744683X, (cited By 46).

Abstract | Links | BibTeX | Tags:

@article{Fraggedakis20165378,

title = {Yielding the yield-stress analysis: A study focused on the effects of elasticity on the settling of a single spherical particle in simple yield-stress fluids},

author = {D Fraggedakis and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84975217898&doi=10.1039%2fc6sm00480f&partnerID=40&md5=5b422b92e1da6fceff002bfdbf35acb4},

doi = {10.1039/c6sm00480f},

issn = {1744683X},

year = {2016},

date = {2016-01-01},

journal = {Soft Matter},

volume = {12},

number = {24},

pages = {5378-5401},

abstract = {The sedimentation of a single particle in materials that exhibit simultaneously elastic, viscous and plastic behavior is examined in an effort to explain phenomena that contradict the nature of purely yield-stress materials. Such phenomena include the loss of the fore-and-aft symmetry with respect to an isolated settling particle under creeping flow conditions and the appearance of the "negative wake" behind it. Despite the fact that similar observations have been reported in studies involving viscoelastic fluids, researchers conjectured that thixotropy is responsible for these phenomena, as the aging of yield-stress materials is another common feature. By means of transient calculations, we study the effect of elasticity on both the fluidized and the solid phase. The latter is considered to behave as an ideal Hookean solid. The material properties of the model are determined under the isotropic kinematic hardening framework via Large Amplitude Oscillatory Shear (Laos) measurements. In this way, we are able to predict accurately the unusual phenomena observed in experiments with simple yield-stress materials, irrespective of the appearance of slip on the particle surface. Viscoelasticity favors the formation of intense shear and extensional stresses downstream of the particle, significantly changing the entrapment mechanism in comparison to that observed in viscoplastic fluids. Therefore, the critical conditions under which the entrapment of the particle occurs deviate from the well-known criterion established theoretically by Beris et al. (1985) and verified experimentally by Tabuteau et al. (2007) for similar materials under conditions that elastic effects are negligible. Our predictions are in quantitative agreement with published experimental results by Holenberg et al. (2012) on the loss of the fore-aft symmetry and the formation of the negative wake in Carbopol with well-characterized rheology. Additionally, we propose simple expressions for the Stokes drag coefficient, as a function of the gravity number, Yg (related to the Bingham number), for different levels of elasticity and for its critical value, under which entrapment of particles occurs. These criteria are in agreement with the results found in the recent work by Ahonguio et al. (2014). Finally, we propose a method to quantify experimentally the elastic effects in viscoplastic particulate systems. © 2016 The Royal Society of Chemistry.},

note = {cited By 46},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

The sedimentation of a single particle in materials that exhibit simultaneously elastic, viscous and plastic behavior is examined in an effort to explain phenomena that contradict the nature of purely yield-stress materials. Such phenomena include the loss of the fore-and-aft symmetry with respect to an isolated settling particle under creeping flow conditions and the appearance of the "negative wake" behind it. Despite the fact that similar observations have been reported in studies involving viscoelastic fluids, researchers conjectured that thixotropy is responsible for these phenomena, as the aging of yield-stress materials is another common feature. By means of transient calculations, we study the effect of elasticity on both the fluidized and the solid phase. The latter is considered to behave as an ideal Hookean solid. The material properties of the model are determined under the isotropic kinematic hardening framework via Large Amplitude Oscillatory Shear (Laos) measurements. In this way, we are able to predict accurately the unusual phenomena observed in experiments with simple yield-stress materials, irrespective of the appearance of slip on the particle surface. Viscoelasticity favors the formation of intense shear and extensional stresses downstream of the particle, significantly changing the entrapment mechanism in comparison to that observed in viscoplastic fluids. Therefore, the critical conditions under which the entrapment of the particle occurs deviate from the well-known criterion established theoretically by Beris et al. (1985) and verified experimentally by Tabuteau et al. (2007) for similar materials under conditions that elastic effects are negligible. Our predictions are in quantitative agreement with published experimental results by Holenberg et al. (2012) on the loss of the fore-aft symmetry and the formation of the negative wake in Carbopol with well-characterized rheology. Additionally, we propose simple expressions for the Stokes drag coefficient, as a function of the gravity number, Yg (related to the Bingham number), for different levels of elasticity and for its critical value, under which entrapment of particles occurs. These criteria are in agreement with the results found in the recent work by Ahonguio et al. (2014). Finally, we propose a method to quantify experimentally the elastic effects in viscoplastic particulate systems. © 2016 The Royal Society of Chemistry.36. Pettas, D; Karapetsas, G; Dimakopoulos, Y; Tsamopoulos, J

On the origin of extrusion instabilities: Linear stability analysis of the viscoelastic die swell Journal Article

In: Journal of Non-Newtonian Fluid Mechanics, 224 , pp. 61-77, 2015, ISSN: 03770257, (cited By 15).

Abstract | Links | BibTeX | Tags: Extrusion, instabilities, polymer melts, sharkskin, stability analysis, swell

@article{Pettas201561,

title = {On the origin of extrusion instabilities: Linear stability analysis of the viscoelastic die swell},

author = {D Pettas and G Karapetsas and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84941640883&doi=10.1016%2fj.jnnfm.2015.07.011&partnerID=40&md5=26f905780f32bf0c9b5cdedda2020487},

doi = {10.1016/j.jnnfm.2015.07.011},

issn = {03770257},

year = {2015},

date = {2015-01-01},

journal = {Journal of Non-Newtonian Fluid Mechanics},

volume = {224},

pages = {61-77},

abstract = {It is well-known that by increasing the flow rate in polymer extrusion, the flow becomes unstable and the smooth extrudate surface becomes wavy and disordered to an increasing degree. In order to investigate the mechanisms responsible for these instabilities we perform a linear stability analysis of the steady extrusion of a viscoelastic fluid flowing through a planar die under creeping flow conditions. We consider the Phan-Thien-Tanner (PTT) model to account for the viscoelasticity of the material. We employ the mixed finite element method combined with an elliptic grid generator to account for the deformable shape of the interface. The generalized eigenvalue problem is solved using Arnoldi's algorithm. We perform a thorough parametric study in order to determine the effects of all material properties and rheological parameters. We investigate in detail the effect of the interfacial tension and the presence of a deformable interface. It is found that the presence of a finite surface tension destabilizes the flow as compared to the case of the stick-slip flow. We recognize two modes, which become unstable beyond a critical value of the Weissenberg number and perform an energy analysis to examine the mechanisms responsible for the destabilization of the flow and compare against the mechanisms that have been suggested in the literature. © 2015 Elsevier B.V.},

note = {cited By 15},

keywords = {Extrusion, instabilities, polymer melts, sharkskin, stability analysis, swell},

pubstate = {published},

tppubtype = {article}

}

It is well-known that by increasing the flow rate in polymer extrusion, the flow becomes unstable and the smooth extrudate surface becomes wavy and disordered to an increasing degree. In order to investigate the mechanisms responsible for these instabilities we perform a linear stability analysis of the steady extrusion of a viscoelastic fluid flowing through a planar die under creeping flow conditions. We consider the Phan-Thien-Tanner (PTT) model to account for the viscoelasticity of the material. We employ the mixed finite element method combined with an elliptic grid generator to account for the deformable shape of the interface. The generalized eigenvalue problem is solved using Arnoldi's algorithm. We perform a thorough parametric study in order to determine the effects of all material properties and rheological parameters. We investigate in detail the effect of the interfacial tension and the presence of a deformable interface. It is found that the presence of a finite surface tension destabilizes the flow as compared to the case of the stick-slip flow. We recognize two modes, which become unstable beyond a critical value of the Weissenberg number and perform an energy analysis to examine the mechanisms responsible for the destabilization of the flow and compare against the mechanisms that have been suggested in the literature. © 2015 Elsevier B.V.37. Fraggedakis, D; Kouris, C; Dimakopoulos, Y; Tsamopoulos, J

Flow of two immiscible fluids in a periodically constricted tube: Transitions to stratified, segmented, churn, spray, or segregated flow Journal Article

In: Physics of Fluids, 27 (8), pp. 082102, 2015, ISSN: 10706631, (cited By 6).

Abstract | Links | BibTeX | Tags:

@article{Fraggedakis2015082102,

title = {Flow of two immiscible fluids in a periodically constricted tube: Transitions to stratified, segmented, churn, spray, or segregated flow},

author = {D Fraggedakis and C Kouris and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84939165022&doi=10.1063%2f1.4928052&partnerID=40&md5=f67838ba630ece69d8b1c2fc1b67febd},

doi = {10.1063/1.4928052},

issn = {10706631},

year = {2015},

date = {2015-01-01},

journal = {Physics of Fluids},

volume = {27},

number = {8},

pages = {082102},

abstract = {We study the flow of two immiscible, Newtonian fluids in a periodically constricted tube driven by a constant pressure gradient. Our volume-of-fluid algorithm is used to solve the governing equations. First, the code is validated by comparing its predictions to previously reported results for stratified and pulsing flow. Then, it is used to capture accurately all the significant topological changes that take place. Initially, the fluids have a core-annular arrangement, which is found to either remain the same or change to a different arrangement depending on the fluid properties, the pressure driving the flow, or the flow geometry. The flow-patterns that appear are the core-annular, segmented, churn, spray, and segregated flow. The predicted scalings near pinching of the core fluid concur with similarity predictions and earlier numerical results [I. Cohen et al., "Two fluid drop snap-off problem: Experiments and theory," Phys. Rev. Lett. 83, 1147-1150 (1999)]. Flow-pattern maps are constructed in terms of the Reynolds and Weber numbers. Our result provides deeper insights into the mechanism of the pattern transitions and is in agreement with previous studies on core-annular flow [Ch. Kouris and J. Tsamopoulos, "Core-annular flow in a periodically constricted circular tube, I. Steady state, linear stability and energy analysis," J. Fluid Mech. 432, 31-68 (2001) and Ch. Kouris et al., "Comparison of spectral and finite element methods applied to the study of interfacial instabilities of the core-annular flow in an undulating tube," Int. J. Numer. Methods Fluids 39(1), 41-73 (2002)], segmented flow [E. Lac and J. D. Sherwood, "Motion of a drop along the centreline of a capillary in a pressure-driven flow," J. Fluid Mech. 640, 27-54 (2009)], and churn flow [R. Y. Bai et al., "Lubricated pipelining-Stability of core annular-flow. 5. Experiments and comparison with theory," J. Fluid Mech. 240, 97-132 (1992)]. © 2015 AIP Publishing LLC.},

note = {cited By 6},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

We study the flow of two immiscible, Newtonian fluids in a periodically constricted tube driven by a constant pressure gradient. Our volume-of-fluid algorithm is used to solve the governing equations. First, the code is validated by comparing its predictions to previously reported results for stratified and pulsing flow. Then, it is used to capture accurately all the significant topological changes that take place. Initially, the fluids have a core-annular arrangement, which is found to either remain the same or change to a different arrangement depending on the fluid properties, the pressure driving the flow, or the flow geometry. The flow-patterns that appear are the core-annular, segmented, churn, spray, and segregated flow. The predicted scalings near pinching of the core fluid concur with similarity predictions and earlier numerical results [I. Cohen et al., "Two fluid drop snap-off problem: Experiments and theory," Phys. Rev. Lett. 83, 1147-1150 (1999)]. Flow-pattern maps are constructed in terms of the Reynolds and Weber numbers. Our result provides deeper insights into the mechanism of the pattern transitions and is in agreement with previous studies on core-annular flow [Ch. Kouris and J. Tsamopoulos, "Core-annular flow in a periodically constricted circular tube, I. Steady state, linear stability and energy analysis," J. Fluid Mech. 432, 31-68 (2001) and Ch. Kouris et al., "Comparison of spectral and finite element methods applied to the study of interfacial instabilities of the core-annular flow in an undulating tube," Int. J. Numer. Methods Fluids 39(1), 41-73 (2002)], segmented flow [E. Lac and J. D. Sherwood, "Motion of a drop along the centreline of a capillary in a pressure-driven flow," J. Fluid Mech. 640, 27-54 (2009)], and churn flow [R. Y. Bai et al., "Lubricated pipelining-Stability of core annular-flow. 5. Experiments and comparison with theory," J. Fluid Mech. 240, 97-132 (1992)]. © 2015 AIP Publishing LLC.38. Dimakopoulos, Y; Kelesidis, G; Tsouka, S; Georgiou, G C; Tsamopoulos, J

Hemodynamics in stenotic vessels of small diameter under steady state conditions: Effect of viscoelasticity and migration of red blood cells Journal Article

In: Biorheology, 52 (3), pp. 183-210, 2015, ISSN: 0006355X, (cited By 10).

Abstract | Links | BibTeX | Tags: blood, cell-depleted layer, Fahraeus-Lindqvist, RBC migration, shear-induced migration, stenotic microvessels

@article{Dimakopoulos2015183,

title = {Hemodynamics in stenotic vessels of small diameter under steady state conditions: Effect of viscoelasticity and migration of red blood cells},

author = {Y Dimakopoulos and G Kelesidis and S Tsouka and G C Georgiou and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84942866811&doi=10.3233%2fBIR-14033&partnerID=40&md5=a436c96da1b62b2b3cce0009de0b99cf},

doi = {10.3233/BIR-14033},

issn = {0006355X},

year = {2015},

date = {2015-01-01},

journal = {Biorheology},

volume = {52},

number = {3},

pages = {183-210},

abstract = {BACKGROUND: In microcirculation, the non-Newtonian behavior of blood and the complexity of the microvessel network are responsible for the high flow resistance and the large reduction of the blood pressure. Red blood cell aggregation along with inward radial migration are two significant mechanisms determining the former. Yet, their impact on hemodynamics in non-straight vessels is not well understood. OBJECTIVE: In this study, the steady state blood flow in stenotic rigid vessels is examined, employing a sophisticated non-homogeneous constitutive law. The effect of red blood cells migration on the hydrodynamics is quantified and the constitutive model's accuracy is evaluated. METHODS: A numerical algorithm based on the two-dimensional mixed finite element method and the EVSS/SUPG technique for a stable discretization of the mass and momentum conservation equations in addition to the constitutive model is employed. RESULTS: The numerical simulations show that a cell-depleted layer develops along the vessel wall with an almost constant thickness for slow flow conditions. This causes the reduction of the drag force and the increase of the pressure gradient as the constriction ratio decreases. CONCLUSIONS: Viscoelastic effects in blood flow were found to be responsible for steeper decreases of tube and discharge hematocrits as decreasing function of constriction ratio. © 2015 - IOS Press and the authors.},

note = {cited By 10},

keywords = {blood, cell-depleted layer, Fahraeus-Lindqvist, RBC migration, shear-induced migration, stenotic microvessels},

pubstate = {published},

tppubtype = {article}

}

BACKGROUND: In microcirculation, the non-Newtonian behavior of blood and the complexity of the microvessel network are responsible for the high flow resistance and the large reduction of the blood pressure. Red blood cell aggregation along with inward radial migration are two significant mechanisms determining the former. Yet, their impact on hemodynamics in non-straight vessels is not well understood. OBJECTIVE: In this study, the steady state blood flow in stenotic rigid vessels is examined, employing a sophisticated non-homogeneous constitutive law. The effect of red blood cells migration on the hydrodynamics is quantified and the constitutive model's accuracy is evaluated. METHODS: A numerical algorithm based on the two-dimensional mixed finite element method and the EVSS/SUPG technique for a stable discretization of the mass and momentum conservation equations in addition to the constitutive model is employed. RESULTS: The numerical simulations show that a cell-depleted layer develops along the vessel wall with an almost constant thickness for slow flow conditions. This causes the reduction of the drag force and the increase of the pressure gradient as the constriction ratio decreases. CONCLUSIONS: Viscoelastic effects in blood flow were found to be responsible for steeper decreases of tube and discharge hematocrits as decreasing function of constriction ratio. © 2015 - IOS Press and the authors.39. Papaioannou, J; Giannousakis, A; Dimakopoulos, Y; Tsamopoulos, J

Bubble deformation and growth inside viscoelastic filaments undergoing very large extensions Journal Article

In: Industrial and Engineering Chemistry Research, 53 (18), pp. 7548-7569, 2014, ISSN: 08885885, (cited By 14).

Abstract | Links | BibTeX | Tags:

@article{Papaioannou20147548,

title = {Bubble deformation and growth inside viscoelastic filaments undergoing very large extensions},

author = {J Papaioannou and A Giannousakis and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84900406735&doi=10.1021%2fie403311n&partnerID=40&md5=5cf47653aace11a62fa10c636ddf2281},

doi = {10.1021/ie403311n},

issn = {08885885},

year = {2014},

date = {2014-01-01},

journal = {Industrial and Engineering Chemistry Research},

volume = {53},

number = {18},

pages = {7548-7569},

abstract = {Motivated by the probe experiment for characterizing the adhesion strength of polymeric materials, we studied the axisymmetric extensional flow of a viscoelastic liquid filament that contains one or three initially spherical bubbles along its axis of symmetry. The filament is confined between two parallel and coaxial disks of the same radius and its initially cylindrical outer surface is surrounded by air. The flow is induced by the axial extension of the upper disk under constant velocity, while the lower disk remains stationary. The rheology of the liquid is described by the exponential Phan-Thien and Tanner viscoelastic model. A quasi-elliptic transformation combined with domain decomposition and local mesh refinement is employed to discretize the domain. The mixed finite element Galerkin method for the mass and momentum balances combined with the EVSS-G method and SUPG weighting for the constitutive equation are used to obtain their weak forms. All these are necessary for the successful simulation of much larger filament extensions and of liquids with higher elasticity than those reported earlier. The evolution of the filament and the bubble(s)-free surfaces depends on the interplay of the viscous, elastic, and capillary forces. It was found that, when the ratio of the elastic and the capillary forces is small compared to the viscous forces, the bubble attains very large deformations. The onset of cusps was observed at the bubble poles for intermediate values of capillarity and elasticity. The force varies with the filament extension (or time) in a way reported in experiments measuring the strength of adhesive materials: Its initial increase up to a maximum is followed by a plateau, and finally it drops to zero when the adhesive tends to fail. Increasing the filament elasticity delays the development of stresses (and the applied force). © 2014 American Chemical Society.},

note = {cited By 14},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

Motivated by the probe experiment for characterizing the adhesion strength of polymeric materials, we studied the axisymmetric extensional flow of a viscoelastic liquid filament that contains one or three initially spherical bubbles along its axis of symmetry. The filament is confined between two parallel and coaxial disks of the same radius and its initially cylindrical outer surface is surrounded by air. The flow is induced by the axial extension of the upper disk under constant velocity, while the lower disk remains stationary. The rheology of the liquid is described by the exponential Phan-Thien and Tanner viscoelastic model. A quasi-elliptic transformation combined with domain decomposition and local mesh refinement is employed to discretize the domain. The mixed finite element Galerkin method for the mass and momentum balances combined with the EVSS-G method and SUPG weighting for the constitutive equation are used to obtain their weak forms. All these are necessary for the successful simulation of much larger filament extensions and of liquids with higher elasticity than those reported earlier. The evolution of the filament and the bubble(s)-free surfaces depends on the interplay of the viscous, elastic, and capillary forces. It was found that, when the ratio of the elastic and the capillary forces is small compared to the viscous forces, the bubble attains very large deformations. The onset of cusps was observed at the bubble poles for intermediate values of capillarity and elasticity. The force varies with the filament extension (or time) in a way reported in experiments measuring the strength of adhesive materials: Its initial increase up to a maximum is followed by a plateau, and finally it drops to zero when the adhesive tends to fail. Increasing the filament elasticity delays the development of stresses (and the applied force). © 2014 American Chemical Society.40. Dimakopoulos, Y; Pavlidis, M; Tsamopoulos, J

In: Journal of Non-Newtonian Fluid Mechanics, 200 , pp. 34-51, 2013, ISSN: 03770257, (cited By 55).

Abstract | Links | BibTeX | Tags: Augmented Lagrangian method, bubble, Free surface flows, Herschel-Bulkley fluids, Papanastasiou model, viscoplastic material

@article{Dimakopoulos201334,

title = {Steady bubble rise in Herschel-Bulkley fluids and comparison of predictions via the Augmented Lagrangian Method with those via the Papanastasiou model},

author = {Y Dimakopoulos and M Pavlidis and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84881025361&doi=10.1016%2fj.jnnfm.2012.10.012&partnerID=40&md5=3ee9dc3fd031d766237c1052ec38fa3b},

doi = {10.1016/j.jnnfm.2012.10.012},

issn = {03770257},

year = {2013},

date = {2013-01-01},

journal = {Journal of Non-Newtonian Fluid Mechanics},

volume = {200},

pages = {34-51},

abstract = {The steady, buoyancy-driven rise of a bubble in a Herschel-Bulkley fluid is examined assuming axial symmetry. The variation of the rate-of-strain tensor around a rising bubble necessitates the coexistence of fluid and solid regions in this fluid. In general, a viscoplastic fluid will not be deforming beyond a finite region around the bubble and, under certain conditions, it will not be deforming either just behind it or around its equatorial plane. The accurate determination of these regions is achieved by introducing a Lagrange multiplier and a quadratic term in the corresponding variational inequality, resulting in the so-called Augmented Lagrangian Method (ALM). Additionally here, the augmentation parameters are determined following a non-linear conjugate gradient procedure. The new predictions are compared against those obtained by the much simpler Papanastasiou model, which uses a continuous constitutive equation throughout the material, irrespective of its state, but does not determine the boundary between solid and liquid along with the flow field. The flow equations are solved numerically using the mixed finite-element/Galerkin method on a mesh generated by solving a set of quasi-elliptic differential equations. The accuracy of solutions is ascertained by mesh refinement and comparison with our earlier and new predictions for a bubble rising in a Newtonian and a Bingham fluid. We determine the bubble shape and velocity and the shape of the yield surfaces for a wide range of material properties, expressed in terms of the Bingham, Bn, Bond, and Archimedes numbers. As Bn increases, the bubble decelerates, the yield surfaces at its equatorial plane and away from it approach each other and eventually merge immobilizing the bubble. For small and moderate Bingham numbers, the predictions using the Papanastasiou model satisfactorily approximate those of the discontinuous Herschel-Bulkley model for sufficiently large values of the normalization exponent (≥104). On the contrary, as Bn increases and the rate-of-strain approaches zero almost throughout the fluid-like region, much larger values of the exponent are required to accurately compute the yield surfaces. Bubble entrapment does not depend on the power law index, i.e. a bubble in a Herschel-Bulkley fluid is entrapped under the same conditions as in a Bingham fluid. © 2012 Elsevier B.V.},

note = {cited By 55},

keywords = {Augmented Lagrangian method, bubble, Free surface flows, Herschel-Bulkley fluids, Papanastasiou model, viscoplastic material},

pubstate = {published},

tppubtype = {article}

}

The steady, buoyancy-driven rise of a bubble in a Herschel-Bulkley fluid is examined assuming axial symmetry. The variation of the rate-of-strain tensor around a rising bubble necessitates the coexistence of fluid and solid regions in this fluid. In general, a viscoplastic fluid will not be deforming beyond a finite region around the bubble and, under certain conditions, it will not be deforming either just behind it or around its equatorial plane. The accurate determination of these regions is achieved by introducing a Lagrange multiplier and a quadratic term in the corresponding variational inequality, resulting in the so-called Augmented Lagrangian Method (ALM). Additionally here, the augmentation parameters are determined following a non-linear conjugate gradient procedure. The new predictions are compared against those obtained by the much simpler Papanastasiou model, which uses a continuous constitutive equation throughout the material, irrespective of its state, but does not determine the boundary between solid and liquid along with the flow field. The flow equations are solved numerically using the mixed finite-element/Galerkin method on a mesh generated by solving a set of quasi-elliptic differential equations. The accuracy of solutions is ascertained by mesh refinement and comparison with our earlier and new predictions for a bubble rising in a Newtonian and a Bingham fluid. We determine the bubble shape and velocity and the shape of the yield surfaces for a wide range of material properties, expressed in terms of the Bingham, Bn, Bond, and Archimedes numbers. As Bn increases, the bubble decelerates, the yield surfaces at its equatorial plane and away from it approach each other and eventually merge immobilizing the bubble. For small and moderate Bingham numbers, the predictions using the Papanastasiou model satisfactorily approximate those of the discontinuous Herschel-Bulkley model for sufficiently large values of the normalization exponent (≥104). On the contrary, as Bn increases and the rate-of-strain approaches zero almost throughout the fluid-like region, much larger values of the exponent are required to accurately compute the yield surfaces. Bubble entrapment does not depend on the power law index, i.e. a bubble in a Herschel-Bulkley fluid is entrapped under the same conditions as in a Bingham fluid. © 2012 Elsevier B.V.