Inflation dynamics of fluid annular menisci inside a mold cavity-I. Deformation driven by small gas pressures


Poslinski A.J., Tsamopoulos J.A.


Axisymmetric inflation of fluid annular menisci under an imposed pressure gradient is analyzed by solving the Navier-Stokes equations for velocities in the meniscus and the kinematic and dynamic conditions for interface deformation subject to surface tension forces. Numerical calculations combine Galerkin/finite-element discretization with a fully implicit time integration algorithm and modified Newton iterative solution of the resulting algebraic equations. The gas-liquid interfaces that evolve with time are accounted for in the finite-element formulation by a nonorthogonal mapping of the deforming fluid domain onto a fixed computational domain. As a result, the unknown locations of the free surfaces appear explicitly in the formulation. The dynamics of the inflation process are governed by the externally applied gas pressure and the Suratman number, which measures the relative importance of inertial, surface tension and viscous forces. Transient calculations verify prior conclusions reached from an equilibrium stability analysis, and the results exhibit meniscus oscillation and fluid recirculation for certain values of the parameters. © 1990.


DOI: 10.1016/0009-2509(91)80131-H