Authors
Foteinopoulou K., Mavrantzas V.G., Dimakopoulos Y., Tsamopoulos J.
Abstract
Our recent finite element-based study of the deformation of a single bubble in a Newtonian or viscoelastic filament undergoing stretching is extended here to the case of multiple bubbles simultaneously growing in the stretched medium. The filament, having initially the shape of a cylinder with uniform radius, is confined between two disks and is continuously stretched by pulling the upper disk along the filament axis with a constant velocity; the lower disk is assumed stationary. All bubbles are taken to lie along the axis of symmetry of the filament and undergo deformation and/or growth with the medium being stretched. The governing equations are solved by a finite element/Galerkin method coupled with an implicit Euler method for the time integration, using an adaptive time step. The problem of the multiple bubble-liquid interfaces is addressed by a robust mesh-generation scheme that solves a set of elliptic differential equations for the locations of the nodal points. The resulting numerical scheme is accurate and extremely stable, independently of the number of bubbles assumed in the filament. It has allowed us to address multiple bubble growth in the filament, and investigate how their interaction affects the response of the system to the applied deformation. Numerical results are presented quantifying the dependence of bubble dynamics on bubble-liquid surface tension, filament aspect ratio (especially as this is decreased to very low values), relative bubble size, and bubble-bubble separation. The tensile force on the upper plate is also calculated and reported as a function of time and number of bubbles present in the film. Overall, our numerical calculations demonstrate the dominant role of the pressure field in the elongating filament: for the case of Newtonian fluids considered here, the force needed to maintain the flow comes solely from the pressure field, while for geometries with small aspect ratio, pressure attains large negative values near the centerline, in accord with the predictions of simple arguments from lubrication theory to the extent this applies to this problem. © 2006 American Institute of Physics.
