NUMERICAL-SOLUTIONS FOR THE DEFORMATION OF A BUBBLE RISING IN DILUTE POLYMERIC FLUIDS

The steady-state deformation of a bubble rising in polymeric liquid ha s been investigated using a general numerical technique for the soluti on of free-boundary problems in non-Newtonian fluid mechanics. The tec hnique is based on a finite-difference solution of the governing equat ions on an orthogonal curvilinear coordinate system, which is construc ted numerically and adjusted to fit the boundary shape exactly at any time. The problem was analyzed based on the constitutive equation prop osed by Chilcott and Rallison [J. Non-Newtonian Fluid Mech. 29, 381 (1 988)], which models a dilute polymer solution as a suspension of dumbb ells with finite extensibility. Computations were carried out to inves tigate the effect of conformation change of polymer chains on the bubb le deformation for various values of the Deborah number, maximum chain extensibility (i.e., roughly proportional to molecular weight), capil lary number, and the Reynolds number. Numerical results show good agre ement with existing experimental findings reported elsewhere. Especial ly, the tendency of transition from a prolate shape to a cusped shape has been observed in the creeping flow limit.