Finite element analysis of axisymmetric creeping motion of a deformable non-Newtonian drop in the entrance region of a cylindrical tube

The finite-element method was employed to analyze axisymmetric creeping mot ion of a deformable drop in the entrance region of a cylindrical tube. In t he present study a non-Newtonian drop suspended in a non-Newtonian medium w as considered, for which a truncated power-law model was employed. The pena lty function method was used to eliminate the pressure variables from the s ystem equations, considerably reducing the computational time required. In solving the system equations an unstructured mesh generator and auto-remesh ing technique were used to describe the shapes of highly deformed drops. Th e results are in good agreement with experiments of Chin and Han [J. Rheol. 23, 557-590 (1979); 24, 1-37 (1980)] describing the deformation as the dro p approaches the inlet from the reservoir section and recoil after it enter s the tube. The present study demonstrates the effects of the capillary num ber and viscosity ratio on the deformation of non-Newtonian drops suspended in non-Newtonian liquids in the entrance region of a cylindrical tube. (C) 2001 The Society of Rheology.