2002 -02 -20
10 :15 at ML J 21

Stress gradient-induced migration effects in the Taylor-Couette flow of a dilute polymer solution

Vlasis Mavrantzas

Institute of Polymers, ETH Zurich

Numerical results are presented concerning the phenomenon of stress gradient-induced migration of dilute polymer solutions in the Taylor-Couette device. This consists of two infinitely-long, concentric cylinders rotating at constant angular velocities. The governing equations, obtained through a two-fluid Hamiltonian model, include the continuity and momentum equations for the bulk velocity, the constitutive equation for the conformation tensor, and the diffusion equation for the polymer number density. The diffusion equation contains an extra term, proportional to the gradient of the stress tensor, which is responsible for the migration effects analyzed.
First, the solution of the steady-state purely azimuthal flow is obtained using a spectral collocation method. The calculations show significant polymer migration towards the inner cylinder, in qualitative agreement with experimental observations. The migration is enhanced for increasing values of the gap thickness, resulting into concentration values that differ by several orders of magnitude in the area between the inner and outer cylinders. This is further seen to affect the flow kinematics in the device.
Additional results will be presented from a linear stability analysis of the steady-state solution against axisymmetric disturbances corresponding to various wavenumbers in the axial direction. The role of the Peclet number on the stability of the flow will be discussed.