SHEAR-INDUCED LATERAL MIGRATION OF BROWNIAN RIGID RODS IN PARABOLIC CHANNEL FLOW

This paper addresses the cross-stream migration of rigid rods undergoi ng diffusion and advection in parabolic flow between flat plates - a s imple model of a polymer that possesses internal (rotational) degrees of freedom for which the probability distribution depends upon the loc al shear rate. Unequivocal results on the observable concentration pro files across the channel are obtained from a finite-difference solutio n of the full Fokker-Planck equation in the space of lateral position y and azimuthal angle phi, the polar angle theta being constrained to pi/2 for simplicity. Steric confinement and hydrodynamic wall effects, operative within thin boundary layers, are neglected. These calculati ons indicate that rods should migrate toward the walls. For widely sep arated rotational and translational timescales asymptotic analysis giv es effective transport coefficients for this migration. Based upon ang ular distributions at arbitrary rotational Peclet number - obtained he re by a least-squares collocation method using trigonometric basis fun ctions - accumulation at the walls is confirmed quantitatively by the effective transport coefficients. The results are extended to free rot ation using spherical harmonics as the basis functions in the (phi, th eta) orientation space. Finally, a critique is given of the traditiona l thermodynamic arguments for polymer migration as they would apply to purely rotational internal degrees of freedom.