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Shear-induced lateral migration of Brownian rigid rods in parabolic channel flow

Published online by Cambridge University Press:  10 February 1997

Ludwig C. Nitsche  and
E. J. Hinch
Ludwig C. Nitsche
Affiliation:
Department of Chemical Engineering, The University of Illinois at Chicago, 810 South Clinton Street, Chicago, IL 60607, USA
E. J. Hinch
Affiliation:
Department of Applied Mathematics and Theoretical Physics, The University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
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Extract

This paper addresses the cross-stream migration of rigid rods undergoing diffusion and advection in parabolic flow between flat plates – a simple model of a polymer that possesses internal (rotational) degrees of freedom for which the probability distribution depends upon the local shear rate. Unequivocal results on the observable concentration profiles across the channel are obtained from a finite–difference solution of the full Fokker–Planck equation in the space of lateral position y and azimuthal angle φ, the polar angle θ being constrained to π/2 for simplicity. Steric confinement and hydrodynamic wall effects, operative within thin boundary layers, are neglected. These calculations indicate that rods should migrate toward the walls. For widely separated rotational and translational timescales asymptotic analysis gives effective transport coefficients for this migration. Based upon angular distributions at arbitrary rotational Péclet number – obtained here by a least–squares collocation method using trigonometric basis functions – accumulation at the walls is confirmed quantitatively by the effective transport coefficients. The results are extended to free rotation using spherical harmonics as the basis functions in the (φ, θ) orientation space. Finally, a critique is given of the traditional thermodynamic arguments for polymer migration as they would apply to purely rotational internal degrees of freedom.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 332 , February 1997 , pp. 1 - 21
Copyright
Copyright © Cambridge University Press 1997

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