W. G. Pritchard Lab Seminar: 4:30-5:30 PM, 101 Osmond Laboratory
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**Tuesday December 2, 2003**
Stokes flow in curvilinear channels - an analytical approach
Vladimir Mityushev
Department of Mathematics
Pedagogical University
Slupsk, POLAND
Abstract:
We consider Stokes flow through a three-dimensional curvilinear channel.
The surface of the walls is described by functions whose amplitudes are
proportional to a dimensionless parameter epsilon. The application of an
analytical-numerical algorithm yields efficient formulas for the
velocities of the fluid and the permeability of the channel; these
formulas include epsilon in a symbolic form. When epsilon increases, the
Poiseuille flow (epsilon=0) is disturbed, and eddies arise above a
critical value of epsilon. These results are generalized to the
stationary Navier-Stokes equations.
A similar analytical-numerical method is applied to diffusion on rough
periodic surfaces. The macroscopic diffusion tensor is determined by
averaging the local flux over the representative cell. The relation
between stationary diffusion on surfaces and two-dimensional non-
homogeneous materials is also discussed.
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