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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