Fluid flow in microporous membranes

In the analysis of fluid flow in microporous membrane tubes and channels, it is tacitly assumed that the no-shp boundary condition that characterises flows with sohd bounding walls is apphcable. This postulate is incorrect because the surface velocity at a porous waU is in fact not zero but proportional to the shear rate at the permeable boundary, i.e. 

Coordinate system for the laminar flow in a channel bounded by one porous surface operating under a uniform suction velocity VD. 

Velocity profiles for Re = 0.1 based on entrance Reynolds number for channel flow. 

The curves show that the velocity at the membrane surface (A = 1) is 0 when is 0 as expected. As the slip velocity increases with increasing (f), the wall shear decreases, and the velocity profiles become flatter, approaching those for plug flow [12-14]. The effect of slip coefficient on axial pressure gradient (P) is as follows an increase in (j) results in a decrease in wall shear stress so that P also decreases. In addition, the transition from laminar to turbulent flow at a porous surface occurs at a Re of less than 2000, which is also the case with membrane systems. 

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