SMALL REYNOLDS-NUMBER FLOW BETWEEN ECCENTRIC ROTATING CYLINDERS WITH A PERMEABLE SLEEVE

Two eccentric rotating cylinders together with a permeable membrane su rrounding the inner cylinder are used to model the flow around a modif ied viscometer. A perturbation method is used to solve for the flow be tween the membrane and the outer cylinder; the how between the inner r otor and the membrane is assumed to be governed by Stoke's equation, a nd the two flow regimes are coupled by the through-flow across the mem brane. For moderate values of Reynolds number and eccentricity, the pe rmeability of the membrane plays a negligible role, and the flow throu gh the membrane is found to be eccentricity dependent. High eccentrici ties result in the formation of eddies which, upon increasing the Reyn olds number, move in a direction opposite to that of the rotation of t he outer bowl.