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Inviscid irrotational flow around a pair of coaxial disks is considered in the limit in which the distance 2h between the disks is small compared to their radius a. The disks have zero thickness and accelerate away from one another along their common axis. The added mass M of each accelerating disk is increased by the presence of the other disk. Analytic predictions are obtained when h/a ≪ 1, with M ~ πa/(8h)-ln(h/a)/2+0.77875+. . . The term O(a/h) can be obtained by means of an inviscid analysis of approximately unidirectional flow within the gap between the disks, but the correction terms have not been reported previously. The irrotational flow problem satisfies Neumann boundary conditions on the surface of the disks, but is otherwise analogous to the Dirichlet problem of the capacitance of a pair of charged disks, which has been the subject of much study and controversy. [ABSTRACT FROM AUTHOR]

A theoretical model of electroosmosisthrough a circular pore ofradius athat traverses a membrane of thickness his investigated. Both the cylindrical surface of the poreand the outer surfaces of the membrane are charged. When h≫ a, end effects are negligible, and theresults of full numerical computations of electroosmosis in an infinitepore agree with theory. When h= 0, end effects dominate,and computations again agree with analysis. For intermediate valuesof h/a, an approximate analysisthat combines these two limiting cases captures the main featuresof computational results when the Debye length κ–1is small compared with the pore radius a. However,the approximate analysis fails when κ–1≫ a, when the charge cloud due to the charged cylindricalwalls of the pore spills out of the ends of the pore, and the electroosmoticflow is reduced. When this spilling out is included in the analysis,agreement with computation is restored. [ABSTRACT FROM AUTHOR]