The microhydrodynamics associated with membrane cross-flow microfiltration processes is analyzed To this end, numerical computations of the flow near a pore of a spatially periodic model porous surface are performed for various porosities and suction conditions. The structure of the fluid capture tube as well as related fluid dynamics aspects, such as the existence of a recirculating eddy in the pore, the slip velocity at the wail, and the pressure drop across the pore, ave investigated. In particular, the influence of the neighbor pores on the structure of the fluid capture tube of a given pore is studied.