Infinite series formulation for slip flow through a finite thickness orifice plate

Liquid transport through membrane nanopores is often modelled as creeping flow through a finite thickness orifice plate. Experiments and molecular simulations have revealed the importance of slip in such pores, where the diameter can be orders of magnitude smaller than the slip length for materials such as carbon nanotubes and graphene. Approximate hydrodynamic resistance models considering access resistance to the pore and fully developed slip flow within the pore are sometimes applied to estimate flow rates. While this approach is very accurate without slip, it can result in large errors for long slip lengths. Even with large slip lengths, flow development in the entry/exit regions contribute significant pressure drops that should be accounted for. In this paper, we extend an infinite series formulation for no-slip creeping flow through a finite thickness orifice plate to slip flow through the same geometry. We develop an algebraic system of equations for the series coefficients that can be efficiently computed to determine the velocity and pressure fields for the selected pore aspect ratio and slip length. Accurate volume flow rates can be quickly calculated, and are tabulated for convenience. We refine the approximate hydrodynamic resistance model for this flow to include losses in the entry region and obtain a fit for the volume flow rate accurate to within 2.5% for all slip lengths and pore aspect ratios.