Slip flow through channels with varying elliptic cross section

The low Reynolds number fluid flow through a channel with varying elliptic cross section is studied, with the inclusion of slip on the fluid–solid interface. An analytical expression for the flux through the channel is obtained, assuming that the slip length is small in comparison to the width of the channel, and a simplified expression for the flux in the limit of small eccentricity is also derived. Numerical results show that there is excellent agreement between the analytical expressions and the finite element solution for three examples presented in this paper. The expression for the flux is reformulated in terms of the semi-major and semi-minor radii, and the area and circumference, in order to estimate the flow through irregular channels. It is shown that the resulting expressions are extensions to existing estimation methods, the ‘Aissen approximation’ and ‘hydraulic radius’ methods, to include the effect of slip flow through channels with non-uniform cross section. Numerical results show that there is good agreement between the suggested flux estimation methods and the finite element solution for a pore throat extracted from a Berea sandstone. Furthermore, the suggested methods significantly outperform two common methods used to estimate the flux through an irregular channel, the ‘volume matching’ and ‘minimum radius’ methods.