Regularization of complex creeping flows through a zero-thickness plate orifice using a patching method

This paper aims to regularize complex flows characterized by a singularity in the orifice region of a zero-thickness plate using the patching method. The entire flow field is divided into three regions: the I -region, which is a sphere sharing the same origin and radius as the orifice; and the O u and O d regions, which represent the upstream and downstream half-infinite domains outside the sphere, respectively. The solution in each region is obtained in closed form. These solutions are subsequently patched over their common hemisphere using the relationship between pressure drop and volumetric flow rate from the Sampson solution. Matching the pressure gradients enables the determination of unknown coefficients in the solution. Consequently, the regularized flows allow for the practical application of the Sampson solution to actual flow problems, such as biofluid flow. The resulting complex velocity field is qualitatively compared with a computational fluid dynamics (CFD) simulation for a rounded orifice edge, which was conducted using the finite volume method.