Stokes Flow between Two Cylinders

Abstract

The two-dimensional slow viscous fluid motion between two co-axial circular cylinders showed the inner cylinder is shear-free and the outer one is rigid. The flow is due to the presence of a line source and a line sink of equal strength on the outer cylinder. The stream function for the flow in the annular region is established. The hydrodynamic force on the inner shear-free cylinder has been evaluated. Some numerical values for the force have been presented in a table and compared with corresponding known values where both inner and outer cylinders are rigid.

Steady Stokes flow between confocal semi-ellipses

“…There are a number of works describing the flow over a rectangular cavity [12][13][14][15][16][17][18]. The solutions for the Stokes equations for the annular cavities were investigated in [19][20][21][22][23][24][25]. Stokes flow in regions partially bounded by segments of ellipses was considered in [26,27].…”