Creeping flow through sinusoidally constricted capillaries

The steady pressure-driven flow of an incompressible Newtonian fluid through an axisymmetric capillary whose diameter varies sinusoidally in the axial direction is studied numerically under conditions of negligible inertial effects. The boundary integral formulation is used to obtain detailed velocity and pressure distributions within the capillary, and to determine the effects of amplitude and wavelength of corrugation on the kinematic structure of the flow. In particular, the critical values of the geometric parameters leading to flow reversal within the expansion region of the capillary are established. The dependence of the pressure drop through the capillary on the geometric parameters is also discussed with reference to the predictions of various effective pore models.