Flow of a liquid with an anisotropic viscosity tensor: inertial effects

Abstract

An anistropic viscous fluid model, presented in an earlier paper [1], is here analysed in simple shearing flows and in channel and pipe flows, the motion in each case being generated from rest. The problems considered are similar to some of those in [1], except that now the inertia of the fluid is taken into account. The numerical solutions obtained show that the approximate analytical solutions of [1] are highly inaccurate at small times, but asymptotically valid for large times. The full solutions are found to ‘overshoot’ the corresponding inertialess solutions, i.e. a full solution, increasing from zero, can go beyond the approximate one, and then decrease to approach it asymptotically from above, rather than from below. As in [1] the volume rate of flow under a constant pressure gradient, and the fluid velocity in simple shearing flow under a constant applied shear stress, will, for a fluid with appropriate initial orientation pattern, eventually decrease and tend to zero.