The inertial draining of a thin fluid layer between parallel plates with a constant normal force. Part 2. Boundary layer and exact numerical solutions

Abstract

The draining of a fluid layer between rigid plane parallel boundaries under a constant normal force is considered. In Part 1 the effect of fluid inertia was considered in the inviscid and low- but finite-Reynolds-number limits along with the inertia of the moving body; in Part 2, we consider the case of negligible inertia of the moving body. We develop an approximate large-Reynolds-number solution, valid until the boundary layers of the rigid surfaces begin to overlap, and present a new exact solution of the full Navier–Stokes equations for a time-dependent double-axisymmetric stagnation-point flow. These solutions exhibit interesting new features that illustrate the coupling of a time-dependent inviscid core flow with the growth of an unsteady boundary layer started from rest and the effect of Reynolds number on the merging of the boundary layers at large time.