Numerical solution for unsteady plane flow of dilatant fluids

In this paper a plane laminar flow of a dilatant fluid under the action of a pulsating pressure gradient superposed to a steady one is examined. The constitutive law describing the rheological behaviour of the fluid is that of Ostwald-de Waele. Two periodic fluctuation have been considered: a sinusoidal and a square wave of some different amplitude. The motion simulates the injection of a fresh concrete in a fracture to consolidate rock masses or constructions. The oscillating pressure gradient which allows a better penetration of the reinforcement fluid in the fracture, gives rise to a small reduction of the discharge. Two parallel plates are used to schematize the geometry. However, a real fracture in has usually rough surfaces and, unlike parallel plates, the walls can be in contact at some locations. Nevertheless, the scheme of plane motion gives reliable results if the aperture variation along a flow path is not large. As injection fluid, two different mixture of fresh concrete with addition of HRWRA have been considered. The problem is solved numerically using an implicit finite difference method.