c © World Scientic Publishing Company LATTICE BOLTZMANN SIMULATION OF THE FLOW OF NON-NEWTONIAN FLUIDS IN POROUS MEDIA

We present a LB study of the flow of single-phase non-Newtonian fluids, using a power law relationship between the eective viscosity and the local shear rate. Channel flow experiments were carried out to measure the velocity proles. The simulation results are found to be in good agreement with theory. We also report simulations of the flow of non-Newtonian fluids in a 2-D porous medium. 1. Non-Newtonian flow The flow behaviour of non-Newtonian fluids is of high interest to a broad range of disciplines in both science and technology. In particular, the oileld industry is interested in fluids for downhole applications, such as hydraulic fracturing to in-crease the oil production from reservoirs with a low natural permeability. These are generally complex fluids (containing polymers, surfactants and/or colloids) which show non-Newtonian behaviour. Because of the nature of the application, the flow of such complex fluids in porous media is extremely important to the industry. In this paper, we describe a non-Newtonian lattice-Boltzmann (LB) model. The LB method is well-suited to study flow problems in complex geometries. Because rea