  The creeping flow of a generalized Newtonian fluid in a non--uniform pore
throat is investigated analytically. The analytical solution determines the
flow regimes and the transition point from Newtonian to the power law flow
regime. As an application of the new model, a regular lattice--based pore
network model is constructed to simulate the flows of shear--thinning and
shear--thickening fluids through porous media. The pore throats have
convergent--divergent geometries.
