THE CONSTANT FLOW-RATE PROBLEM FOR FLUIDS WITH INCREASING YIELD STRESS IN A PIPE

Experiments show that the degradation effect observed during both stir ring and pipelining tests of some coal-water slurries is mainly to be ascribed to the increase of the yield stress. Regardless of the partic ular mathematical model adopted to investigate the dynamics of these f luids, engineering applications force us to consider the problem of ho w long a constant flow rate can be maintained during the pipelining pr ocess. We choose a Bingham model where the yield stress is assumed to increase with the dissipated energy as in [5]. It is first shown that the constant flow rate problem is equivalent to solving a nonlinear fu nctional equation in the unknown pressure gradient that generalizes th e classical algebraic Buckingham equation for the same problem with co nstant theological parameters. By means of a fixed-point argument we a lso prove that the functional equation has one and only one solution w hich is local in time. We finally find an estimate from below of the i nterval of existence. Numerical results are rather good and agree with those expected from the engineering point of view.