UNSTEADY COUETTE FLOW OF A BINGHAM FLUID

Many fluids which are of interest in engineering, as bentonite, slurries, fresh concrete, ceramic past, molten polymers, behave as Bingham fluids, i.e. fluids which present a yield stress. This paper investigates numerically the unsteady motion between two coaxial cylinders when the internal one rotates about its axis. The constitutive law of the fluid presents a discontinuity for zero shear rate which introduces severe difficulties in solving any problem of unsteady motion, both analytically and numerically. A suitable way to avoid the obstacle is to regularize the constitutive equation using a smooth function to approximate the Bingham law: in this paper the adopted law is based on the error function. Different procedures of start-up and cessation of flow and some periodical flows are examined numerically using an implicit finite difference method.