Steady plane-parallel flow of an anomalously viscous fluid between parallel plates

The authors consider the plane-parallel flow of an anomalously viscous fluid between two parallel plates, one of which is fixed while the other moves at constant velocity. An empirical power law is used as the rheological equation of state. It is shown that in the presence of a counterpressure exceeding a certain value, which is a function of the rheological properties of the polymer, the geometry and the flow regime, a counterflow develops near the bottom of the channel. The existence of a counterflow leads to the appearance of a minimum on the V_X(y) curve. This additional boundary condition makes it possible to obtain an approximate solution of the differential equations of motion and to describe the velocity distribution in the flow by means of two exponential equations. Integration of the velocity distribution thus obtained over the height of the channel gives an equation for the volume flow rate in plane-parallel flow in the presence of a counterpressure. It is shown that if the counterpressure gradient exceeds a critical value, the volume flow rate decreases much more sharply than for a Newtonian fluid.Mekhanika Polimerov, Vol. 1, No. 6, pp. 138–145, 1965