PERTURBATION ANALYSIS OF THE HELICAL FLOW OF NON-NEWTONIAN FLUIDS WITH APPLICATION TO A RECIRCULATING COAXIAL CYLINDER RHEOMETER

This paper analyzes the flow of non-Newtonian fluids between infinitel y long coaxial cylinders, when the inner cylinder rotates with given a ngular velocity OMEGA, and a given axial flow rate, Q, is superimposed on this rotational motion. Such helical flow is of significance in th e modelling of the action of a recirculating coaxial cylinder rheomete r, where the axial flow is superimposed on the standard cup-and-bob rh eometer to allow accurate rheological measurements involving fluids th at are settling in nature. Such fluids are encountered in many mineral , food, and chemical processes of industrial significance. The analysi s presented here applies the perturbation approach to analyze the abov e flows in two situations of physical interest: 1. the case of low axi al flow rates; and 2. the case where the radial separation of the cyli nders is small, In each case, the appropriate perturbation parameter i s identified, and appropriate expressions for the velocity field are o btained for non-Newtonian fluids of interest. More significantly, this analysis allows the construction of approximate forms of the Reiner-R ivlin relation for this flow, which relates the angular velocity OMEGA to the observed torque, M, at the inner cylinder, through the rheolog ical parameters defining the fluid. Subsequent measurement of OMEGA an d M allows these parameters to be determined for a given fluid model. Where possible, the findings of the perturbation analysis are compared directly with experimental measurements involving a model of such a r ecirculating rheometer.