Study of co-rotational Maxwell fluid in helical screw rheometer

Abstract

In this paper, the steady flow of an incompressible, co-rotational Maxwell fluid in a helical screw rheometer is studied by ‘unwrapping or flattening’ the channel, lands, and the outside rotating barrel. The geometry is approximated as a shallow infinite channel, by assuming the width of the channel large as compared to the depth. The developed second order nonlinear coupled differential equations are transformed to a single differential equation. Using perturbation methods, analytical expressions are obtained for the velocity components in the x- and z-directions and the resultant velocity in the direction of the screw axis. Volume flow rates, shear and normal stresses, shear at wall, and forces exerted on fluid and average velocity are also calculated. The behavior of the velocity profiles are discussed with the help of graphs. We observe that the velocity profiles are strongly dependent on the non-dimensional parameter (Wi)2 $(Wi)^{2}$, the flight angle ϕ and the pressure gradients.