The numerical solution of the steady flow of Newtonian and non-Newtonian fluids through a contraction

The equations describing the steady two-dimensional flow of a dilute suspension of macromolecules, a non-Newtonian fluid, are numerically modeled using a finite difference technique. The flow domain is composed of a parallel walled inflow region, a contraction region in which the walls are rectangular hyperbolae, and a parallel walled outflow region. The problem is formulated in terms of the vorticity, stream function and appropriate rheological equation of state, the constitutive equation. An explicit differencing scheme is used to model the governing equations, with the advection terms in the equations modeled using upstream differencing. The structure of the basic Newtonian solvent flow is examined, and estimates of boundary layer thickness and discretizing errors are discussed.