Steady non-swirling axisymmetric flows: flow classification and rheological consequences

Abstract

For steady non-swirling axisymmetric flow ( $u_{\varphi} = 0$ ) of an incompressible fluid two invariants of the rate of strain dyadic D are introduced, which directly enter into the expression for D. This being the case they - in conjunction with the vorticity - allow a flow classification into strong and weak flows. For a generalized Newtonian fluid an expression for the viscosity function $\eta$ is listed, which reduces for model fluids to correct results in shearing and, respectively, extensional flow. A possible modification of $\eta$ is proposed, which involves the relative vorticity as well (quasi-Newtonian fluid), since this allows $\eta$ to adjust itself to the local nature of the flow. As such it should prove useful for numerical calculation.