Pattern Formation In Anomalous Thermo-Viscous Media

The temperature dependence of fluid viscosity is getting important in the flows with an intensive heat exchange. Examples are molten metals, polymer solutions and natural lava. For most of the fluids their viscosities change monotonically with temperature. However, some complex fluids, capable for polymerization in a liquid state and de-polymerization at a certain temperature interval, may have non-monotone temperature dependency for viscosity. Examples are liquid sulfur, phosphorus and organic compounds. Fluid dynamics study of the systems having anomalous thermo-viscous properties may be useful for an account and prediction of spreading parameters of high-sulfur magma layers. It is also important in technological processes of sulfur utilization at sour petroleum refining and for efficiency increase of methylcellulose solutions use as baffling reagents for increase of enhanced oil recovery. In this paper we consider flow of anomalous thermoviscous liquid in a channel with specific heat exchange on its walls. A mathematical model of the process is based on the Navier-Stokes generalized equation, accounting for the Bacon & Fanelli data for sulfur viscosity vs. temperature dependence. It is found that the liquid sulfur flow is characterized by “a viscous barrier” - a stable high viscosity localized zone. As a whole, the flow has essentially non-Poiseuille’s character, and the velocity field acquires Poiseuille’s flow distribution only after complete cooling of the liquid. The intensity of heat exchange largely determines flow hydrodynamic parameters. This research is supported by the Grant of the Ministry of Education and Science of the Russian Federation (G34.31.0040).