Shinsuke Takase

A Method of Numerical Viscosity Measurement for Solid-Liquid Mixture

We present a space-time homogenization procedure for multiscale modeling of solid-liquid mixture. The derived mathematical model enables us to set up two separate governing equations at both macro- and micro-scales. The fluid in the macroscopic governing equation is teated as an equivalent homogeneous medium with average or homogenized viscosity and is regarded as an incompressible Newtonian fluid, whose motion is assumed to be governed by the Navier-Stokes equations. The microscopic equations of motion governing the coupling phenomenon of the fluid and solid particles in a certain local domain and are solved to determine the microscopic flow fields under adequate boundary and loading conditions. Then the macrosopic viscosity is determined as the quantity averaged over the microscopic domain and within a certain time interval. The numerical viscosity measurement (NVM) can be realized by this space-time homogenization procedure. A set of NVMs is presented to demonstrate that the solid-liquid mixture considered in this study possibly exhibits a macroscopic flow characteristics of a special type of non-Newtonian fluids.