Bridging the Gap Between Continuum Mechanical Microrotation Viscosity and Lagrangian Point Particles

Abstract

The microrotation viscosity is an essential fluid property in micropolar fluid dynamics. By considering a dilute suspension of inertial spherical pointparticles in an otherwise Newtonian fluid, an explicit analytical expression for the microrotation viscosity is derived. This nonNewtonian continuum mechanical fluid property is seen to be proportional with the viscosity of the carrier fluid and the local particle loading. A number of assumptions were made in order to arrive at this simple relation, which implies that the microrotation viscosity should be considered as a flow variable rather than as a constant fluid property.