Microcontinuum Balance Equations Revisited: The Mesoscopic Approach

Abstract

This paper models a microcontinuum as a mixture with continuous diversity. Balance equations for a microcontinuous medium are discussed from the viewpoint of mesoscopic continuum mechanics. The macroscopic field quantities are redefined in terms of the mesoscopic averages rather than by taking spatial averages in a macroelement. The averages of the mesoscopic balance equations of mass, linear momentum, angular momentum, and energy produce their macroscopic counterparts. With the mixture formulation, the kinetic fluxes, which are missing in the derivations by other macroscopic approaches, are naturally incorporated into the stress tensor, couple stress tensor, and heat flux. For a microcontinuum, the balance equation of microinertia is the second-moment equation for the mesoscopic balance of mass. Introducing the mesoscopic distribution function can produce the explicit expression for the general macroscopic n -th moment equation.