Fundamental balance equations and fluxes

Abstract

This chapter starts by discussing the concepts of a point, velocity and flux. The general balance is developed for any extensive quantity, for a point at the microscopic level, i.e., at a point within a fluid phase present in the void space, and at a point in the solid matrix. Then, the phenomenological approach is used to present this balance equation at the macroscopic level. The two approaches are briefly described. Then, the balance equations for the transport at the macroscopic level of mass, momentum and energy are derived. The Advective and diffusive flux appearing in both the microscopic and macroscopic balance equations are introduced, as well as e dispersive flux appearing only the latter. Special attention is devoted to the coefficients appearing the macroscopic balance equations. The macroscopic balance equation is also obtained by volume and mass averaging. Interphase transfers and sources appearing in the balance equations are also discussed, with their appropriate expressions and coefficients. Special attention is devoted to the meaning and role of coefficients. Dimensionless numbers and are discussed and used for determining non-dominant effects.