The ramifications of diffusive volume transport in classical fluid mechanics

Abstract

The thesis that follows consists of a collection of work supporting and extending a novel reformulation of fluid mechanics, wherein the linear momentum per unit mass in a fluid continuum, m, is supposed equal to the volume velocity v[sub]v. The latter differs from the barycentric velocity V[sub]m by the vector field j[sub]v, where j[sub]v = v[sub]v - v[sub]m represents the heretofore largely ignored diffusive transport of volume. We will begin by giving a motivating discussion containing example problems which point to the possible need for a change in the constitutive choice for in. This will be followed by a brief outline of the kinematic concepts necessary to understand and utilize volume transport, including a general expression for j[sub]v. We will conclude by presenting the modified governing equations that result from the constitutive choice m = v[sub]v. Upon completing the required overview of existing ideas, a detailed linear irreversible thermodynamic study of the modified governing equations which result from the choice m = v[sub]v is presented. This analysis yields, inter alia, an expression for the entropy production per unit volume in the fluid which requires that the deviatoric stress tensor be expressed in terms of the volume velocity. Furthermore, an expression for the diffusive flux of internal energy is derived that differs from classical results by a term proportional to the diffusive flux of volume. This change in the internal energy flux stems from the explicit recognition of a diffusive volume flux, and precedes any specific choice of constitutive expression for the molecular flux of heat or species.

(cont.) The remainder of the thesis, which constitutes the bulk of the work performed, focuses on testing the proposed equation set against known experimental data. Each of the physically measurable phenomena treated herein was previously believed outside the realm of classical continuum fluid dynamics. We begin by considering the thermophoretic and diffusiophoretic motion of particles suspended in gases or liquids. We continue by studying the thermo-molecular pressure drop which results from applying a temperature gradient across the ends of a closed capillary. We conclude by presenting a hydrodynamic/Brownian motion model of thermal diffusion in liquids, wherein theoretical predictions for the Soret coefficient in a binary liquid system are presented that may be evaluated from readily available physicochemical data. It is shown, in each case, that the predictions of our modified theory are in agreement with experimental data. The final chapter of this dissertation is dedicated to utilizing the results derived in the previous chapters to comment on the veracity of the claim that the specific linear momentum in a fluid is given by the volume, rather than the barycentric, velocity. General arguments supporting this claim are presented and then followed by a list of questions which remain to be answered. Finally, a list of proposed experiments are detailed which could further test the predictions made herein.