The ramifications of diffusive volume transport in classical fluid mechanics

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Chemical Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2004

Author dc:creator

• Bielenberg, James R. (James Ronald), 1976-

Advisor dc:contributor.advisor

• Howard Brenner.

• Chemical Engineering.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/30061

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/30061