Friday, November 5, 2004 - 5:00pm - 5:30pm
Howard Brenner (Massachusetts Institute of Technology)
This talk builds upon the pioneering work of Dan Joseph and co-workers in clarifying the notion of what is meant by an incompressible fluid when density gradients are present. In particular, we introduce the notion of volume as an extensive transportable physical property of a fluid continuum in both liquids and gases. Of special interest is the kinematical notion of the diffuse transport of volume, above and beyond the conventional (albeit implicit) view of convective volume transport, the latter being simply and inseparably linked to mass transport through the agency of the fluid's density; that is, in the presence of density gradients, volume can be transported through space without a concomitant movement of mass. Beyond the purely kinematical aspects of volume transport reflected in the work of Joseph et al., the diffuse transport of volume is accompanied by both momentum and energy transport in amounts above and beyond the amounts heretofore considered in standard continuum-mechanical theories of diffuse momentum and energy transport. This leads to constitutive revisions of both Newton's law of viscosity governing the diffuse transport of momentum and Fourier's law of heat conduction governing the diffuse transport of energy (the latter when a clear distinction is drawn between the respective fluxes of heat and internal energy). Experimental evidence based upon the phenomena of thermophoresis and thermal transpiration in single-component gases undergoing heat transfer, together with replacement of the no-slip mass-velocity condition by a comparable no-slip volume-velocity condition, is used to quantitatively support the proposed constitutive revisions to Newton's and Fourier's laws.