ISSN:
1089-7550
Source:
AIP Digital Archive
Topics:
Physics
Notes:
The effect of pressure gradients that develop in diffusion systems consisting of particulates dispersed in a continuous fluid is considered. It is shown that the gradient of chemical potential which drives the diffusion flux induces a pressure gradient that opposes this flux. This effect, which exists in addition to the induced bulk flow, is expressed in terms of a diffusive buoyancy force (DBF). For dispersions consisting of monodisperse particulates in a single-component fluid, the net driving force is the negative product of the volume fraction occupied by the fluid and the gradient of the chemical potential of the particulates. For polydisperse particulates, the DBF is the negative product of the total volume fraction occupied by the particulates and the expectation of gradient of their chemical potential. The joint effect of the DBF and the hydrodynamic hindrance is expressed in terms of a concentration-dependent diffusion coefficient. It is shown that the effect of the DBF yields a fundamental diffusion coefficient Dφ, which is the product of the volume fraction occupied by the fluid 1−φ, and the Stokes–Einstein diffusion coefficient D. The intrinsic diffusion coefficient, which is defined as the product of 1−φ and Dφ, thus becomes the product of the square of 1−φ and D. At steady state the concentration profile cannot be analytically linear unless the buoyancy and hydrodynamic effects are offset by changes of size, energy per particulate and the activity coefficient. Finally, implications regarding the diffusion equation and effects of combined fields on the DBF are considered.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.357230
