The objectives of this research program are: 1) To apply the effective continuum method recently developed by the PI to a host of mass and heat transport processes involving two-phase media, and, thereby, obtain theoretical expressions for the relevant effective parameters; 2) To place this method, which is presently only ad hoc, on a firmer theoretical foundation; 3) To develop a theory for determining the pair probability function in flowing systems and thereby compute the dependence of these effective parameters on the strength and structure of the impressed flow; and 4) To derive theoretical expressions for the shear induced particle diffusion coefficient in flowing suspensions and for the enhancement of the mass transfer rate in flowing liquids by the addition of inert solid particles. These two effects, which play an important role in a wide variety of physical and biological operations, can at present be modeled only qualitatively. Effective parameters are currently computed either via variational techniques (which are generally inaccurate), exact calculations (which are either very time consuming or very specialized), or approximate ad hoc models containing adjustable factors which are often unreliable. In contrast, the effective continuum method developed by the PI is relatively simple and straightforward, is of great generality and versatility, and, has been successfully tested against experimental results. This method also extends the applicability of the continuum representation to systems where the micro and macro length scales are of comparable magnitude.
