1995 McCoy Award Recipient
John H. Cushman
Professor of Agronomy

Physics of fluids in porous media

The recipient of the Herbert Newby McCoy Award for 1995 is John H. Cushman, Professor of Agronomy. Professor Cushman was born in Ames, Iowa, where he later attended Iowa State University, obtaining a B.S. in mathematics and then a Ph.D. jointly in mathematics and agronomy. He joined the Purdue agronomy department in 1978, served as director of the Indiana Water Resources Research Center 1984-1988, and became professor of mathematics in 1995. Cushman was twice appointed to the Office of Health and Environmental Research Advisory Committee, a committee that oversees environmental and human health research at the Department of Energy. Professor Cushman is editor in chief of the International Journal of Stochastic Hydrology and Hydraulics. His research on the physics of fluids in porous media is described in more than 120 refereed publications and one book. Cushman has given approximately 75 lectures at national and international meetings in such diverse fields as mathematics, chemistry, physics, engineering, and agriculture.

Research
The focus of Professor Cushman's research is the physics of fluids in porous media. His work is unique in that it spans time/ space scales ranging from picoseconds/angstroms to years/miles. Cushman's research contributes significantly to problems involving (i) species separation and phase change in micropores, (ii) dispersion in media with continuously evolving heterogeneity, (iii) swelling colloidal systems, and (iv) reservoir-scale dispersion of environ- mental contaminants in natural geologic media.

Species separation and phase change in micropores: Consider a fluid contained in a pore when that pore is only a few fluid-molecular diameters wide in at least one dimension. Such fluids are of importance in condensed matter physics (model systems for the study of critical phenomena), in biology (protein folding and transport through membranes), in engineering and materials science (nanotechnologies), and in environmental science (chemical ad- sorption on soil colloids). Computational statistical mechanical experiments carried out by Cushman's group significantly enhance our understanding of such fluids. Even a fluid as simple as a rare gas mixture displays an extremely rich and anomalous behavior when confined to a structured planar system of width on the order of a few fluid-molecular diameters. The fluid's phase diagram is changed, its transport coefficients are radically altered from those in the fluids bulk phase, and it becomes inhomogeneous and an- isotropic. The properties of the fluid depend in a complex way on the initial structure of the liquid, the structure and commensurability of the confining walls, the wall-fluid interaction, the separation of the walls, asperities within the pore walls, and, if the pore-fluid is in equilibrium with its bulk-phase, then the pore-fluid depends strongly on the bulk-phase composition.

Dispersion in media with continuously evolving heterogeneity: If a porous medium looks inhomogeneous at every scale on which it can be viewed, then it is said to have continuously evolving heterogeneity. Many natural geologic media, and more generally fractal porous media, are of this category. By using nonequilibrium statistical mechanics, Cushman's group was first to develop general theories of conservative chemical transport in this type of system. The theories are non-Markovian, but they reduce to their appropriate Fickian counterparts in the asymptotic limits. Interestingly, these theories can be applied to turbulent bulk-phase dispersion as well as to fluids in porous media.

Swelling colloidal systems: Swelling porous media include many natural soils, baked foodstuffs (chips, cookies, pasta, breads), many drug delivery substrates, and living organisms such as sponges. Cushman's group provided the first correct derivations and statements of Darcy's and Fick's laws for such systems. The group showed that contrary to classical belief, flow in swelling systems is not driven by gradients in pressure and external fields (e.g. gravity) alone, but is also driven by changes in Helmholz free energy with volume fraction (the "interaction" potential). This result is of major significance in problems of drying that involve crust formation in soils and food polymers. The Cushman group also pro- vided rational definitions for the nonequilibrium capillary and swelling (disjoining) pressures in such systems. Nonequilibrium swelling pressure gives rise to the well-known exponential swelling law when applied at equilibrium. Prior to the efforts of Cushman's group, the exponential law had only an empirical basis.

Reservoir-scale dispersion of environmental contaminants in natural geologic media: Large-scale heterogeneities in an aquifers hydraulic and chemical character play a fundamental role in the evolution of contaminants in the environment. The work of Cushman's group shows that uncertainty in the parameters that characterize an aquifer give rise to spatially and temporally nonlocal constitutive laws for chemical transport. When computationally implemented, these laws often lead to different conclusions regarding groundwater contamination scenarios than those commonly employed by litigators and by the Environmental Protection Agency when enforcing environmental regulations.