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Where Does the Fluid Go?

Revised model will help scientists better understand transport of fluid constituents, with a wide range of applications.

Combined mechanisms of transport have important applications—transport of nutrients across cell membranes in plants and animals, the aeration of agricultural soils, performance of chemical reactors, the design of membranes for desalting brackish water, and the design of clay membranes for retaining dangerous chemicals.

Because mass transport of fluid constituents has important roles in biology, physics, and chemistry, one would assume that such transport would be well understood by the scientific community. However, transport of fluid constituents continues to be a source of confusion, particularly regarding models for combining transport by molecular diffusion and advection.

In a recent article in Vadose Zone Journal, A.T. Corey, W.D. Kemper (both of Colorado State Univ., Fort Collins), and J.H. Dane (Auburn Univ., Auburn, AL) show that the developers of popular models of diffusion have made invalid assumptions. Currently popular models define diffusion of a particular constituent as a flux relative to mass average flux so that diffusive flux of all constituents in a fluid mixture must sum to zero, and self-diffusion of a single-specie fluid cannot exist, contradicting experimental evidence previously reported in the literature. Research conducted and referenced by the authors shows that these assumptions and their models do not provide a satisfactory description of the flux taking place in media with small pores.

The authors provide an improved analysis, based on the principle that driving forces (for both advection and diffusion) are each equal in magnitude (and opposite in direction) to the associated rate of change of momentum. Mass average flux resulting from combined advection and diffusion is shown to be evaluated as the vector sum of advective and diffusive fluxes, rather than diffusive flux being evaluated as a flux relative to a mass average flux. This procedure is necessary because “mean flux” cannot be determined independent of an evaluation of diffusive flux.

Corey et al. describe two experiments with transport of gas constituents through porous media (providing data consistent with their revised model) that contradict widely accepted models. One of the experiments presents previously published data and the other describes new data obtained by the authors. Three additional experiments are presented (one representing new data) showing that self-diffusion of pure liquid water occurs in response to a temperature gradient, contradicting theory that diffusion of a single-specie fluid cannot occur, and showing that the sum of diffusion fluxes do not sum to zero in the general case. The measured diffusion of water was proportional to the gradient of the vapor pressure, which is a well-documented measure of the kinetic energy of water.

The full article is available for no charge for 30 days following the date of this summary. View the abstract at

Vadose Zone Journal, is a unique publication outlet for interdisciplinary research and assessment of the biosphere, with a focus on the vadose zone, the mostly unsaturated zone between the soil surface and the permanent groundwater table. VZJ is a peer-reviewed, international, online journal publishing reviews, original research, and special sections across a wide range of disciplines that involve the vadose zone, including those that address broad scientific and societal issues. VZJ is published by Soil Science Society of America, with Geological Society of America as a cooperator.

The Soil Science Society of America (SSSA) is a progressive, international scientific society that fosters the transfer of knowledge and practices to sustain global soils. Based in Madison, WI, and founded in 1936, SSSA is the professional home for 6,000+ members dedicated to advancing the field of soil science. It provides information about soils in relation to crop production, environmental quality, ecosystem sustainability, bioremediation, waste management, recycling, and wise land use.

SSSA supports its members by providing quality research-based publications, educational programs, certifications, and science policy initiatives via a Washington, DC, office. For more information, visit

SSSA is the founding sponsor of an approximately 5,000-square foot exhibition, Dig It! The Secrets of Soil, which opened July 19, 2008 at the Smithsonian's National Museum of Natural History in Washington, DC.

Sara Uttech | EurekAlert!
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