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Theory of Capillary Flow: I. Practical Implications¹

ABSTRACT

The authors describe elsewhere certain general consequences of assuming that the classical differential equations of surface tension and viscous flow govern the behavior of liquids within the microscopic pores and channels of an unsaturated porous medium. These consequences appear as macroscopic differential equations expressed in reduced variables and containing two time-independent functionals of pressure which exhibit hysteresis and are characteristic of the medium. The present paper interprets these equations in practical terms.

Because of time independence, the term K appearing in L. A. Richard's analogous equation (1931) becomes
. Accordingly it is possible to solve for the conductivity and capacity functionals from experimental flow system data, provided the accuracy is sufficient for evaluation of required derivatives of pressure.

The combination of reduced variables and time independence permits scale modeling of flow systems. In a small-scale replica, the time scale is shortened, while "gravity" must be increased by means of a centrifuge. One possible application is to laboratory measurement of field capacity.

The reduced variables telescope into groups macroscopic flow systems that are equivalent except for scaling factors. Reducing the microscopic geometry by comparison to a characteristic pore size may prove useful in simplifying physical description of soils.

¹ Presented before Div. I, Soil Science Society of America, St. Paul, Minn., Nov. 10, 1954.

² Departments of Physics and Soils, University of Wisconsin, and Agronomy Department, Cornell University.

Received for publication October 20, 1954.