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Simultaneous Flow of Water and Salt Through Unsaturated Porous Media: I. Rate Equations¹

ABSTRACT

The thermodynamic theory of irreversible proceses was used as a basis in developing two rate equations for the simultaneous movement of potassium chloride and water through porous media under isothermal conditions. The two rate equations are
where T is Kelvin temperature, J_w and J_s are flux of water and salt, P and C_s are the pressure and salt concentration differences across the sample, _s is the mean salt concentration, r is the concentration ratio, _w is the partial molar or specific volume of matric water, depending upon units selected for measuring J_w and R, L_ww and L_ss are the direct transfer coefficients for water and salt, and L_sw and L_ws are the interaction or linked transfer coefficients. The equations were tested under conditions of flow through unsaturated kaolinite and Millville silt loam at constant temperatures of 15, 25, 35C. The results showed that the interaction coefficients, L_ws and L_sw, were equal, suggesting that the Onsager theorem was met in both kaolinite and soil systems at the temperatures, pressure, and concentrations used.

¹ The research reported here was done under Western Regional Research Project W-68 with 12 Western States and the ARS, USDA cooperating. Published with the approval of the Director, Utah Agr. Exp. Sta., as Journal Paper 429. Presented before Div. S-1, Kansas City, Nov. 17, 1964.

² Formerly graduate student, now researcher at Desert Institute, Cairo, Egypt, and Professor of Agronomy (Soil Physics), Utah State University, Logan, respectively.

Received for publication August 5, 1964. Accepted for publication October 2, 1964.