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Internal Energy Balance and the Richards Equation¹

ABSTRACT

The energy concept of soil water introduced by Buckingham and developed by Richards is employed to derive a differential balance equation for the partial specific internal energy of water in an unsaturated soil. This equation is shown to comprise both heat flux and chemical work terms, in correspondence with the first law of thermodynamics. For the case of isothermal water flow through a rigid, homogeneous soil, the balance law for internal energy reduces to the Richards Equation with the soil water matric potential as the dependent variable. This result, which does not require the conventional direct appeal to the law of mass balance, demonstrates that the energy concept of soil water provides a self-consistent method for obtaining the Richards Equation. Either the energy balance concept or the traditional mass-balance approach can be used to establish the macroscopic physical foundations of the Richards equation.

¹ Contribution from the Dep. of Soil and Environmental Sciences, University of California, Riverside, CA 92521.

² Professor of Soil Science and Research Soil Physicist, respectively.

Received for publication February 22, 1982. Accepted for publication June 8, 1982.