MATHEMATICS OF ISOTHERMAL WATER CONDUCTION IN UNSATURATED SOIL

Abstract

THE PHYSICAL PROPERTIES OF SOILS INFLUENCE WATER MOVEMENT IN TWO WAYS: (1) THE SIZE AND STRUCTURAL ARRANGEMENTS OF THE SOIL PARTICLES DETERMINE THE SPACE CONFIGURATION THROUGH WHICH WATER MOVES, AND (2) THE INTERACTION BETWEEN THE SOIL AND THE SOIL WATER GIVES RISE TO WATER-MOVING FORCES. IN SOILS IN WHICH THE PORES ARE COMPLETELY FILLED WITH WATER, THE FLUID IS A SINGLE PHASE. FORCES ORIGINATING FROM GRAVITY, INCLUDING THE PRESSURE GRADIENT, DETERMINE THE FLOW. THE SATURATED FLOW PROCESS IS DESCRIBED MATHEMATICALLY BY DARCY'S LAW AND LAPLACE'S EQUATION. THE FREEZING POINT DEPRESSION OF THE SOIL WATER WAS USED TO MEASURE THE POTENTIAL, AND METHODS FOR MEASURING THE VAPOR PRESSURE OF THE SOIL WATER ARE BEING DEVELOPED. THE CAPILLARY CONDUCTIVITY AND DIFFUSIVITY VARY MARKEDLY AS A FUNCTION OF WATER CONTENT WITHIN A GIVEN SOIL AND FROM SOIL TO SOIL. A FLOW EQUATION IS SOLVED FOR THE REMOVAL OF WATER FROM A SOIL IN THE PRESSURE PLATE APPARATUS. SOLUTIONS ARE PRESENTED FOR THE FOLLOWING PARTICULAR FLOW PROBLEMS: (1) ENTRY OF WATER INTO SOIL, (2) STEADY STATE EVAPORATION, AND (3) THE DRYING OF SOILS. A PLOT IS PRESENTED OF THE THEORETICAL FRACTIONAL LOSS OF WATER FROM THE FINITE SOIL SAMPLE. IT IS TO BE EXPECTED THAT FOR EVAPORATION FROM A SOIL PROFILE THESE CURVES WILL BE SOMEWHAT MODIFIED BY THE INCLUSION OF GRAVITY, WHICH TENDS TO DECREASE THE EVAPORATION RATE, AND VAPOR MOVEMENT, WHICH TENDS TO INCREASE IT. IN ADDITION TO HELPING UNDERSTAND UNSATURATED FLOW PROBLEMS OF PRACTICAL IMPORTANCE, THE FLOW EQUATION AND ITS SOLUTIONS CAN BE HELPFUL IN STUDYING THE ROLE OF VARIOUS SOIL AND WATER PROPERTIES IN THEIR INFLUENCE ON WATER MOVEMENT. THE EQUATION PROVIDES MEANS TO EVALUATE THE DIFFUSIVITY AND THE CONDUCTIVITY.

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