Comparing and Contrasting Travelling Wave Behaviour for Groundwater Flow and Foam Drainage

Abstract

AbstractLiquid drainage within foam is generally described by the foam drainage equation which admits travelling wave solutions. Meanwhile, Richards’ equation has been used to describe liquid flow in unsaturated soil. Travelling wave solutions for Richards equation  are also available using soil material property functions which have been developed by Van Genuchten. In order to compare and contrast these solutions, the travelling waves are expressed as dimensionless height, $$ {\hat{\xi }} $$ ξ ^ , versus moisture content, $$ \varTheta $$ Θ . For low moisture content, $$ {{\hat{\xi }}} $$ ξ ^ exhibits an abrupt change away from the dry state in Richards equation compared to a much more gradual change in foam drainage. When moisture content nears saturation, $$ {\hat{\xi }} $$ ξ ^ reaches large values (i.e. $$ {\hat{\xi }} \gg 1 $$ ξ ^ ≫ 1 ) for both Richards equation and foam drainage, implying a gradual approach of $$ \varTheta $$ Θ towards the saturated state. The $$ {\hat{\xi }} $$ ξ ^ values in Richards equation tend, however, to be larger than those in the foam drainage equation, implying an even more gradual approach towards saturation. The reasons for the difference between foam drainage and Richards equation solutions are traced back to soil material properties and in particular a soil specific parameter “m” which is determined from the soil-water retention curve.