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

Liquid 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, (xi) over cap, versus moisture content, Theta. For low moisture content, xi 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, (xi) over cap reaches large values (i.e. (xi) over cap >> 1) for both Richards equation and foam drainage, implying a gradual approach of Theta towards the saturated state. The (xi) over cap 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.

Automated summary

By comparing and contrasting the solutions of foam drainage equation and Richards equation, significant differences in the traveling wave solutions at low moisture content and near saturation are found, mainly attributed to the soil material properties and the soil specific parameter m determined from the soil-water retention curve.