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, \( {\hat{\xi }} \), versus moisture content, \( \varTheta \). For low moisture content, \( {{\hat{\xi }}} \) 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, \( {\hat{\xi }} \) reaches large values (i.e. \( {\hat{\xi }} \gg 1 \)) for both Richards equation and foam drainage, implying a gradual approach of \( \varTheta \) towards the saturated state. The \( {\hat{\xi }} \) 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.

泡沫内的液体排放通常由允许行波解的泡沫排放方程来描述。同时，理查兹方程已被用来描述非饱和土壤中的液体流动。使用Van Genuchten开发的土壤材料特性函数，也可以得到Richards方程的行波解。为了比较和对比这些解决方案，将行波表示为无量纲高度\（{\ hat {\ xi}} \）与水分含量\（\ varTheta \）。对于低水分含量，与泡沫排水中的逐渐变化相比，在Richards方程中\（{{\ hat {\ xi}}} \）表现出远离干燥状态的突然变化。当水分接近饱和时对于Richards方程和泡沫排水，\（{\ hat {\ xi}} \）达到较大的值（即\（{\ hat {\ xi}} \ gg 1 \）），这意味着\（\ varTheta的渐进方法\）趋向饱和状态。但是，Richards方程中的\（{\ hat {\ xi}} \）值倾向于大于泡沫排水方程中的\（{\ hat {\ xi}} \）值，这意味着逐渐趋于饱和。泡沫排水和Richards方程解之间存在差异的原因可追溯到土壤的材料特性，尤其是土壤特定参数“ m ”，该参数是根据土壤保水曲线确定的。