Surfactant induced one dimensional unsaturated flow through porous media: a classical mathematical approach

Surfactants reduce the interfacial tension, amend the solid-liquid contact angle and greatly influence the capillarity action in unsaturated porous media. Solubility studies of surfactants in inducing similar flow through such medium has been described to be of great importance to hydrologists, agriculturists and for the people related with water sciences to confine the flow problems in water infiltration system, seepage delinquent and the underground disposal of wastewater. Present article reviews the current state of knowledge to understand such one dimensional, unsteady surfactant flow phenomenon due to the capillary pressure gradients and is represented mathematically using one parameter group theory of similarity analysis. For the sake of definiteness in the analysis, we assumed certain specific relationships viz. the permeability of the medium as a specific linear function of moisture content and time which are consistent with the physical problem. We have not included any graphical or numerical illustrations due to our particular interest in deriving the classical solution to our problem.