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A classical mathematical solution for surfactant induced flow behaviour through porous media

RAKHEE C. KUPERKAR1*, KETAN C. KUPERKAR2
*Corresponding author
1. Department of MATHEMATICS, Sir P. T. Sarvajanik College of Science, Surat – 395001, Gujarat, India
2. High Energy Accelerator Research Organization (KEK), J-PARC Centre, Materials and Life Science Division, 203-1 Shirakata, Tokai-Mura, Naka-gun, Ibaraki, 319-1106, Japan

Abstract

Solubility studies of surfactants have merited great importance to hydrologists, agriculturists and for those concerning in water sciences as they reduce the liquid surface tension by manifold, influence the capillarity pressure gradients and induce unsaturated flow through porous media in the aqueous solution. However the magnitude of its effect is predicted to be system-specific and depends on the porous medium characteristics. Such behavior is due to the relative aqueous-phase flow concentration and degree of hydrophobicity. This article reviews the current state of knowledge dealing in one-dimensional, unsteady surfactant flow through unsaturated porous media and is represented by a non-linear partial differential equation which is transformed into an ordinary differential equation using one parameter group theory of similarity analysis.


EXTRAPOLATED SENTENCE

Analytical methodology in terms of confluent hypergeometric functions of the non-linear partial differential equation governing one dimensional surfactant induced unsaturated flow through porous media.

INTRODUCTION
Surface active agents (Surfactants), in particular are well conditioned and known organic compounds possessing both the hydrophilic head group which is either charged (anionic, cationic, zwitter-ionic) or uncharged (non-ionic) with polar links (polyoxyethylene chains, amine oxides) and a hydrophobic alkyl tail region generally the hydrocarbons with partial saturated/unsaturated or aromatic functional groups (Figure 1) (1-3).

Since decades, these amphiphiles due to their unique surface-active nature and solution conduct are hired for various commercial applications viz. skin and oral care, in coating and encapsulation, in rheology powder technology, as color boosters, in fragrances and aerosols, in emulsions, in microbiology preservation and biocides. They impart very strong tendency to self-associate into the solution as nano-scale micellar aggregates at low critical surfactant con ...




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