• Existence and uniqueness of similarity solutions of imbibition equation

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      https://www.ias.ac.in/article/fulltext/pmsc/088/05/0409-0417

    • Keywords

       

      Porous media; imbibition; similarity; existence; shooting technique

    • Abstract

       

      The existence and uniqueness of the similarity profiles for the imbibition phenomenon which may arise due to the difference in the wetting abilities of the two immiscible fluids involved in the displacement process through porous media is discussed. By assuming the validity of the Darcy’s law, a mathematical model has been described and it is found that the investigated flow system is governed by a nonlinear diffusivity type equation. The existence and uniqueness of its similarity solutions have been proved by considering the bounds on the saturation coefficient,N(Sw) which is regarded as positive and piecewise continuously differentiable.

    • Author Affiliations

       

      A P Verma1 S Rama Mohan1

      1. Department of Mathematics, S V R College of Engineering and Technology, Surat - 395 007
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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