Advances and Applications in Mathematical Sciences Volume 19, Issue 9, July 2020, Pages 859-865 © 2020 Mili Publications 2010 Mathematics Subject Classification: 51Axx. Keywords: orthogonal collocation, Lagrangian interpolation polynomial, axial dispersion coefficient, Péclet number, bed porosity, displacement ratio. Received November 5, 2019; Accepted November 25, 2019 STUDY OF TWO PHASE NON-LINEAR MODEL OF ADVECTION DISPERSION FOR DISPLACEMENT WASHING OF POROUS PARTICLES SHELLY ARORA, V. K. KUKREJ and HAPPY KUMAR Department of Mathematics Punjabi University Patiala, Punjab, India Department of Mathematics SLIET Longowal, Punjab, India Department of Mathematics GNK College, Budhlada, Punjab, India E-mail: aroshelly@gmail.com Abstract Two phase non-linear diffusion dispersion model for cylindrical particle geometry has been presented. Model equations have been divided into two phases namely, bulk fluid phase and particle phase. Particle phase has been characterized by particle geometry. Inter-pore and intra- pore solute concentrations have been related by Langmuir adsorption isotherm. Non-linear set of model equations has been solved using the technique of orthogonal collocation on finite elements with Lagrangian basis. Applicability of the model has also been discussed through industrial parameters. Introduction Removal of soluble and insoluble impurities adsorbed on particle surface, with the help of weak wash liquor or clean water is called washing process. It involves a number of complex phenomenon of adsorption-desorption, diffusion and dispersion etc. During this process, the solute present in irregular void channels of bed diffuse out of particle pores. Displacement of solute is associated with dispersion of wash liquid in the direction of flow. Various