Analytical Investigation of Fingero-Imbibition Phenomenon with Gravitational and Heterogeneity Effect: A Mathematical Approach

Abstract

The current study presents a comprehensive mathematical analysis of fingero-imbibition phenomenon within a heterogeneous porous medium. Fingero-imbibition, characterized by the preferential flow of a wetting liquid through porous media, plays a pivotal role in various natural and engineered systems. In this study, we focus on vertical heterogeneity, acknowledging the significance of gravity-driven effects on fluid movement in porous structures. The variational iteration method is employed to conduct a rigorous mathematical analysis for this study, considering suitable initial and boundary conditions. The findings are presented through numerical analyses and graphical representations, utilizing MATLAB for the visualization of results.