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A Mathematical Model For Transport And Growth Of Microbes In Unsaturated Porous Soil, Harihar Khanal, Andrei Ludu, Ramesh Chandra Timsina, Kedar Nath Uprety

Publications

In this work, we develop a mathematical model for transport and growth of microbes by natural (rain) water infiltration and flow through unsaturated porous soil along the vertical direction under gravity and capillarity by coupling a system of advection diffusion equations (for concentration of microbes and their growth-limiting substrate) with the Richards equation. (e model takes into consideration several major physical, chemical, and biological mechanisms. (e resulting coupled system of PDEs together with their boundary conditions is highly nonlinear and complicated to solve analytically. We present both a partial analytic approach towards solving the nonlinear system and finding the main …