Mathematical modeling of flow of fertilizer-water mixture through soil and its effect on concentration and plant growth

Abstract

In this research we aim to demonstrate and explore how mathematical modeling can be used to aid people gain knowledge and understanding of plants and, in particular, interactions between plants, fertilizers, soil, and water. The primary objective is to convince members of the agricultural, mathematical and biological culture of the need to work together in establishing mechanistic simulations with quantitative data to help them understand flow of soil solutions and their effect on plant growth. The mathematical models used are based on the fundamental knowledge of fluid flows and plant growth that is necessitated by nutrient absorption from the soil by plant roots. Such models allow for a deeper understanding of plant science at the most basic level and can aid us in dealing with real-world issues such as food scarcity, soil pollution and global warming in developing countries, Kenya as a target. We used mathematical model equations which have been made to describe fertilizer (contaminant) as well as soil water flow, their concentrations, uptake by a plant root system and plant growth then solve the equations by finite difference and volume methods with the help of MATLAB program. The technique of explicit difference was used to solve the governing equations analytically. The results indicate that as time of simulation increases, the concentration of fertilizer also increases thus increasing the growth factor which in turn affects the length of plant growth