MATHEMATICAL MODELLING OF FLOW OF FERTILIZER-WATER MIXTURE THROUGH SOIL AND ITS EFFECT ON PLANT GROWTH.

Abstract

The demand for food in developing countries is increasing daily due to population growth and dropping crop yields caused by climatic changes and acidic soils due to continuous use of inorganic fertilizers that are meant to boost soil fertility. This study aims to demonstrate and explore how mathematical modelling 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 cultures 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 the world, Kenya as a target country. We used mathematical model equations which have been made to describe fertilizer as well as soil water flow, their concentrations, uptake by a plant root system and plant growth then solved the equations by finite difference methods with the help of MATLAB program. The technique of explicit finite difference was used to solve the governing equations with the help of analytical descriptions. 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.