Modelling and analysis of a mixture problem using first-order differential equations

Mixture problems are general in various scientific and engineering disciplines, providing critical insights into how substances interact within dynamic systems. This study focuses on a classical scenario where salt concentration in a tank is influenced by the continuous inflow of brine and simultaneous outflow of the mixture. The system is modelled using first-order differential equations, which allow for the analysis of how the salt concentration evolves over time. Through analytical solutions and simulations, this study reveals the transient and steady-state behaviors of the system, highlighting the practical utility of differential equations in solving complex real-world problems. It will contribute to a deeper understanding of the dynamics involved in mixture processes, with implications for fields such as environmental engineering and chemical process control.