Mixture Purification Model With Cascading Tank Configuration

Abstract

Consider mixing problems which are often found in Calculus or Differential Equation courses. Under some assumptions, this problem can be used to model the purification process in a polluted mixture. In this case, the cascading configuration will be investigated for modelling the spread of pollution from one mixture to another. There are two main problems: finding time needed so the amount of pollutant in mixture inside the certain tank does not exceed certain threshold and finding the number of tanks needed so that the amount of mixture in the last tank does not exceed certain threshold. The solution for the second problem will be simplified by using Stirling approximation, which approximates factorial into exponential term. For the first problem, the time needed depends on the number of tanks, initial value of the pollutant, the rate of flow, and the volume of solution inside the tanks. For the second problem, the number of tanks only depends on the initial value of the pollutant.