A Study On The Mathematical Model Of Chemostat With Incomplete Mixing
Keywords:Chemostat model, Incomplete mixing, Stability analysis
This study aims to investigate the mathematical model of incomplete mixing in a continuously stirred tank reactor (CSTR) and to study the impact of the size of a stagnant area on the steady-state. The chemical model used is a quadratic autocatalysis scheme with linear decay of autocatalyst, and these reactors represent the 'highly agitated' and 'stagnant' regions. The effect of imperfect mixing in a chemostat is analyzed by adjusting the size values in the stagnant region, while the stability of the mathematical model of incomplete mixing is determined by identifying the stability analysis and stability diagrams such as phase plane and time series plot. The study of the chemostat model with incomplete mixing is done by obtaining the dimensionless equations, steady-states, Jacobian Matrix, trace, and determinant. From the stability analysi, the obtained washout is stable while the no-washout has no physically meaningful solutions. For the steady-state diagrams, it shows that the size of the stagnant region does not affect much on the steady-state diagram, but there is a “poor mixing” region for extremely small values of the mixing parameter . Therefore, the mixing parameter does affect the steady-state diagrams more than size of the stagnant region.