(370c) A Generalized Stochastic Model for Bacterial Disinfection: Non-Linear Approach
AIChE Annual Meeting
2010
2010 Annual Meeting
Computing and Systems Technology Division
Poster Session: Applied Mathematics and Numerical Analysis
Wednesday, November 10, 2010 - 6:00pm to 8:00pm
The current contribution introduces a generalized Markovian stochastic model for disinfection of bacteria whose intensity of transition is given in terms of a power function of time, thereby rendering it highly non-linear. The thorough disinfection of bacteria, of the utmost importance in various industries, especially those involving food and pharmaceuticals, is crucial in eliminating pathogenic bacteria to guard against their deleterious effects on humans and animals. The disinfection of bacterial populations in fluid media entails the elimination or attenuation of vast numbers of microorganisms, which are discrete and mesoscopic in nature. These microorganisms exhibit incessant and irregular motion as well as complex non-linear behavior: Their motion is self-propelled due to their motility and is strongly affected by the flow of the surrounding fluid media and also by collision among themselves as well as with the surrounding vessel surfaces, and mixing devices. Hence, it is highly likely that some of the attributes of the bacteria during disinfection, e.g., their number concentration, will exhibit random, or stochastic, fluctuations as time progresses. Such fluctuations are particularly pronounced at the termination stage of disinfection when the number of bacteria becomes minute. It might be profoundly insightful, therefore, to explore the resultant random fluctuations via stochastic paradigms; nevertheless, relatively little has been done hitherto in this regard. The generalized stochastic model for bacterial disinfection proposed herein aims at amending the apparent lack of such stochastic analyses. The model gives rise to the master equation, which has been simulated via the Monte Carlo method to circumvent the inherent complexity of solving it analytically or numerically by conventional numerical techniques. For illustration, the mean, variance (standard deviation), and coefficient of variation of the number concentration of bacteria during disinfection have been estimated through Monte Carlo simulation. The results of simulation are in line with the available experimental data as well as with those computed from the corresponding deterministic models.