in Wiley Online Library (wileyonlinelibrary.com).Bacteria being disinfected in fluid media are discrete entities and mesoscopic in size; moreover, they are incessantly as well as irregularly in motion and in collision among themselves or with the surrounding solid surfaces. As such, it is highly likely that some of the attributes of the bacterial population, for example, their number concentration, will fluctuate randomly. This is especially the case at the tail-end of disinfection when the population of bacteria is sparse. It might be effectual, therefore, to explore the resultant random fluctuations via a stochastic paradigm. Proposed herein is a Markovian stochastic model for the rate of bacterial disinfection, whose intensity of transition takes into account the contact time of the bacteria with the disinfecting agent to eliminate any given percentage of the bacteria in terms of a nonlinear function of time. The model's master equation has been simulated by resorting to the Monte Carlo method to circumvent the undue complexities in solving it analytically or numerically via conventional numerical techniques. For illustration, the mean, the variance (standard deviation), and the coefficient of variation of the number concentration of bacteria during disinfection have been estimated through Monte Carlo simulation. The results of simulation compare favorably with the available experimental data as well as with those computed from the corresponding deterministic model.

This contribution presents a sequel to our previously published nonlinear stochastic model for bacterial disinfection whose intensity function is explicitly proportional to the contact time of the bacteria with the disinfecting agent. In the current model, the intensity function is proportional to the square of the contact time to account for an accelerated rate of a disinfection process. The model gives rise to the process’ master equation whose solution renders it possible to obtain the analytical expressions of the process’ mean, variance (or standard deviation), and coefficient of variation. Moreover, the master equation has been simulated via the Monte Carlo method, thereby yielding the numerical estimates of these quantities. The estimates’ values are compared with those computed via the analytical expressions; they are in excellent accord. They are also compared with the available experimental data as well as with the results obtained from our earlier model.

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To simulate the performance of a deep bed filter in terms of the pressure drop dynamics under a constant flow condition, a fairly general stochastic model, namely, the birthdeath process, which takes into account both blockage of the pores by suspended particles and scouring of deposited particles, is combined with the Carman-Kozeny equation. This model is relatively simple in that the entire bed is spatially lumped and it contains only two parameters, CY and 8, which are fairly easy to identify. In spite of this simplicity, the model is capable of representing the majority of the available experimental data. SCOPEThe use of stochastic models to simulate deep bed filtration has been proposed by J.

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A Markovian model has been derived for a process involving reversible physisorption and irreversible chemical adsorption of simple gaseous molecules on a solid surface, which obey linear rate laws. The model is written in terms of the conditional probability of transition between two populations, physisorbed and chemisorbed molecules. The resultant expression, the master equation of the process, has given rise to the governing differential equations for the mean and variance of the coverage of the solid surface by the gaseous molecules; these equations have been solved analytically. The variance or coefficient of variation, expressing the magnitude of fluctuations, is substantial for a small-size system, e.g., a highly evacuated and/or dilute system. It is not unwmmon to find such a system at the commencement and conclusion of any process; these periods are the most critical from the standpoint of operation, monitoring and control.