In this paper, mathematical models of biofilteration of mixtures of hydrophilic (methanol) and hydrophobic (α-pinene) volatile organic compounds (VOC's) biofilters were discussed. The model proposed here is based on the mass transfer in air-biofilm interface and chemical oxidation in the air stream phase. An approximate analytical expression of concentration profiles of methanol and α-pinene in air stream and biofilm phase have been derived using the Adomian decomposition method (ADM) for all possible values of parameters. Furthermore, in this work, the numerical simulation of the problem is also reported using the Matlab program to investigate the dynamics of the system. Graphical results are presented and discussed quantitatively to illustrate the solution. Good agreement between the analytical and numerical data is noted.

A mathematical model for biofilms inhibition for steady-state conditions is discussed. The model involves the reaction-diffusion equations which have variety of non-linear reaction rate functions for various types of inhibition. Simple and an approximate polynomial expression of concentration and effectiveness factor are derived for general non-linear monod kinetics models. Comparison of the analytical results and numerical simulation is also presented. A good agreement between theoretical predictions and numerical results is observed. The concentrations and the effectiveness factors are also computed for the limiting cases of monod kinetics models. The optimum value of the parameters for effectiveness factors is also discussed.ª 2014 Production and hosting by Elsevier B.V. on behalf

A mathematical modelling of diagnostic biosensors system at three basic types of enzyme kinetics is discussed in the presence of diffusion. Enzyme kinetics is adopted to be first order, Michaelis-Menten and ping-pong mechanism. In this paper, approximate analytical solutions are obtained for the non-linear equations under steady-state conditions by using the new Homotopy perturbation method. Simple and closed forms of analytical expressions for concentrations of substrate, product and co-substrate and corresponding current response have been derived for all possible values of parameters. Furthermore, the numerical simulation of the problem is also reported here by using Matlab program. Good agreement between analytical and numerical results is noted.

A mathematical model developed by Abdekhodaie and Wu (J Membr Sci 335:21-31, 2009), which describes a dynamic process involving an enzymatic reaction and diffusion of reactants and product inside glucose-sensitive composite membrane has been discussed. This theoretical model depicts a system of non-linear non-steady state reaction diffusion equations. These equations have been solved using new approach of homotopy perturbation method and analytical solutions pertaining to the concentrations of glucose, oxygen, and gluconic acid are derived. These analytical results are compared with the numerical results, and limiting case results for steady state conditions and a good agreement is observed. The influence of various kinetic parameters involved in the model has been presented graphically. Theoretical evaluation of the kinetic parameters like the maximal reaction velocity (V ) and Michaelis-Menten constants for glucose and oxygen (K and K ) is also reported. This predicted model is very much useful for designing the glucose-responsive composite membranes for closed-loop insulin delivery.