Abstract:A mathematical model of steady-state and non-steady-state responses of a pH-based potentiometric biosensor immobilizing organophosphorus hydrolase was developed. The model is based on non-stationary diffusion equations containing a nonlinear term related to the Michaelis-Menten kinetics of an enzymatic reaction. An analytical expression for the substrate concentration was obtained for all values of parameter a (Thiele modulus) using the homotopy perturbation method. From this result, the concentrations of the … Show more
“…The complete description of the problem is given in [4] [10]. For the sake of completeness the brief description is given in this section and Appendix-A.…”
Section: Mathematical Formulation Of the Problemmentioning
confidence: 99%
“…In the enzyme membrane, the reaction-diffusion equations for the concentration of species for non-steady state condition can be represented as follows [4] [10]. ,…”
Section: Appendix a The Dimensionless Reaction-diffusion Equationsmentioning
A theoretical model for the non steady-state response of a pH-based potentiometric biosensor immobilizing organophosphorus hydrolase (OPH) is discussed. The model is based on a system of five coupled nonlinear reaction-diffusion equations under non steady-state conditions for enzyme reactions occurring in potentiometric biosensor that describes the concentration of substrate and hydrolysis products within the membrane. New approximate analytical expressions for the concentration of the substrate (organophosphorus pesticides (OPs)) and products are derived for all values of Thiele modulus and buffer concentration using new approach of homotopy perturbation method. The analytical results are also compared with numerical ones and a good agreement is obtained. The obtained results are valid for the whole solution domain.
“…The complete description of the problem is given in [4] [10]. For the sake of completeness the brief description is given in this section and Appendix-A.…”
Section: Mathematical Formulation Of the Problemmentioning
confidence: 99%
“…In the enzyme membrane, the reaction-diffusion equations for the concentration of species for non-steady state condition can be represented as follows [4] [10]. ,…”
Section: Appendix a The Dimensionless Reaction-diffusion Equationsmentioning
A theoretical model for the non steady-state response of a pH-based potentiometric biosensor immobilizing organophosphorus hydrolase (OPH) is discussed. The model is based on a system of five coupled nonlinear reaction-diffusion equations under non steady-state conditions for enzyme reactions occurring in potentiometric biosensor that describes the concentration of substrate and hydrolysis products within the membrane. New approximate analytical expressions for the concentration of the substrate (organophosphorus pesticides (OPs)) and products are derived for all values of Thiele modulus and buffer concentration using new approach of homotopy perturbation method. The analytical results are also compared with numerical ones and a good agreement is obtained. The obtained results are valid for the whole solution domain.
“…Initially methods like Pade approximation method [6] and variational iteration method [7][8] have been widely used to study the nonlinear problems, later on Liao employed the fundamental ideas of homotopy in topology to propose a general analytic method for solving differential and integral equations, linear and non-linear, namely homotopy analysis method (HAM) [9]. A special case of HAM is homotopy perturbation method (HPM) [10] which was introduced by He, and Elçin Yusufoglu extended it to improved homotopy perturbation method [11], latter Rajendran introduced a new approach to homotopy perturbation method [12]. Adomian decomposition method [13] and modified Adomian decomposition method [14] are frequently used for solving non-linear problems till now.…”
Section: Analytical Expression Of Concentrations Using Asymptotic Metmentioning
confidence: 99%
“…In this appendix, we derive the general solution of non-linear reaction Eq. (9), (10), (11), (12) using Homotopy analysis method. To find the solution of Eq.…”
Section: Solution Of the Non-linear Equations Using Homotopy Analysismentioning
The coupled nonlinear system of differential equations in 1-butanol dehydration under atmospheric and isothermal conditions are solved analytically for the microchannel reactor. Approximate analytical expressions of concentrations of 1butanol, 1-butene, water and dibutyl ether are presented by using homotopy analysis method. The homotopy analysis method eliminated the classical perturbation method problem, because of the existence a small parameter in the equation. The analytical results are compared with the numerical solution and experimental results, satisfactory agreement is noted.
“…Solving systems of nonlinear differential equations has gained importance and popularity in recent years, mainly due to the necessity of analytical solutions for the large scale of nonlinear differential systems in diverse fields of science and engineering. Many authors have focused on studying the solutions of nonlinear ordinary differential equations by using various analytical methods like the homotopy perturbation method 21, the homotopy analysis method 22, the variational iteration method 23, the Laplace Adomian decomposition method 24, a new approach to the homotopy perturbation method 25, and others. Among these, the new approach to the homotopy perturbation method is employed to solve the nonlinear ordinary differential equations (1)–(3).…”
Section: Analytical Solutions For Eqs (1)–(3) Using a New Approachmentioning
The mathematical model for hydrogen production by the photosynthetic bacterium Rhodobacter capsulatus in a batch photobioreactor is discussed. An analytical method -the homotopy perturbation method -is presented to solve the nonlinear differential equations that describe the biomass formation, substrate utilization, and hydrogen production with respect to time. Approximate analytical expressions for the concentrations of biomass, substrate and hydrogen are derived for various values of the relevant parameters. The analytical results are compared with experimental data. In addition, the sensitivity of the kinetic parameters is also analyzed. The time required to achieve the maximum growth of biomass and complete degradation of the substrate is reported.
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