Page - 30 - in Advanced Chemical Kinetics

electrode surface; C0S is the bulk concentration of substrate;C 0 E is the total concentration of enzyme; k1, k2,2, and k2 are the reaction rate constants; andt is the time. The initial and boundaryconditions forEqs. (14)and(15)aregivenby: t¼0,x≥0,andx¼∞,x≥0, Q½ �¼0, S½ �¼C0S (16) x¼0,t≥0 : Q½ �¼ C 0 P 1þexp FRT E�E0PQ � �h i , ∂S½ � ∂x ¼0 (17) x¼∞,∂Q½ �=∂x¼0 (18) The analytical expressions corresponding to the concentration of co-substrate for steady and nonsteadystate conditionshavebeenobtainedbysolving theabovenonlinear equationusing a new approach to homotopy perturbation method (HPM). Analytical expressions of the plateaucurrentarealsopresented for steadyandnonsteadystate conditions: i¼FSDP ∂Q½ �∂x � � x¼0 (19) where E is the electrode potential, E0PQ is the standard potential of the P/Q couple, F is the Faraday constant, and S is the surface area of the electrode. The aboveproblem is discussed theoreticallybyRasi etal. [34]. 5.Analytical solutions Tostudymanyof thephysicalphenomena, theexact solutionsofnonlinearpartialorordinary differential equations playan important role. In order to understand themechanismof com- plicated dynamical processes and physical phenomena modeled by nonlinear differential equations, the existence of approximate analytical and exact solutions is very important. In Figure1. Reactionschemefor substrateandco-substrate. Advanced Chemical Kinetics30