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1.
To measure rate constants while performing biomolecular interaction analysis (BIA), scientists often use resonant mirror devices such as the IAsysTM. A full mathematical model of the IAsysTM consists of a convection–diffusion equation in a closed well with a reacting surface at the bottom. The flow in the well is complex, but near the sensor, the qualitative nature of the reaction can be analyzed by reducing to stagnation point flow. The concentration of the reacting species in several cases is analyzed using singular perturbation techniques. Linear and nonlinear integral equations result from the analysis; explicit and series solutions are constructed for physically realizable cases. These solutions, which include the effects of transport on the reaction, provide improved estimates for the rate constants from raw IAsysTM binding data.  相似文献   

2.
The process of the formation of a stationary mass transfer mode for a moving reacting particle is examined. An analytic expression valid for a nonstationary distribution of the concentration of matter in a steady stream of viscous fluid, flowing past a spherical particle, was obtained for the case when at a certain instant a chemical reaction of the first order begins at the surface of the sphere. The problem is solved for small finite Reynolds and Péclet numbers. The solution of the corresponding stationary problem has been obtained in [1]. Paper [2] examined a nonstationary heat transfer of a fluid spherical drop in an inviscid flow with spasmodic change of initial temperature at high Péclet numbers. Paper [3] contains an analysis of the problem of a nonstationary heat transfer of a rigid spherical particle for small Reynolds and Péclet numbers at spasmodic change of temperature of the particle surface. The results obtained in [3] can be used to describe the mass transfer for a moving reacting particle only in the case of a diffusion mode of the chemical reaction.  相似文献   

3.
** Email: ajm{at}maths.strath.ac.uk Particle dispersion from a high chimney is considered and anexpression for the subsequent concentration of the particulatedeposited on the ground is derived. We consider the generalcase wherein the effects of both diffusion and convection onthe steady state ground concentration of particulate are incorporated.Two key parameters emerge from this analysis: the ratio of diffusionto convection and the nondimensionalised surface mass transferrate. We also solve the inverse problem of recovering thesetwo parameters given the boundary concentration profile andprovide an estimate of the concentration flux above the chimneystack.  相似文献   

4.
We study a nonlinear reaction–diffusion system modeled by a system of two parabolic-type equations with power-law nonlinearities. Such systems describe the processes of nonlinear diffusion in reacting two-component media. We construct multiparameter families of exact solutions and distinguish the cases of blow-up solutions and exact solutions periodic in time and anisotropic in spatial variables that can be represented in elementary functions.  相似文献   

5.
Summary The influence of combustion on heat and mass transfer is investigated on the following model. A mixture of an inert with a combustible gas (air) flows in steady, laminar flow over a flat plate. A mass flux of gaseous fuel away from the plate surface is produced by some means. Combustion is assumed to occur with very fast reaction rate so that the process is purely controlled by diffusion and the equilibrium is assumed as very close to complete combustion. It is studied under which conditions the combustion occurs at the surface or when the flame is displaced into the boundary layer. The influence of combustion on the heat transfer from a hot gas to the plate surface is calculated, for the condition that combustion occurs at the surface.   相似文献   

6.
One-, two- and three-dimensional time-dependent smoulder propagationthrough solid reactants with plane bounding surfaces is considered.Propagation is maintained by the diffusion of oxidizer fromthe boundaries to the smouldering reaction zone. The resultingburnt solid is assumed to be porous and the unreacted solidis taken to be sufficiently dense for no oxidizer to be present.The activation energy of the reaction is taken to be so largethat the exothermic reaction term has a delta-function behaviour.This enables the reaction zone to be approximated by a narrowreaction front and results in the equations of heat and masstransfer being decoupled away from the front. The assumption,based on experimental observations, that the reaction frontspropagate with a speed proportional to t–1/2, where tis the time, permits the introduction of similarity variables.The resulting intermediate asymptotic equations, lying betweenthose for very small and very large times, are solved and theequation of the smouldering fronts determined for each geometryis considered.  相似文献   

7.
The effects of an applied electric field on an ionic autocatalyticreaction with a quadratic rate law are considered, where thereacting species, A+ and B+, are present in a system which alsoincludes non-reacting species C- and D+. The conditions areestablished under which the general terms which describe theelectric field effects in the reaction-diffusion equations canbe simplified to those used in previous studies, where theseeffects are modelled by linear advection terms. The resultingequations are then studied in detail by first obtaining conditionsfor the existence of travelling waves of permanent form. Thisdiscussion shows that B, the ratio of the diffusion coefficientsof B+ and A+, is a critical parameter, with different formsof behaviour arising for B < 1 and B > 1. This analysisis augmented by obtaining solutions valid for large times andlarge values of (the dirnensionless applied field). Numericalsolutions of initial-value problems are obtained for a rangeof values of and B, guided by and interpreted through the analysispreviously obtained. These numerical integrations show the formationof reaction fronts, with the possibility of greatly increasedreaction rates caused by the applied electric field, as wellas propagating electrophoretic fronts in B+ being formed incases where a reaction front is also initiated. There is alsothe possibility of separate electrophoretic fronts in A+ andB+ being formed, which become increasingly separated as timeincreases with the reaction being completely inhibited.  相似文献   

8.
A new numerical technique for simulating gas-solid reactionsincluding diffusion through the reactant and product layers,reaction on the shrinking surface and internal reaction is presented.Some transformations are introduced, and this model can be reducedto dimensionless form including a selfadjoint, singularly perturbed,two-point boundary-valve problem and two initial-value problems.A combination of the Petrov-Galerkin finite element method andpredictor-corrector method is applied to solve the problem.It is shown that the shrinking-core model including both surfacereaction and product layer diffusion can arise for low initialrelative permeability and the diffusion-controlled shrinking-coremodel occurs when the product layer diffusional resistance islarge relative to the surface reaction. This method is simpleand there is no limit on the range of the parameters. Computedresults are numerically evaluated for comparison with resultsof previous authors.  相似文献   

9.
The paper is concerned with the uniqueness and existence problemfor a multidimensional reacting and convection system with thevanishing viscosity method. The uniqueness theorem is obtainedfrom the stability with respect to the initial data. To solvethe existence problem, the uniqueness and existence of solutionsto a viscous system are first proved, and then the L1-modulusof continuity of solutions independent of the small viscosityis obtained.  相似文献   

10.
In this paper, the temporal, spatial, and spatiotemporal patterns of a tritrophic food chain reaction–diffusion model with Holling type II functional response are studied. Firstly, for the model with or without diffusion, we perform a detailed stability and Hopf bifurcation analysis and derive criteria for determining the direction and stability of the bifurcation by the center manifold and normal form theory. Moreover, diffusion-driven Turing instability occurs, which induces spatial inhomogeneous patterns for the reaction–diffusion model. Then, the existence of positive non-constant steady-states of the reaction–diffusion model is established by the Leray–Schauder degree theory and some a priori estimates. Finally, numerical simulations are presented to visualize the complex dynamic behavior.  相似文献   

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