Modelling of catalytic reactivity of inhomogeneous surfaces in monomer-monomer reactions

The kinetics of a A1 + A2 -> A1A2 reaction on inhomogeneous surfaces with continuously distributed adsorption sites is investigated numerically using two phenomenological models. One of them includes: the bulk diffusion of reactants from a bounded vessel towards the adsorbent and the product bulk one from the adsorbent into the same vessel, adsorption and desorption of molecules of both reactants, and surface diffusion of adsorbed and product particles before their desorption. The other model describes surface reaction provided that concentrations of both reactants at the surface are given. Both models are based on the Langmuir–Hinshelwood reaction mechanism coupled with the Eley–Rideal step. Two surface diffusion mechanisms are used. According to one of them, the diffusion flux of the adsorbed and product particles is described by the standard Fick law, while in the other one the surface diffusion flux is based on the particle jumping into a nearest vacant adsorption site. Simulations were performed using the finite difference technique. The kinetic rate constants, Eley–Rideal steps, and surface diffusion mechanisms influence on the catalytic reactivity of surf aces is studied

On the kinetics of the Langmuir-type heterogeneous reactions

In this paper we investigate three two-dimensional in space mathematical models of the kinetics of unimolecular heterogeneous reactions proceeding onto planar surfaces. All models include the diffusion of the reactant from a bounded vessel towards an adsorbent, adsorption of the molecules of the reactant, their desorption, conversion (reaction) of the adsorbate into a product, instantaneous product desorption, and the diffusion of the product from the adsorbent into the same vessel. One of these models is based on the Langmuir-type kinetics of the surface reactions, the other one is based on the local steady-state value of the surface coverage, and the last one, in addition to the first model, involves the diffusion of the adsorbate along the adsorbent. Diffusivity of all species is assumed to be constant. Models were solved numerically by using the finite difference technique. By changing input parameters the effects of the rate constants of the reactant adsorption, desorption, and reaction and the influence of the surface diffusion of the adsorbate and approximation of the surface coverage by its steady-state value on the kinetics of surface reactions were studied numerically

A reaction-diffusion model of the receptor-toxin-antibody interaction

<p>Abstract</p> <p>Background</p> <p>It was recently shown that the treatment effect of an antibody can be described by a consolidated parameter which includes the reaction rates of the receptor-toxin-antibody kinetics and the relative concentration of reacting species. As a result, any given value of this parameter determines an associated range of antibody kinetic properties and its relative concentration in order to achieve a desirable therapeutic effect. In the current study we generalize the existing kinetic model by explicitly taking into account the diffusion fluxes of the species.</p> <p>Results</p> <p>A refined model of receptor-toxin-antibody (RTA) interaction is studied numerically. The protective properties of an antibody against a given toxin are evaluated for a spherical cell placed into a toxin-antibody solution. The selection of parameters for numerical simulation approximately corresponds to the practically relevant values reported in the literature with the significant ranges in variation to allow demonstration of different regimes of intracellular transport.</p> <p>Conclusions</p> <p>The proposed refinement of the RTA model may become important for the consistent evaluation of protective potential of an antibody and for the estimation of the time period during which the application of this antibody becomes the most effective. It can be a useful tool for <it>in vitro </it>selection of potential protective antibodies for progression to <it>in vivo </it>evaluation.</p

The robust finite-volume schemes for modeling nonclassical surface reactions

A coupled system of nonlinear parabolic PDEs arising in modeling of surface reactions with piecewise continuous kinetic data is studied. The nonclassic conjugation conditions are used at the surface of the discontinuity of the kinetic data. The finite-volume technique and the backward Euler method are used to approximate the given mathematical model. The monotonicity, conservativity, positivity of the approximations are investigated by applying these finite-volume schemes for simplified subproblems, which inherit main new nonstandard features of the full mathematical model. Some results of numerical experiments are discussed

The robust finite volume schemes for modeling non-classical surface reactions

A coupled system of nonlinear parabolic PDEs arising in modeling of surface reactions with piecewise continuous kinetic data is studied. The nonclassic conjugation conditions are used at the surface of the discontinuity of the kinetic data. The finite-volume technique and the backward Euler method are used to approximate the given mathematical model. The monotonicity, conservativity, positivity of the approximations are investigated by applying these finite-volume schemes for simplified subproblems, which inherit main new nonstandard features of the full mathematical model. Some results of numerical experiments are discussed

Toksino neutralizavimo antikūnu, gerai išmaišytame tirpale, kompiuterinis tyrimas

A mathematical model decribing the interaction of toxin, antibody and cell receptors when cell is placed in the well-mixed solution of toxin, antibody and toxin–antibody complex is studied. The protective properties of an antibody against toxin are investigated numerically choosing the model parameters.Nagrinėjamas netiesinis matematinis modelis, aprašantis toksino, antikūno ir ląstelės receptorių sąveiką, kai ląstelę supa gerai išmaišytas toksino ir antikūno mišinys. Keičiant modelio parametrus, skaitiniais metodais tiriamas antikūno panaudojimo efektyvumas, apsaugant ląstelę nuo toksino

Bakterijų dinamikos kompiuterinis modeliavimas

The system of partial differential equations, describing the dynamics of the oxygen consuming bacteria in a chamber with an open top, is investigated. The finite difference method is used for solving the problem. Solutions of two different numerical schemes are compared and analyzed when values of oxygen concentration become negative in the case of a shallow layer.Nagrinėjama netiesinių diferencialinių lygčių sistema, kuri aprašo deguonimi mintančių bakterijų dinamiką atvirame inde. Uždavinys sprendžiamas baigtinių skirtumų metodu. Analizuojami skaitiniai sprendiniai, gaunami taikant skirtingus skaičiavimo būdus, kai deguonies koncentracijos reikšmės sekliame sluoksnyje mažesnės už leistiną ribinę reikšmę

Phenomenological model of bacterial aerotaxis with a negative feedback

A phenomenological model for the suspension of the aerotactic swimming microorganisms placed in a chamber with its upper surface open to air is presented. The model was&nbsp;constructed to embody some complexity of the aerotaxis phenomenon, especially, changes in&nbsp;the average bacteria drift velocity under changing environmental conditions. It was assumed that&nbsp;effective forces applied to the cell (gravitational, drag, and thrust) should be essential for the&nbsp;overall system dynamics; and that bacterial propulsion force, but not their swimming velocity, is&nbsp;proportional to the gradient of the oxygen concentration. Mathematically, the model consists of&nbsp;three coupled equations for the oxygen dynamics; for the cell conservation; and for the balance of&nbsp;forces acting on bacteria. An analytical steady-state solution is given for the shallow and deep layers&nbsp;and numerical results are given for the steady-state and initial value problems which are compared&nbsp;with corresponding ones to the Keller–Segel model

Dviejų modelių, aprašančių dimerų katalitinę reakciją kompozitinio katalizatoriaus paviršiuje, palyginimas

In this paper two mathematical models of the dimer–dimer reaction on supported catalysts are compared. The PDE model describe the bulk diffusion of both reactants and product, adsorption and desorption, the surface diffusion of adsorbates and intermediate. The ODE model is derived from the first, assuming that all materials are well-mixed. The catalytic reactivity, calculated using the PDE and ODE models, is compared for two variants of reactants adsorption and variuos bulk and surface diffusion.&nbsp; &nbsp;Palyginami du dimerų katalitinės reakcijos, vykstančios kompozitinio katalizatoriaus paviršiuje, modeliai. Dalinių išvestinių modelis aprašo reagentų ir produkto tūrinę bei adsorbatų ir tarpinio produkto paviršinę difuziją, adsorbciją ir desorpciją. Paprastųjų išvestinių modelis išvedamas iš pirmojo, kai reakcijoje dalyvaujančios medžiagos yra vienodai pasiskirsčiusios. Lyginamas abiem metodais apskaičiuotas katalitinis reaktyvumas, keičiant difuzijos koeficientus. Raktiniai žodžiai: paviršinė reakcija, adsorbcija, desorbcija, spiloveris

Monomerų reakcijų kompozitinių katalizatorių paviršiuje skaitinis tyrimas: gerai išmaišytų medžiagų modelis

A nonlinear mathematical model describing the kinetics of a bimolecular heterogeneous catalytic reaction proceeding on a supported catalyst is studied. The model is based on the Langmuir–Hinshelwood surface reaction mechanism assuming that all species are well-mixed. The catalytic surface size influence on the catalytic reactivity and product concentration is investigated numerically for different arrangements of the adsorption sites.Nagrinėjamas netiesinis modelis aprašantis heterogeninę katalitinę dviejų reagentų reakciją, vykstančią kompozitinių katalizatorių paviršiuje. Modelis pagrįstas Langmiūro ir Hinšelvudo paviršinių reakcijų mechanizmu, laikant, kad reakcijoje dalyvaujančios medžiagos yra tolygiai pasiskirsčiusios. Tiriama aktyvios katalizatoriaus paviršiaus dalies dydžio įtaka katalitiniam reaktyvumui ir produkto koncentracijai, esant skirtingam adsorbcijos centrų išsidėstymui