Modelling of simultaneous mass and heat transfer with chemical reaction using the Maxwell-Stefan theory I. Model development and isothermal study

A general applicable model has been developed which can predict mass and heat transfer fluxes through a vapour/gas-liquid interface in case a reversible chemical reaction with associated heat effect takes place in the liquid phase. In this model the Maxwell-Stefan theory has been used to describe the transport of mass and heat. The description of the transfer rates has been based on the film model in which a well-mixed bulk and a stagnant zone are thought to exist. In this paper results obtained from the Maxwell-Stefan theory have been compared with the results obtained from the classical theory due to Fick. This has been done for isothermal absorption of a pure gas A in a solvent containing a reactive component B. Component A is allowed to react by a unimolecular chemical reaction or by a bimolecular chemical reaction with B to produce component C. Since the Maxwell-Stefan theory leads to implicit expressions for the absorption rates, approximate explicit expressions have been derived. In case of absorption with chemical reaction it turned out that the mass transfer rate could be formulated as the product of the mass flux for physical absorption and an enhancement factor. This enhancement factor possesses the same functional dependency in case Fick's law is used to describe the mass transfer process. The model which has been developed in this work is quite general and can be used for a rather general class of gas-liquid and vapour-liquid transfer processes. In this paper (Part I) only isothermal simulations will be reported to show the important features of the model for describing mass transfer with chemical reaction. In many processes such as distillation, reactive distillation and some absorption processes, heat effects may play an important additional role. In Part II non-isothermal processes will be studied to investigate the influence of heat effects on mass transfer rates

Lie symmetries of nonlinear boundary value problems

Nonlinear boundary value problems (BVPs) by means of the classical Lie symmetry method are studied. A new definition of Lie invariance for BVPs is proposed by the generalization of existing those on much wider class of BVPs. A class of two-dimensional nonlinear boundary value problems, modeling the process of melting and evaporation of metals, is studied in details. Using the definition proposed, all possible Lie symmetries and the relevant reductions (with physical meaning) to BVPs for ordinary differential equations are constructed. An example how to construct exact solution of the problem with correctly-specified coefficients is presented and compared with the results of numerical simulations published earlier.Comment: Published versio

Kinetic Intersections as a Source of Information on Rate Coefficients

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Diffusion flame extinction in slow convenctive flow under microgravity environment

A theoretical analysis is presented to study the extinction characteristics of a diffusion flame near the leading edge of a thin fuel plate in slow, forced convective flows in a microgravity environment. The mathematical model includes two-dimensional Navier-Stokes momentum, energy and species equations with one-step overall chemical reaction using second-order finite rate Arrhenius kinetics. Radiant heat loss on the fuel plate is applied in the model as it is the dominant mechanism for flame extinguishment in the small convective flow regime. A parametric study based on the variation of convective flow velocity, which varies the Damkohler number (Da), and the surface radiant heat loss parameter (S) simultaneously, is given. An extinction limit is found in the regime of slow convective flow when the rate of radiant heat loss from fuel surface outweighs the rate of heat generation due to combustion. The transition from existent envelope flame to extinguishment consists of gradual flame contraction in the opposed flow direction together with flame temperature reduction as the convective flow velocity decreases continuously until the extinction limit is reached. A case of flame structure subjected to surface radiant heat loss is also presented and discussed

On Similarity Solutions and Interface Reactions for a Vector-Valued Stefan Problem

In this paper first it is shown for several geometries that classical similarity solutions for particle growth exist if and only if the Stefan problem is well-posed in the sense of being mass conserving. The extension of the similarity solutions to multicomponent alloys, which makes the problem nonlinear, is illustrated by the application to a hypothetic alloy with realistic input values. The similarity solutions are based on the assumption of local equilibrium at the interface. In the second part, the assumption of local equilibrium is relaxed using a first-order interface reaction. The influence of the interface reaction on the movement of the interface and on the interface concentrations is evaluated using Finite Difference calculations. A Newton scheme is used to solve the nonlinear problem