Non-Linear Mass Transfer and Hydrodynamic Stability

C.B. Boyadjiev, V.N. Babak, C.B. Boyadjiev, V.N. Babak

• Verlag: Elsevier Science
• Jahr: 2000
• ISBN:
  9780080537702
• Thema: Physical Sciences
• Thema: Physical & Theoretical Chemistry

Surveyed in this book are the kinetics of non-linear mass transfer and its effects on hydrodynamic stability in systems with intensive interphase mass transfer, in electrochemical systems with high current density and in chemically reacting systems.
In Part 1 the non-linear mass transfer as a result of an intensive interphase mass transfer in the gas (liquid)-solid surface, gas-liquid and liquid-liquid systems is considered in the duffusion boundary layer approximation as well as in flat channel taking the longitudinal diffusion into account. The influence of the direction of the intensive interphase mass transfer on heat transfer and multi-component mass transfer is illustrated.
Part 2 discusses non-linear mass transfer in electrochemical systems with high current density using the examples of the anode dissolving of metals in the electrolyte flow and the electro-separation of metals out of concentrated solutions. The theory of the measured electrochemical treatment of metals and alloys, which is a method of wide practical use, has been elaborated on this basis.
In Part 3 the non-linear mass transfer in chemically reacting systems is considered in the cases of: non-linearity of the equations of the chemical reaction's kinetics and intensive interphase mass transfer or thermo-capillary effect due to chemical reactions. On this basis, the mechanisms and the macro-kinetics of the chemical transformations in the gas-liquid systems are discussed.
Part 4 is dedicated to the chemical reaction kinetics in stationary two phase systems at an arbitrary contact time between phases.
In Part 5 the effects of concentration gradients are considered in the approximations of the linear theory of the hydrodynamic stability of almost parallel flows.
In systems with intensive interphase mass transfer, the Marangoni effect could also be observed, beside the effect of non-linear mass transfer. A comparative analysis of both effects is made in this book.

Introduction

The contemporary development of the chemical, power, biotechnological and other industries, and especially the creation of apparatuses with big unit power, pose the problem of decreasing the equipment size. This can be achieved by introducing high rate processes.

The implementation in industry of apparatuses for highly intensive heat and mass transfer processes is prevented by the fact that under conditions of interphase mass transfer significant differences are noticed between the actual process rate and the rate, predicted by the linear theory of mass transfer. This makes difficult their optimal design.

The basic reasons for the deviations from the linear theory are the occurrence of several non-linear effects as a result of the gradients of pressure (Stephan flow), density (natural convection), concentration (non-linear mass transfer), and surface tension (Marangoni effect). The appearance of the temperature and concentration dependencies of the parameters in the equations of momentum, mass and heat transfer, as well as the chemical reactions (especially if their order is higher than unity), lead to other type of non-linear effects.

All these effects represent the influence of the temperature and concentration on the flow rate of a fluid, in which heat and / or mass transfer takes place. They may occur in two ways. In the first case the changes in the field of velocity lead to changes in the fields of concentration and temperature, and therefore to changes in the kinetics of the mass and heat transfer. In the second case the change in the velocity field leads to loss of stability of the flow, appearance of stable dissipative or turbulent structures, which on their hand lead to a new mechanism of heat and mass transfer and to an essential increase of the heat and mass transfer rate.

In most cases the models of non-linear processes will be treated as a superposition of the linear theory and the separate non-linear effects, which gives a reason for a short statement of the linear theory.

LINEAR MASS TRANSFER THEORY

A balance of the convective and the diffusive transfer determines the mass transfer in a moving fluid. If are marked by u(x,y,z) and c(x,y,z) the fields of velocity and concentration, the mass flow (j) through an unit surface of a given elementary volume is the sum of the convective and the diffusive flows:

(0.1)

where D is a diffusivity.

In the cases of stationary processes and absence of a volume source (stock) of a substance, the material balance of the substance in the elementary volume is obtained through integration of the flow over the whole surface of this volume:

(0.2)

From (0.1) and (0.2) one is directly obtained:

(0.3)

From (0.3) one possible problem for a mass transfer in a two-dimensional area with dimensions L and h, where y = 0 is the surface, through which the mass transfer wi...