Mass transfer by diffusion

An analogy exists between mass transfer by diffusion and heat transfer by conduction. Each involves coHisions between molecules and a gradient as the driving force which causes flow. Eor diffusion, this is a concentration gradient for conduction, the driving force is an energy gradient. Eourier s... 

Axial diffusion Mass transfer by diffusion along streamlines that occurs at... 

The inverse of the time eonstant tmicro (mieromixing) ean be interpreted as a transfer eoeffieient for mass transfer by diffusion. 

In the previous discussion it has been assumed that the vapour is a pure material, such as steam or organic vapour. If it contains a proportion of non-condensable gas and is cooled below its dew point, a layer of condensate is formed on the surface with a mixture of non-condensable gas and vapour above it. The heat flow from the vapour to the surface then takes place in two ways. Firstly, sensible heat is passed to the surface because of the temperature difference. Secondly, since the concentration of vapour in the main stream is greater than that in the gas film at the condensate surface, vapour molecules diffuse to the surface and condense there, giving up their latent heat. The actual rate of condensation is then determined by the combination of these two effects, and its calculation requires a knowledge of mass transfer by diffusion, as discussed in Chapter 10. 

Interest extends from transfer to single particles to systems in which the particles are in the form of fixed or fluidised beds. The only case for which there is a rigorous analytical solution is that for heat by conduction and mass transfer by diffusion to a sphere. 

This model assumes that the air/water interface from the blade to the Wilhelmy plate can be divided into a number of equal small cells. We apply a simple argument that the rate of mass transfer by diffusion is proportional to the difference in concentration between the neighboring cells, while the concentration and the surface pressure within each cell are assumed homogeneous. 

The commonest multiple step control mechanism in use is that of diffusion to the surface of the catalyst combined with one of the adsorption or surface reaction steps. Mass transfer by diffusion is proportional to the difference between partial pressures in the bulk of the gas and at the catalyst surface,... 

This chapter will focus on three types of membrane extracorporeal devices, hemodialyzers, plasma filters for fractionating blood components, and artificial liver systems. These applications share the same physical principles of mass transfer by diffusion and convection across a microfiltration or ultrafiltration membrane (Figure 18.1). A considerable amount of research and development has been undertaken by membrane and modules manufacturers for producing more biocompatible and permeable membranes, while improving modules performance by optimizing their internal fluid mechanics and their geometry. 

For all of the general techniques of Figure 2, the separations are achieved by enhancing the rate of mass transfer by diffusion of certain species relative to mass transfer of all species by bulk movement within a particular phase. The driving force and direction of mass transfer by diffusion is governed by thermodynamics, with the usual limitations of equilibrium. Thus, both transport and thermodynamic considerations are crucial in separation operations. The rate of separation is governed by mass transfer, while the extent of separation is limited by thermodynamic equilibrium. Fluid mechanics also plays an important role, and applicable principles are included in other chapters. 

These rate determining steps are shown in Figure 5.6. As the reaction is written in equation (5.26), mass transfer in the boundary layer and mass transfer by diffusion in the product layer can be limiting for the reactant gas. A, making its way in from the bulk gas to the unreacted core, or for the product gas, R, making its way out. 

Here is the (diffusive) mass flux of species A (mass transfer by diffusion per unit time and per unit area normal to the direction of mass transfer, in kg/s m ) and is the (diffusive) molar flux (in kmol/s m ). The mass flux of a species at a location is propoitional to the density of the mixture at that location. Note that p = Px + Pb density and C = Q + is the molar concentration of the binary mixture, and in general, they may vary throughout the mixture. Therefore, pd(pjp) dp or Cd(C /C) + dC - But in the special case of constant mixture density p or constant molar concentration C, the relations above simplify to... 

From a macroscopic standpoint molecular diffusion is mass transfer due to a concentration difference. Other types of diffusion, namely diffusion due to pressure differences (pressure diffusion) or temperature differences (thermal diffusion) will not be discussed here. The mechanism of molecular diffusion corresponds to that of heat conduction, whilst mass transfer in a flowing fluid, known for short as convective mass transfer corresponds to convective mass transfer. Mass transfer by diffusion and convection are the only sorts of mass transfer. Radiative heat transfer has no corresponding mass transfer process. 

The calculation of mass transfer by diffusion requires several definitions and relationships which will be outlined in the following. 

For example, an obvious plateau was observed at 13 A dm-2 and identified as the limiting current density [70] determined by the maximum rate of mass transfer by diffusion. When the negative potential increased above this plateau region, the current density dramatically increased and intense hydrogen bubble formation dominated the electrochemical reaction, and the clear threshold, as seen in Figure 20.5, indicated the onset of water electrolysis. 

In virtue of the characteristic small dimensions and the applied low flow rates, the flow is laminar in perfusion based microfluidic cell culture chips. Consequently, convection only exists in the direction of the applied flow (x-direction), whereas in the directions perpendicular to the flow (y- and z-direction) only diffusion contributes to mass transfer. This is schematically illustrated in Fig. 2b, depicting a pronounced flow in x-direction. Due to short distances, mass transfer by diffusion is sufficiently effective in providing nutrients and removing metabolic waste during continuous perfusion, eliminating formation of concentration gradients, and hence accumulation of metabolic waste. Furthermore, the small dimensions of microfluidic cell... 

This is obtained from (9.3.12). As with the RDE, symmetry considerations require that the concentrations be independent of , so that the derivatives in (f> vanish. In addition, the mass transfer by diffusion in the radial direction, represented by the terms + ( / )( Co/dr)], is, at usual flow rates, small compared to convection in the radial direction, (v dCo/dr) hence the diffusive terms are neglected. The boundary conditions for the limiting ring current are ... 

Since the same physical mechanism is associated with heat transfer by conduction (i.e., heat diffusion) and mass transfer by diffusion, the corresponding rate equations are of the same form. The rate equation for mass diffusion is known as Fick s law, and for a transfer of species 1 in a binary mixture it may be expressed as... 

If Da>, this implies the rate of species production by reaction is large compared to the rate of mass transfer by diffusion, and the boundary condition at the reaction surface becomes... 

Diffusion. Mass transfer by diffusion is the natural transport or movement of a substance under the influence of a gradient of chemical potential, that is, due to the concentration gradient-, substances move from regions of high concentration to regions of low concentration in order to minimize or eliminate concentration differences. Diffusion is perhaps the most widely studied means of mass transport. 

Because of the analogy between mass transfer by diffusion and heat transfer by conduction in a boundary layer, correlations for mass transfer and heat transfer to particles are similar. For mass transfer to a single isolated sphere,... 

Peclet (mass) Pe u 1 D mass transfer by convection mass transfer by diffusion... 

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