Mass-transfer modes

Mass transfer of chemical or electrochemical specie j, known as ions can be a complex phenomenon because the solution (fluid) containing the ions may be strongly influenced by turbulent flow, and to a lesser extent to laminar flow, diffusion and an electrical field. For a stationary chemical or electrochemical system, such as a tank, pipe or battery, as observed by a stationary observer, under internal laminar flow the mass transfer is quantified by the molar or mass flux. For a one-dimensional treatment in the x-diiection, the mass transfer 

The model indicates that a plane of area dA containing specie j moves in the x-direction from position 1 to position 2, and then to position 3. This motion is influenced by modes of mass transfer, such as diffusion due to a molar concentration gradient, migration due to an electrical field, natural or forced convection due to the kinematic velocity or a combination of these modes, mass transfer of species j can be quantified by the absolute value of the molar flux J or the mass flux J. Notice that J is perpendicular to the moving plane of species j and represents the absolute value of the vector molar flux J. The total flux can be defined as 

In addition,/ represents the number of moles of specie j that pass per unit time through a unit area. Thus, the units of J are rrudxm. s and that of J are g/.cm. 8. For a steady-state conditions and stationary x-axis, the concentration rate is dCj/dt = 0 and the total molar flux is defined by the Nemst-Hank equation [16,1921] 

Jc = Convective molar flux due to fluid motion nuA/err a) dC/dx = Concentration gradient mol/cm ) d(f /dx = Potential gradient (V/cm) 

In an electrical field, the rate of reaction process for metal reduction or oxidation is normally represented by the current density (t). Using eq. (321) the generalized Faraday s equation for the current density is 

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It is obvious that following hydrodynamic similarity eq. (6.40), the mass transfer mode is different between the two scales due to the change in the respective dimensionless parameters, and as a result the conversion will be also different ... 

The governing heat transfer modes in gas-solid flow systems include gas-particle heat transfer, particle-particle heat transfer, and suspension-surface heat transfer by conduction, convection, and/or radiation. The basic heat and mass transfer modes of a single particle in a gas medium are introduced in Chapter 4. This chapter deals with the modeling approaches in describing the heat and mass transfer processes in gas-solid flows. In multiparticle systems, as in the fluidization systems with spherical or nearly spherical particles, the conductive heat transfer due to particle collisions is usually negligible. Hence, this chapter is mainly concerned with the heat and mass transfer from suspension to the wall, from suspension to an immersed surface, and from gas to solids for multiparticle systems. The heat and mass transfer mechanisms due to particle convection and gas convection are illustrated. In addition, heat transfer due to radiation is discussed. 

The present theoretical model is used here to analyze the entire ignition and combustion process for a single droplet and to examine the eflFects of nonsteady droplet heating and droplet motion relative to the hot gas environment. The computations pertain to a 300 fx furfuryl alcohol droplet with an initial droplet temperature of 295 K, and the conditions for the hot gas environment are taken to be = 1400 K and iVo) = 0.1355 g 02/g air. The rate constants used for the ignition criterion are those determined in Ref. 7. The eflFect of droplet relative motion on ignition and combustion is illustrated in Figures 2-6 as a function of the gas-phase heat and mass transfer mode namely, pure diflFusion, free convection, and forced convection with the droplet relative velocity taken as Vd — Voo = 25 cm/sec. 

In the most general situation, all three mass transfer modes cooperate algebraically thus the number of moles crossing a surface of unit area per unit of time is given in Eq. (133), which constitutes an extension of the Pick s first law. 

Belles and Fair evaluated a large data bese of published tests ou the performance of columns containing random packing and developed a mass transfer mode) that appeals to be superior to those previously... 

Mass Transfer Mode—Vacuum/Atmospheric Pressure.1118... 

Fig.2 Mass-Transfer Modes in Electrochemical Reactors, 1- direction of current flow, 2- flow-by, 3- flow-through perpendicular to current flow, and, 4- flow-through parallel to current flow...

Substituting eqs. (4.3) through (4.5) into ((4.9) yields the total current density for the above mass transfer modes... 

Mass Transfer Mode— Vacuum/ Atmospheric Pressure... 

There is a close similarity between heat and mass transfer in terms of transport rate equation and transport conservation equation. The diffusion and convective mass transfer modes are similar to the conduction and convection modes of heat transfer. Both diffusion and convection mass transfer play a significant role in the transport of reactant gas species through the gas flow channels and gas diffusion layers/electrodes. 

A word of explanation may be needed here. It was said in Section B of Chapter 3 that migration of ions under the influence of electric field is not an important mass transfer mode in fairly concentrated solutions. Here we say that the field of the interphase changes the concentrations of ions. Are these statements not contradictory That this is only an apparent contradiction becomes obvious when we remember that the thickness of the diffusion layer is commonly ten thousand times that of the double layer. Thus it is true that species move most of the distance from the bulk of the solution to the electrode surface in the gradient of forces other than electrical. At the same time the concentration at the electrode surface in the presence of field differs from that in the absence of one. 

The simulation discussed here was performed using the convection and diffusion application mode of Multiphysics v3.5a (COMSOL, Stockholm, Sweden). The Nemst-Planck equation, which is solved numerically, can be written assuming diffusion and migration mass transfer modes as... 

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