Resistance, mass transfer defined

As illustrated ia Figure 6, a porous adsorbent ia contact with a fluid phase offers at least two and often three distinct resistances to mass transfer external film resistance and iatraparticle diffusional resistance. When the pore size distribution has a well-defined bimodal form, the latter may be divided iato macropore and micropore diffusional resistances. Depending on the particular system and the conditions, any one of these resistances maybe dominant or the overall rate of mass transfer may be determined by the combiaed effects of more than one resistance. 

The comparison of the magnitude of the two resistances clearly indicates whether tire metal or the slag mass transfer is rate-determining. A value for the ratio of the boundary layer thicknesses can be obtained from the Sherwood number, which is related to the Reynolds number and the Schmidt number, defined by... 

However, under working conditions, with a current density j, the cell voltage E(j) decreases greatly as the result of three limiting factors the charge transfer overpotentials r]a,act and Pc,act at the two electrodes due to slow kinetics of the electrochemical processes (p, is defined as the difference between the working electrode potential ( j), and the equilibrium potential eq,i). the ohmic drop Rf. j, with the ohmic resistance of the electrolyte and interface, and the mass transfer limitations for reactants and products. The cell voltage can thus be expressed as... 

The permeability coefficients, PD and PR, are influenced by hydrodynamics. Depending upon the geometric symmetry or asymmetry of stirring in the donor and receiver chambers, their values may be equal or unequal. To analyze these situations, let us define PAm, as the effective permeability coefficient of the ABLs therefore, the geometric average of the mass transfer resistance of the ABLs is... 

Thus, in an isothermal system, the mass flow rate depends on the difference in pressures of the gas across the orifice and does not depend upon the thickness of the plate. One may define an area-normalized resistance, R, for mass transfer through the orifice using a generalization of Ohm s law, i.e., Resistance = force/ flux. For Knudsen flow, the force is the pressure difference (analogous to voltage difference in Ohm s law) and the flux is the mass flow per unit area of the hole (analogous to the electrical current density in Ohm s law). Thus, we have... 

Heat transfer from the shelves to the sublimation front depends on the pressure and the distance between shelf and product (Fig. 1.58). Mass transfer (g/s) increases with the pressure, but also depends on the flow resistance of the already dry product and of the packing of the bones. If the maximum tolerable Tke is defined, the drying time depends only on the two processes mentioned above. It cannot be shortened under a given geometric situation and the chosen Tke. This method of Tkt control does not require thermocouples, and does not contaminate the product. 

Mass transfer rates within the porous residue are difficult to assess because it is impossible to define the shape of the channels through which transfer must take place. It is possible, however, to obtain an approximate indication of the rate of transfer from the particles to the bulk of the liquid. Using the concept of a thin film as providing the resistance to transfer, the equation for mass transfer may be written as ... 

The last part of the polarization curve is dominated by mass-transfer limitations (i.e., concentration overpotential). These limitations arise from conditions wherein the necessary reactants (products) cannot reach (leave) the electrocatalytic site. Thus, for fuel cells, these limitations arise either from diffusive resistances that do not allow hydrogen and oxygen to reach the sites or from conductive resistances that do not allow protons or electrons to reach or leave the sites. For general models, a limiting current density can be used to describe the mass-transport limitations. For this review, the limiting current density is defined as the current density at which a reactant concentration becomes zero at the diffusion medium/catalyst layer interface. 

The resistance to mass transfer of reactants within catalyst particles results in lower apparent reaction rates, due to a slower supply of reactants to the catalytic reaction sites. Ihe long diffusional paths inside large catalyst particles, often through tortuous pores, result in a high resistance to mass transfer of the reactants and products. The overall effects of these factors involving mass transfer and reaction rates are expressed by the so-called (internal) effectiveness factor f, which is defined by the following equation, excluding the mass transfer resistance of the liquid film on the particle surface [1, 2] ... 

The experimental determination of the film coefficients kL and kc is very difficult. When the equilibrium distribution between the two phases is linear, over-all coefficients, which are more easily determined by experiment, can be used. Over-all coefficients can be defined from the standpoint of either the liquid phase or gas phase. Each coefficient is based on a calculated over-all driving force Ac, defined as the difference between the bulk concentration of one phase (cL or cc) and the equilibrium concentration (cL or cc ) corresponding to the bulk concentration of the other phase. When the controlling resistance is in the liquid phase, the over-all mass transfer coefficient KLa is generally used ... 

A convention used in most literature on ozone mass transfer and in the rest of this book is to define the mass transfer coefficient as the one that describes the mass transfer rate without reaction, and to use the enhancement factor E to describe the increase due to the chemical reaction. Furthermore, the simplification that the major resistance lies in the liquid phase is used throughout the rest of the book. This is also based on the assumption that the mass transfer rate describes physical absorption of ozone or oxygen, since the presence of a chemical reaction can change this. This means that KLa - kLa and the concentration gradient can be described by the difference between the concentration in equilibrium with the bulk gas phase cL and the bulk liquid concentration cL. So the mass transfer rate is defined as ... 

To measure the extent which the reaction rate is lowered because of resistance to mass transfer, we can define the effectiveness factor of an immobilized enzyme, 17, as... 

In some references, it appears the term resistance to the mass transfer, fimy, defined as mt, i Jui. ... 

The membrane system considered here is composed of two aqueous solutions wd and w2, separated by a liquid membrane M, and it involves two aqueous solution/ membrane interfaces WifM (outer interface) and M/w2 (inner interface). If the different ohmic drops (and the potentials caused by mass transfers within w1 M, and w2) can be neglected, the membrane potential, EM, defined as the potential difference between wd and w2, is caused by ion transfers taking place at both L/L interfaces. The current associated with the ion transfer across the L/L interfaces is governed by the same mass transport limitations as redox processes on a metal electrode/solution interface. Provided that the ion transport is fast, it can be considered that it is governed by the same diffusion equations, and the electrochemical methodology can be transposed en bloc [18, 24]. With respect to the experimental cell used for electrochemical studies with these systems, it is necessary to consider three sources of resistance, i.e., both the two aqueous and the nonaqueous solutions, with both ITIES sandwiched between them. Therefore, a potentiostat with two reference electrodes is usually used. 

The overall specific resistance for heat or mass transfer is the reciprocal of the heat or mass transfer coefficient, U or K, where U and K are the common parameters characterizing heat and mass transfer rates, respectively, defined as... 

This equation expresses the fact that in a process with the various flow rates /, work is continuously dissipated to overcome the barriers, the resistance, or the friction that all the processing such as heat and mass transfer and chemical conversion introduce. In Chapter 5, we refer to this as the result of the "magic triangle." There is no clearer way to illustrate the origin of the process s energy bill, nor a better way to calculate it. This relation also defines the challenge that in order to keep the energy bill as low as possible one should find, as Bejan calls it, "the path of least resistance" [6]. 

An important performance characteristic of passive samplers that operate in the TWA regime is the diffusion barrier that is inserted between the sampled medium and the sorption phase. This barrier is intended to control the rate of mass transfer of analyte molecules to the sorption phase. It is also used to define the selectivity of the sampler and prevent certain classes (e.g., polar or nonpolar compounds) of analytes, molecular sizes, or species from being sequestered. The resistance to mass transfer in a passive sampler is, however, seldom caused by a single barrier (e.g., a polymeric membrane), but equals the sum of the resistances posed by the individual media (e.g., aqueous boundary layer, biofilm, and membrane) through which analyte diffuses from the bulk water phase to the sorption phase.19 The individual resistances are equal to the reciprocal value of their respective mass transfer coefficients and are additive. They are directly proportional to the thickness of the barrier... 

For a zero-order process, the effectiveness factor (defined as the ratio of the actual consumption of reactant to that which would occur in the absence of mass transfer resistance) is equal to unity whenever the following inequality holds ... 

According to the film theory, in reactive-absorption processes the resistance to mass transfer is concentrated in a small region near the gas/liquid interface. The ratio between tbe rate of chemical reaction and liquid-phase mass transfer is given by the Hatta number. For a second-order reaction (12.1), the Hatta number is defined as ... 

This form is particularly appropriate when the gas is of low solubility in the liquid and "liquid film resistance" controls the rate of transfer. More complex forms which use an overall mass transfer coefficient which includes the effects of gas film resistance must be used otherwise. Also, if chemical reactions are involved, they are not rate limiting. The approach given here, however, illustrates the required calculation steps. The nature of the mixing or agitation primarily affects the interfacial area per unit volume, a. The liquid phase mass transfer coefficient, kL, is primarily a function of the physical properties of the fluid. The interfacial area is determined by the size of the gas bubbles formed and how long they remain in the mixing vessel. The size of the bubbles is normally expressed in terms of their Sauter mean diameter, dSM, which is defined below. How long the bubbles remain is expressed in terms of gas hold-up, H, the fraction of the total fluid volume (gas plus liquid) which is occupied by gas bubbles. 

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