Coefficient, diffusion transfer

Mutual Diffusivity, Mass Diffusivity, Interdiffusion Coefficient Diffusivity is denoted by D g and is defined by Tick s first law as the ratio of the flux to the concentration gradient, as in Eq. (5-181). It is analogous to the thermal diffusivity in Fourier s law and to the kinematic viscosity in Newton s law. These analogies are flawed because both heat and momentum are conveniently defined with respec t to fixed coordinates, irrespective of the direction of transfer or its magnitude, while mass diffusivity most commonly requires information about bulk motion of the medium in which diffusion occurs. For hquids, it is common to refer to the hmit of infinite dilution of A in B using the symbol, D°g. 

Tafel slope (Napieran loop) transfer coefficient diffusion layer thickness dielectric constant, relative electric field constant = 8.85 x 10 F cm overvoltage, polarization ohmic voltage drop, resistance polarization specific conductance, conductivity electrochemical potential of material X,... 

When the two liquid phases are in relative motion, the mass transfer coefficients in either phase must be related to the dynamical properties of the liquids. The boundary layer thicknesses are related to the Reynolds number, and the diffusive transfer to the Schmidt number. Another complication is that such a boundary cannot in many circumstances be regarded as a simple planar interface, but eddies of material are transported to the interface from the bulk of each liquid which change the concentration profile normal to the interface. In the simple isothermal model there is no need to take account of this fact, but in most industrial circumstances the two liquids are not in an isothermal system, but in one in which there is a temperature gradient. The simple stationary mass transfer model must therefore be replaced by an eddy mass transfer which takes account of this surface replenishment. 

FIGURE 5.16 Schematic of resistance model for diffusion, uptake, and reaction of gases with liquids. Tg represents the transport of gases to the surface of the particle, a the mass accommodation coefficient for transfer across the interface, rso, the solubilization and diffusion in the liquid phase, riM the bulk liquid-phase reaction, and rinlcrl.ll c the reaction of the gas at the interface. 

Here d> is the matrix of pair correlation functions obeying the auxiliary equation (3.529) with helpful initial condition (r, 0) = W(r). Still the problem remains rather complex. Solving it in Ref. 194, all the kernels were specified using as input data only the diffusion coefficients and transfer rates W/ (r), WB (r), Wr (r), and Wrr(r). 

The description of diffusion involves three complimentary mathematical models, often dignified as laws. The most fundamental, Fick s law of diffusion, uses a diffusion coefficient. In other cases, where convection is strong, the mixing will occur following the same mathematics as Fick s law but with a dispersion coefficient replacing the diffusion coefficient. In still others cases, where there is transport across some type of interface, the mixing is described as mass transfer and correlated with a mass transfer coefficient. Mass transfer coefficients... 

Phase Binary diffusion coefficients Mass transfer correlations... 

Transfer through the mobile phase is more complicated because diffusion and flow both act to shuttle molecules to and from the stationary phase (see Chapter 11). The effective coefficient for transfer is DT = Derr + D, Eq. 5.34, where Derr arises from random flow currents. Equation 9.17 assumes the form... 

Mass transport coefficient (also called mass transport rate coefficient, mass transfer coefficient, heterogeneous diffusion rate constant) is defined as... 

The physical and thermal properties of the gas and liquid, interfacial area and liquid holdup, physical mass transfer coefficients, diffusion coefficients, and volumetric flow rate of the liquid are independent of temperature and conversion. 

The Microscopic Origin of the Diffusion Coefficient Mass Transfer Rates and Diffusion Layer Thickness... 

Estimation of liquid-side mass transfer coefficients for gas-liquid transport through the upper surface of the film can be most readily made by assumption of a purely diffusive transfer. Under these conditions, a mass transfer coefficient can be approximated using the following equation for mass transfer ... 

We see from the above equation that the concentration profile will be a hnear function of y (i.e., dCldy = constant) for the entire electrolyte region between the anode and cathode when the current density is constant, fluid convection is nonexistent (diffusion and migration are the only modes of transport), and the diffusion coefficient and transference number are constant and independent of concentration. 

Equilibrium of adsorption on a solid is characterized by an adsorption isotherm, which shows the concentration on the solid as a function of the concentration in the contacting fluid. A quantitative measure of uptake of a gaseous species by a liquid is the distribution coefficient, defined as the ratio of the concentration on the solid to that in the contacting fluid. If concentration-independent, the coefficient is also called Henry coefficient. Diffusion of a species in a porous solid is expressed in terms of an effective diffusion coefficient, whose value accounts for the retardation by the solid matrix. Mass transfer to or from a solid is expressed in terms of a mass-transfer coefficient, the flux being the product of that coefficient and a concentration difference as "driving force."... 

INTERNAL AND EXTERNAL MASS-TRANSFER COEFFICIENTS. The overall coefficient depends on the external coefficient and on an effective internal coefficient Diffusion within the particle is actually an unsteady-state process, and the value of decreases with time, as solute molecules must penetrate further and further into the particle to reach adsorption sites. An average coefficient can be used to give an approximate fit to uptake data for spheres ... 

To explain the seeming paradox discussed, we consider the limiting case in which the transfer of surfactant takes place only by surface convection. We assume the capillary number is small, and essentially we follow Herbolzheimer s approach. If we make Eq. (10.5.22) appropriately dimensionless, choosing U as the characteristic velocity, a as the characteristic length, and D as the diffusion coefficient, then both terms on the right side of Eq. (10.5.22) are on the order of Pe, where Pc =Ua/D. For the steady flow configuration examined with Pe l, surface convection is large compared with diffusive transfer, and Eq. (10.5.22) reduces to = From continuity Vj-Uj = 0, whence the... 

Heat, mass and momentum transfers are respectively characterized by thermal diffusivity coefficient diffusion coefficient D and kinematic viscosity coefficient, all expressed in cm s". ... 

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