Binary molecular diffusion

Use your best judgment in estimating the binary molecular diffusivity. However, it may be assumed that we are still in the region where the binary molecular diffusivity is inversely proportional to the pressure. 

The free parameters of this model are the ratio of porosity to tortuosity, e/r, the binary molecular diffusivities, D-j, the Knudsen coefficient, Ko (which determines specific effective Knudsen diffusivities, D j) and the permeability constant, Bo. 

The binary molecular diffusion coefficient, DAB, can be derived from the kinetic gas theory. A more accurate empirical correlation is given by ... 

Consider the problem of steady-state one-dimensional diffusion in a mixture of ideal gases. At constant T and P, the total molar density, c = P/RT is constant. Also, the Maxwell-Stefan diffusion coefficients D m reduce to binary molecular diffusion Dim, which can be estimated from the kinetic theory of gases. Since Dim is composition independent for ideal gas systems, Eq. (6.61) becomes... 

An alternative to the complete Maxwell-Stefan model is the Wilke approximate formulation [103]. In this model the diffusion of species s in a multicomponent mixture is written in the form of Tick s law with an effective diffusion coefficient instead of the conventional binary molecular diffusion coefficient. Following the ideas of Wilke [103] we postulate that an equation for the combined mass flux of species s in a multicomponent mixture can be written as ... 

The binary molecular diffusivities are calculated from Wilke and Lee... 

Steady-State Binary Molecular Diffusion in Porous Solids... 

The binary molecular diffusion coefficient, ab> has units of length /time and characterizes the microscopic motion of species A in solvent B, for example. Hab is also the molecular transport property that appears in the linear law that relates diffusional fluxes and concentration gradients. In this respect, the same quantity, Bab. represents a molecular transport property for mass transfer and a diffusion coefficient. This is not the case for the other two transport processes. 

When there are only two components in the mixture, diffusional fluxes are written in terms of a driving force and a binary molecular diffusion coefficient via Pick s first law. For example, if the diffusional mass flux with respect to a reference frame that translates at the mass-averaged velocity of the mixture is based on a mass fraction driving force, then Pick s first law for component A is... 

SOLUTION, (a) The Stokes-Einstein diffusion equation, which is applicable for creeping flow of an incompressible Newtonian fluid around spherical particles (i.e., solids or bubbles) at extremely low particle concentrations, reveals that liquid-phase binary molecular diffusion coefficients exhibit the following temperature dependence ... 

If one focuses on the three dissimilar binary gas pairs with methane, then it is straightforward to estimate collision diameters, potential well depths and binary molecular diffusivities for each gas pair. For example ... 

The molar diffusional flux of reactant A toward the catalytic surface is governed by Pick s law with a concentration-independent binary molecular diffusion coefficient. Thermal (Soret), pressure, and forced diffusion are neglected relative to concentration diffusion. 

The mass transfer-chemical reaction process occurs isothermally. This critical assumption allows one to neglect energy transport processes within the reactor. Hence, the physical properties of the reactive mixture—overall mass density, viscosity, binary molecular diffusion coefficient, and surface-averaged kinetic rate constant—are treated as constants throughout the reactor. 

The Stokes-Einstein equation for binary molecular diffusion coefficients of dilute pseudo-spherical molecules subject to creeping flow through an incompressible Newtonian fluid is (see equation 25-98) ... 

Calculate the following ratio of liquid-phase binary molecular diffusion coefficients for hydrogen chloride and chlorobenzene in benzene (solvent) at low concentrations of the solute (hydrogen chloride or chlorobenzene) ... 

Identify two reasons why liquid-phase binary molecular diffusion coefficients increase at higher temperature. 

The Stokes-Einstein equation provides an estimate of the binary molecular diffusion coefficient for dilute mixtures of spherical molecules of A in an incompressible Newtonian solvent B. This correlation is applicable to liquids, not gases. When the interface between solvent B and molecule A is characterized best by no slip and high shear. 

The coefficient of kp in (26-14) is written in terms of the concentration dependence of cpA via the definition of the binary molecular diffusivity in equation (25-76a) ... 

An eqnation has been derived relating the effective diffusivity of porous foodstuffs to various physical properties such as molecular weight, bulk density, vapor space permeability, water activity as a function of material moisture content, water vapor pressure, thermal conductivity, heat of sorption, and tanperature [80]. A predictive model has been proposed to obtain effective diffusivities in cellular foods. The method requires data for composition, binary molecular diffusivities, densities, membrane and cell wall permeabilities, molecular weights, and water viscosity and molar volume [81]. The effect of moisture upon the effective diffusivity is taken into account via the binding energy of sorption in an equation suggested in Ref. [77]. 

Modern gas-diffusion medium in low-temperature fuel cells is typically a highly porous carbon paper with porosity in the range of sgdl = 0.6-0.8 and with the mean pore radius in the order of 10 pm (10 cm). By the order of magnitude, the mean free path of molecules in atmospheric pressure air is = l/(A LO-fci ), where Nl = 2.686 10 cm is the Loschmidt number (number of molecules in a cubic centimetre of atmospheric pressure gas at standard temperature) and akin — 10 cm is the molecular cross-section for kinetic collisions. With this data we get 3 10 cm, or 3 10 pm. Obviously, mean pore radius in the GDL is nearly 3 orders of magnitude greater than I f and the physical mechanism of molecule transport is binary molecular diffusion. 

The binary molecular diffusion coefficient values were computed from the Fuller et al. [44] relation ... 

If a gas or liquid mixture is ideal, then Da/ is the binary molecular diffiisivity of A in species i . Binary molecular diffusivities are almost independent of concentration for ideal gas and liquid systems. Values of Dy for many common binary pairs are tabulated in handbooks, and methods for predicting binary diffusivities as a function of temperature and pressure are... 

For this case of binary, equimolar counterdiffusion, the diffusivity of A in the imxture (DA,m) is just the binary molecular diffusivity of A in B (Dab)- Moreover, the flux Na is purely... 

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