Diffusion coefficient effective diffusivity

Molecular bulk diffusion coefficient Effective diffusivity... 

FWS surface per volume of water c Concentration of solute c Concentration at inlet Cp Concentration in matrix pore water D Apparent diffusion coefficient Effective diffusion coefficient Dl Dispersion coefficient Dp Diffusion coefficient in pore water D , Diffusion coefficient in free water i Hydraulic gradient K Volume based sorption coefficient Kg Hydraulic conductivity L Length of flowpath M Mass of solute injected in a stream... 

Reactant concentration on the outer catalyst surface Reference tracer concentration Diameter of the channel (tube), hydraulic diameter Molecular diffusion coefficient Effective diffusion coefficient Diameter of particle... 

Continuous stirred tank reactor Dispersion coefficient Effective diffusivity Knudsen diffusivity Residence time distribution Normalized residence time distribution... 

The analysis of outlet peaks is based on the model of processes in the column. Today the Kubi n - Kucera model [14,15], which accounts for all the above-mentioned processes, as long as they can be described by linear (differential) equations, is used nearly exclusively. Several possibilities exist for obtaining rate parameters of intracolumn processes (axial dispersion coefficient, external mass transfer coefficient, effective diffusion coefficient, adsorption/desorption rate or equilibrium constants) from the column response peaks. The moment approach in which moments of the outlet peaks are matched to theoretical expressions developed for the system of model (partial) differential equations is widespread because of its simplicity [16]. The today s availability of computers makes matching of column response peaks to model equations the preferred analysis method. Such matching can be performed in the Laplace- [17] or Fourier-domain [18], or, preferably in the time-domain [19,20]. 

D.C. Stone, J.F. Tyson, Flow cell and diffusion coefficient effects in flow injection analysis, Anal. Chim. Acta 179 (1986) 432. 

Avalanche coefficient Linear absorption coefficient Effective absorption coefficient Ablation depth per pulse (=ablation rate) Diameter of ablated (modified) area Thermal diffusivity... 

Effective moisture diffusivity Air boundary mass transfer coefficient Effective thermal conductivity Air boundary heat transfer coefficient... 

Radial (transverse) dispersion of mass During passage of the fluid through the fixed bed, the repeated lateral displacement combined with mixing of fluid elements of different streamlines lead to radial mixing perpendicular to the main flow in axial direction. This can be characterized by an apparent radial dispersion coefficient (effective radial diffusivity) D a. which is in most practical cases much higher than the molecular diffusion coefficient. 

Gibbs free energy change on reaction reaction enthalpy enthalpy (specific) enthalpy, Henry s law constant electric current diffusive mass flux conduction heat flux W m reaction velocity thermal conductivity Boltzmann constant chemical equilibrium constant resistance coefficients effective thermal conductivity first-order reaction rate constant characteristic half thickness Lewis number... 

In fact the piston flow model, as well as the diffusion model, gives too ideal picture of the structure of the flows. They take into account neither the diffusion boundary layer nor the real movement of the phases. These models are especially far from the real situation in flie apparatus in respect to the liquid phase which moves not like a piston flow but in the form of film, drops and jets which are not only separate in space but have also different and continuously changing velocities. Nevertheless, not only the diffusion model but in some cases also its simpler variant, the piston flow model, gives oflxm very good description of the mass transfer processes in industrial apparatuses. This can be explained with the comparatively weak influence of the real structure of the flows on the mass transfer. On the other side using in the model such experimentally obtained values as mass transfer coefficient, effective surface, and Peclet number, it is possible to take into account the important for the mass transfer rate characteristics of the flows structures. In Chaptra 8 the cases when it is possible to use the simpler piston flow model, and when it is necessary to use the diffusion model are considered and specified. 

Mampallil, D., Mathwig, K., Kang, S., and Lemay, S. G. 2013. Redox couples with unequal diffusion coefficients Effect on redox cycling. A a/. Chem. 85 6053-6058. 

Although the model provides a mechanism to measure the total activity of enzyme immobilized on an electrode, it also allows estimation of the combined mass transfer parameter (A/nad+) for the diffusing substrate (in this case, NAD" ). This value, however, is limited somewhat by the fact that the term is cumulative for several variables that may individually contribute to overall electrode mass transfer combined contributions of the molecular diffusion coefficient, effective surface area, diffusion length, pore structure, and mass transfer through the film. Unfortunately, this approach will remain limited unless additional modeling is incorporated that can specifically differentiate these parameters. If more parameters are to be added to the... 

The rate of dissolving of a solid is determined by the rate of diffusion through a boundary layer of solution. Derive the equation for the net rate of dissolving. Take Co to be the saturation concentration and rf to be the effective thickness of the diffusion layer denote diffusion coefficient by . 

The coefficients, L., are characteristic of the phenomenon of thermal diffusion, i.e. the flow of matter caused by a temperature gradient. In liquids, this is called the Soret effect [12]. A reciprocal effect associated with the coefficient L. is called the Dufour effect [12] and describes heat flow caused by concentration gradients. The... 

If a fluid is placed between two concentric cylinders, and the inner cylinder rotated, a complex fluid dynamical motion known as Taylor-Couette flow is established. Mass transport is then by exchange between eddy vortices which can, under some conditions, be imagmed as a substantially enlranced diflfiisivity (typically with effective diflfiision coefficients several orders of magnitude above molecular difhision coefficients) that can be altered by varying the rotation rate, and with all species having the same diffusivity. Studies of the BZ and CIMA/CDIMA systems in such a Couette reactor [45] have revealed bifiircation tlirough a complex sequence of front patterns, see figure A3.14.16. 

However, we would expect the binary pair diffusion coefficients to be replaced by effective diffusion coefficients in the mediuTn, so that... 

The solute species therefore diffuse independently, rather as in Knudsen diffusion, but with effective diffusion coefficients D, where... 

The limiting cases of greatest interest correspond to conditions in which the mean free path lengths are large and small, respectively, compared with the pore diameters. Recall from the discussion in Chapter 3 that the effective Knudsen diffusion coefficients are proportional to pore diameter and independent of pressure, while the effective bulk diffusion coefficients are independent of pore diameter and inversely proportional to pressure. 

It may seem curious that Knudsen diffusion coefficients still appear in equations (5.18) and (5.19), which supposedly give the flux relations at the limit of bulk diffusion control. However, inspection reveals that only ratios of these coefficients are effectively present, and from equation (2,11) it follows that... 

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