Diffusional flow technique

Metallic alloys are usually designed to resist power-law creep diffusional flow is only rarely considered. One major exception is the range of directionally solidified ( DS ) alloys described in the Case Study of Chapter 20 here special techniques are used to obtain very large grains. 

Given the availability of hollow fiber membranes adequately permeable to substrates and products, and the control of fluid flow all around the fibers in the bundle in order to assure uniform flow distribution and to avoid stagnation (in order to reduce mass transfer diffusional resistances), the technique offers several advantages. Enzyme proteins can be easily retained within the core of the fibers with no deactivation due to coupling agents or to shear stresses, and the enzyme solution can be easily recovered and/or recycled. 

The simplest treatments of convective systems are based on a diffusion layer approach. In this model, it is assumed that convection maintains the concentrations of all species uniform and equal to the bulk values beyond a certain distance from the electrode, 8. Within the layer 0 x < 5, no solution movement occurs, and mass transfer takes place by diffusion. Thus, the convection problem is converted to a diffusional one, in which the adjustable parameter 8 is introduced. This is basically the approach that was used in Chapter 1 to deal with the steady-state mass transport problem. However, it does not yield equations that show how currents are related to flow rates, rotation rates, solution viscosity, and electrode dimensions. Nor can it be employed for dual-electrode techniques or for predicting relative mass-transfer rates of different substances. A more rigorous approach begins with the convective-diffusion equation and the velocity profiles in the solution. They are solved either analytically or, more frequently, numerically. In most cases, only the steady-state solution is desired. 

Aside from the relative position of the profile, the shape of the effluent profile contains information concerning the kinetics of the adsorption process. All concentrations of protein from zero to cQ are brought into contact with the column surface as the protein solution flows through the column, as a function of the position of the profile, and therefore as a function of time. Working with small molecules, previous researchers have shown that compounds exhibiting Langmuir isotherms produce sharp fronts, and diffuse tails, if pure solvent is used to desorb the column (21,22). However, Equation 7 shows that both diffusional and adsorption effects can alter the shape of the effluent profile. The former effect includes both normal molecular diffusion, and also diffusion due to flow properties in the column (eddy diffusion), which broadens (decreases the slope) the affluent profiles. To examine the adsorption processes, apart from the diffusional effects, the following technique can be applied. 

Most of the experimental applications of the ZLC technique have been with gaseous systems, and for these systems the technique may now be regarded as a standard method. Based on our experience it is possible to suggest some guidelines as to how the experiments should be carried out. The key parameter is L, which from its definition (Eq. 17) can be considered the ratio of the diffusional and washout time constants R /D and KVs/F. This parameter is also equal to the dimensionless adsorbed phase concentration gradient at the surface of the solid at time zero. From either of these definitions it is evident that L gives an indication of how far removed the system is from equilibrium control. This parameter is proportional to the flow rate, so it can be easily varied, and to extract a reliable time constant, it is necessary to run the experiment at at least two different flow rates. 

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