Driving forces concentration differences

Mass transfer in real absorption equipment resembles a molecular diffusion process only in the basic idea of a concentration difference driving force. However, the two-film theory of Whitman can be used to construct a model similar in many respects to molecular diffusion equations. Fig. 1 is a schematic representing the Whitman two-film theory ... 

In this case, there is no bulk-motion contribution to the flux, and the flux is related linearly to the concentration difference driving force. Special k -type mass-transfer coefficients are defined specifically for equimolar counterdiffusion as follows ... 

Compound A is transferred from phase PI to phase P2 across the phase boundary and it happens at a rate Xy which is proportional to e concentration difference driving force (Cm - Q2)/ thaf is... 

Figure 6.1-3. Graphical identification of the different concentrations and driving forces.

The minus sign and prime on reabsorption indicate a different driving force concentration than for filtration and secretion and drug transport in the opposite direction. Elimination is the generic term given to the first-order rate constant K, or sometimes [h describing the parent drug lost by both metabolism km and excretion ke (Eq. 1.17) ... 

Fig. 13.44. Different driving forces of aldol additions depending on whether they involve quantitatively prepared enolates (top) or only small equilibrium concentrations of enolates (bottom).

The primary factor in the design of filters is the cake resistance or cake permeability. Because the value of the cake resistance can be determined only on the basis of experimental data, laboratory or pilot-plant tests are almost always necessary to supply the information needed for a filter design. After the basic constants for the filter cake have been determined experimentally, the theoretical concepts of filtration can be used to establish the effects of changes in operating variables such as filtering area, slurry concentration, or pressure-difference driving force. 

The driving force represents the chemical affinity of the overall reaction to reach thermodynamic equilibrium. It is proportional to the concentration difference of the reactants with respect to their equilibrium concentrations. The driving force term does not contain parameters associated with the catalyst, consistent with the fact that the catalyst does not affect chemical equilibrium. 

The Irreversible Thermodynamics Model (Kedem and Katchalsky (1958)) is founded on coupled transport between solute and solvent and between the different driving forces. The entropy of the system increases and free energy is dissipated, where the free energy dissipation function may be written as a sum of solute and solvent fluxes multiplied by drivir forces. Lv is the hydrodynamic permeability of the membrane, AII v the osmotic pressure difference between membrane wall and permeate, Ls the solute permeability and cms the average solute concentration across the membrane. 

It is noted that the system coefficients are not the properties of the epidermis itself rather, they are properties of the absorption system composed of the epidermis and the medium of the chemical mixture. Only an absorption system has specific permeation properties that can be measured quantitatively by the system coefficients. This situation is also appfied to the permeabifity measurement, that is, a given permeabihty of a chemical is for a specific absorption system consisting of the epidermis and the medium of the donor solution. The permeation coefficients of chemicals caimot simply be compared if they are measured in different media (e.g., water vs. ethanol). At a given dose concentration, different media could provide a significantly different driving force for the passive diffusion, which governs the absorption processes. 

The LC phases, illustrated by examples in Figures 2 to 4, originate from different driving forces. In the first example, heat transfer causes transition from isotropic to LC state. The order parameter in the second example is ruled by concentration of MBBA in solution. In the last example the mesophase is formed by light exposure of the material. We see, liquid crystals develop either under thermotropic or lyotropic conditions depending on the driving force for organization of the system. 

The different driving forces lead to LC phases in these low molecular compounds. Rod-like systems display LC behaviour in a certain range of temperature therefore, they are thermotropic. Amphiphiles are lyotropic LCs they show LC behaviour in a certain range of concentration. 

The mass/heat wall fluxes and the concentration/temperature driving forces exhibit different dependences on the wall reaction rate, which is made dimensionless by the Damkohler number. Therefore, Sh is also a function of Da. The previously examined correlations are valid for uniform wall concentration (S/ioo when Da — oo) or uniform wall flux Sho when Da —> 0). Values of S/Ik, are lower than those for Sho for the same value of aPemIz. The difference between both values can be around 20%. 

A special type of driving force arises in Item 4 of Table 1.2. The process here is the selective transport of water through a semipermeable membrane from a dilute solution (high water concentration) to a more concentrated solution (low water concentration). The driving force is in this case the difference of the so-called osmotic pressure n, which makes its appearance in transport through cell membranes as well as in industrial processes termed reverse osmosis. We have occasion to take a closer look at osmotic-pressure-driven processes in Chapter 8. 

In multiphase reactive flows, the interfacial transfer fluxes of momentum, heat and species mass are of great importance. These interfacial transfer fluxes are generally modeled as a product of the interfacial area concentration, the driving force denoting the difference in the phase values of the primitive variables, and the transfer (proportionality) coefficients. Mathematically, a generic flux 4 can be expressed on the form ... 

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