The Generalized Driving Force

The physical interpretation of c RTd is that it represents the force acting on species i per unit volume of mixture tending to move species i relative to the solution. The quantity represents the volume fraction of species /, / , and so we may rewrite Eq. 2.3.9 as 

It is sometimes convenient to express Eqs. 2.3.10 and 2.3.11 in terms of the external body force exerted per mole of / the corresponding equations are 

What we have achieved so far is to express the rate of entropy production due to mass diffusion in terms of a convenient driving force c RTd per unit volume of mixture. Equation 2.3.8 shows that the rate of entropy production is a sum of the products of two quantities the force acting on /, per unit volume, tending to move i relative to the mixture and the relative velocity of the movement of i with respect to the mixture Ojiif is, therefore, the dissipation due to diffusion. 

---

To be able to describe the presence of electrolytes in the system, the electrical driving force also needs to be taken into account (57). Therefore, the gradient of the electrical potential V

[Pg.382]

R depends linearly on the generalized driving force A (corresponding... 

In Eq. (13-88), 4 is termed the generalized driving force. For an ideal gas mixture the driving force is related to the partial pressure gradient and the mole fraction gradient as follows ... 

Equations 2.3.18 together with Eqs. 2.3.10 defining the generalized driving force are the starting point for the analysis of diffusion in systems where external force fields influence the process the ultracentrifuge, for example, in electrolyte systems and in porous media where pressure gradients become important. We examine the first two of these topics in the Sections 2.3.3 and 2.4. 

For diffusion in isothermal multicomponent systems the generalized driving force was written as a linear function of the relative velocities (m/ — My). In the general case, we must allow for coupling between the processes of heat and mass transfer and write constitutive relations for and q in terms of the (m — My) and V(l/r). With this allowance, the complete expression for the conductive heat flux is... 

Using the Maxwell-Stefan equations for nonideal fluids, Eqs. 2.2.1, as a basis, develop a general expression for an effective diffusivity defined in terms of the generalized driving force as... 

The general driving force across the films and the membrane is proportional to the flux. The proportionality constants are the resistances to flow. Equations 18.2 and... 

Since the ion is electrically charged, we use the electrochemical potential, A/, in this equation. We divide by to obtain the force acting on a single particle. The proportionality factor, Wf, is a generalized mobility it is the velocity attained by the ion under a unit value of the generalized driving force, — [5(/ij/A/ A)/5x]j ... 

As already mentioned in the previous section, any hollow nanoparticle should shrink. The general driving force of shrinkage is the same for a pure component shell (Model 1) and for an IMC shell (Models 2-4) - a decrease in the total surface energy (in other formulation - Gibbs-Thomson effect). Yet, the kinetics are different. 

The reactions proceed in toluene at insigniHcant pressure of CO (80 psi). The general driving force for these processes is the strong reduction potential of Sm(II) species. 

---