Potential gradients as the driving force

If a diffusion potential occurs inside the membrane, the relation between mass transport and electrochemical potential gradient — as the driving force for the diffusion of ions — has to be examined in more detail. This can be done by three different approaches ... 

To describe the effect of the above parameters on interdiflfusion, de Gennes [67] used the chemical potential gradient as the driving force for interdiffusion. Assuming that the fluxes of the two components were equal, but opposite, Brochard-Wyart et al. [68] derived the slow-mode theory for interdiffusion at polymer interfaces. 

The primary difference between D and D is a thermodynamic factor involving the concentration dependence of the activity coefficient of component 1. The thermodynamic factor arises because mass diffusion has a chemical potential gradient as a driving force, but the diffusivity is measured proportional to a concentration gradient and is thus influenced by the nonideality of the solution. This effect is absent in self-diffusion. 

In chemistry we are used to thinking of the gradient of the chemical potential, t, as the driving force. 

For diffusion in liquid electrolytes such as molten salts, two forces acting on an ion of interest should be taken into account the gradient of the chemical potential and the charge neutrality. Thus the electrochemical potential rather than the chemical potential should be the driving force for diffusion. 

The original electrochemical potential hypothesis postulated that the energy provided by the coupled proton transport is stored in the form of a transmembrane bulk electrochemical gradient of protons, and is used therefrom by the membrane-bound ATP synthase [33]. Unquestionably, the data briefly discussed above support the contention that (a) bulk electrochemical gradients are formed by coupled proton flow, and (b) such bulk electrochemical gradients can serve as the driving force for ATP synthesis. 

Here q is the concentration of species i, and the quantity RT/ci has been absorbed into the diffusion coefficient D. Eq. (6.3.4) is known as Pick s Law of diffusion. The coefficient is clearly concentration dependent. In Eq. (6.3.4) the concentration gradient serves as the driving force , but in actuality it is the gradient in chemical potential that activates the particle flow, as shown in Eq. (6.3.3). 

The driving force in dialysis is the gradient of chemical activatives across the membrane barrier, whereas electrodialysis involves the gradient of electric potential as the driving force [l5 ]. 

Since entropy of the system must increase with each spontaneous change, it is used as the potential function in the Q-space whose gradient is the driving force. Suppose, for a region near the equilibrium point, that the rates are linear functions of the gradient of entropy ... 

There remain a couple of things to say about the conditions of equilibrium, equations (14.21). One is that just as inequalities (gradients) in T or P are driving forces for the transfer of heat and work, a chemical potential gradient is a driving force for the transfer of matter. Consider for example equation (14.13) in the case of two coexisting phases at a constant T and P, each of which is a homogeneous solution of two components. Thus... 

Chemical potential difference will affect the flow rate of dissolved solute ions and solvent (or pore fluid - the mud filtrate is considered to be pore fluid once it has infiltrated the pores of the shale). The main consideration of dissolved ions is their contribution to osmotic pressure. This is achieved by keeping track of the concentration of the dissolved ions (Equation 7). The effect of osmotic pressure on the flow of pore fluid is taken into account by including the osmotic pressure in the rock water potential, and use the spatial gradient of rock water potential (Equation 6) as the driving force for pore fluid flow. 

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