Driving forces chemical potential gradients

A reverse osmosis membrane acts as the semipermeable barrier to flow ia the RO process, aHowiag selective passage of a particular species, usually water, while partially or completely retaining other species, ie, solutes such as salts. Chemical potential gradients across the membrane provide the driving forces for solute and solvent transport across the membrane. The solute chemical potential gradient, —is usually expressed ia terms of concentration the water (solvent) chemical potential gradient, —Afi, is usually expressed ia terms of pressure difference across the membrane. 

Solution—Diffusion Model. In the solution—diffusion model, it is assumed that (/) the RO membrane has a homogeneous, nonporous surface layer (2) both the solute and solvent dissolve in this layer and then each diffuses across it (J) solute and solvent diffusion is uncoupled and each is the result of the particular material s chemical potential gradient across the membrane and (4) the gradients are the result of concentration and pressure differences across the membrane (26,30). The driving force for water transport is primarily a result of the net transmembrane pressure difference and can be represented by equation 5 ... 

The most important driving forces for the motion of ionic defects and electrons in solids are the migration in an electric field and the diffusion under the influence of a chemical potential gradient. Other forces, such as magnetic fields and temperature gradients, are commonly much less important in battery-type applications. It is assumed that the fluxes under the influence of an electric field and a concentration gradient are linearly superimposed, which... 

The ionic mobilities Uj depend on the retarding factor 0 valid for a particular medium [Eq. (1.8)]. It is evident that this factor also influences the diffusion coefficients. To find the connection, we shall assume that the driving force of diffusion is the chemical potential gradient that is, in an ideal solution,... 

The percutaneous absorption picture can be qualitatively clarified by considering Fig. 3, where the schematic skin cross section is placed side by side with a simple model for percutaneous absorption patterned after an electrical circuit. In the case of absorption across a membrane, the current or flux is in terms of matter or molecules rather than electrons, and the driving force is a concentration gradient (technically, a chemical potential gradient) rather than a voltage drop [38]. Each layer of a membrane acts as a diffusional resistor. The resistance of a layer is proportional to its thickness (h), inversely proportional to the diffusive mobility of a substance within it as reflected in a... 

The ideas of Overton are reflected in the classical solubility-diffusion model for transmembrane transport. In this model [125,126], the cell membrane and other membranes within the cell are considered as homogeneous phases with sharp boundaries. Transport phenomena are described by Fick s first law of diffusion, or, in the case of ion transport and a finite membrane potential, by the Nernst-Planck equation (see Chapter 3 of this volume). The driving force of the flux is the gradient of the (electro)chemical potential across the membrane. In the absence of electric fields, the chemical potential gradient is reduced to a concentration gradient. Since the membrane is assumed to be homogeneous, the... 

The driving force for solvent permeation is the total pressure gradient across the membrane, which is related to the chemical potential gradient, according to... 

The flux jA of component A is given by the sum (yA e + Ja 1c)< the flux jB of component B by yBxe- In Section 2.2, we showed that the component-driving forces are composed of the chemical potential gradients of those combinations of SE s which constitute the corresponding building units. Thus, in the present case, we have... 

Chemical kinetics concerns the evolution in time of a system which deviates from equilibrium. The acting driving forces are the gradients of thermodynamic potential functions. Before establishing the behavior and kinetic laws of interfaces, we need to understand some basic interface thermodynamics. The equilibrium interface is characterized by equal and opposite fluxes of components (or building elements) in the direction normal to the boundary. Ternary systems already reflect the general... 

Although this equation is reminiscent of the rules given earlier in this chapter, there are differences. In Eqn. (11.21), the two independent concentration gradients of the ternary system are introduced instead of real driving forces, which are the chemical potential gradients. Also, other simplifying assumptions have been made in order to arrive at Eqn. (11.21), assumptions which hardly pertain to real systems. 

Fluxes of chemical components may arise from several different types of driving forces. For example, a charged species tends to flow in response to an applied electrostatic field a solute atom induces a local volume dilation and tends to flow toward regions of lower hydrostatic compression. Chemical components tend to flow toward regions with lower chemical potential. The last case—flux in response to a chemical potential gradient—leads to Fick s first law, which is an empirical relation between the flux of a chemical species, J, and its concentration gradient, Vcj in the form J, = —DVcj, where the quantity D is termed the mass diffusivity. 

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 Chapter 2 we considered diffusion in a closed system containing TV components, exclusive of any mediating point defects.1 If only chemical potential gradients are present and all other driving forces—such as thermal gradients or electric fields—... 

A driving force for diffusion includes any influence that increases the jump frequency. Examples of driving forces include chemical potential, thermal, and stress gradients. If a chemical potential gradient is present, the flux of species i at the diffusion plane is given by = —D (dc-Jdx), where D is the intrinsic diffusion coefficient of species i. Assuming Henry s law for the tracer element in binary alloys, Darken30 has shown that... 

Continuous systems. The membrane is considered as a quasi-homo-geneous intermediate phase. The driving forces are the gradients of the electrical potential, the pressure and the chemical potential. 

Thermal diffusion is a process in which solute is driven through solvent by the action of a temperature gradient rather than by a concentration (or chemical potential) gradient [46]. It is a natural outgrowth of the laws of irreversible thermodynamics (Section 3.2) in which all driving forces are expected to be associated with some transport of matter. 

Care has to be taken when considering simple concentrations of the permeant since the driving force for diffusion is really the chemical potential gradient. As stated above the maximum flux should occur for a saturated solution of the permeant. However, if supersaturated solutions are applied to the skin, it is possible to obtain enhanced fluxes [27]. This can only be true if the outer skin lipids are capable of sustaining a supersaturated state of the diffusant. Figure 4.4 shows the linear increase in skin permeation with degree of supersaturation, and Fig. 4.5 demonstrates... 

The phenomenon of ambipolar conduction is not limited to chemical potential gradients only, and may occur in systems with several driving forces (e.g., chemical-potential and temperature gradients in combination with external electrical field). However, this phenomenon is always related to conjugate transport of several charge carriers. 

If no forces are pushing particles in the direction of the flow, then what about the driving force for diffusion, i.e., the gradient of chemical potential (Section 4.2.1) The latter is only formally equivalent to a force in a macroscopic treatment it is a sort of pseudoforce like a centrifugal force. The chemical-potential gradient is not a true force that acts on the individual diffusing particles and from this point of view is quite unlike, for example, the Coulombic force, which acts on individual charges. 

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