Driving forces transport processes

Equations (10.152) and (10.153) can be used to analyze sodium flow in frog skin. The flow of sodium chloride across the skin comprises the flow of sodium ions. /Na, which is coupled to the metabolic process Jrtot, while the flow of the chloride ions JC may be assumed to be passive transport. The driving forces for the ionic flows are the electrochemical potential differences, and are given for a component i in a simple system as follows ... 

In facilitated transport of metal ions through LM, the metal ions are transported through the membrane against their own concentration gradient, termed as the uphill transport. The driving force in such processes is provided by the chemical potential difference of the species other than the diffusing ones on either side of the membrane. The permeability of the transported species is decided by the parameters such as membrane thickness, pore structure, aqueous diffusion coefficient of the species, aqueous diffusion layer thickness, and distribution and diffusion coefficients of the transported species in the LM phase. The diffusion of the species in the carrier solvent depends on the membrane characteristics (viz., porosity and tortuosity) and viscosity of the solvent, while the aqueous diffusion of the metal ions depends upon the flow rate and diffusivity of metal species in the aqueous phase. On the other hand, the overall transport rates of the species can be controlled through various parameters such as feed composition, carrier concentration, and receiver phase composition. 

The tme driving force for any diffusive transport process is the gradient of chemical potential rather than the gradient of concentration. This distinction is not important in dilute systems where thermodynamically ideal behavior is approached. However, it becomes important at higher concentration levels and in micropore and surface diffusion. To a first approximation the expression for the diffusive flux may be written... 

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. 

The pressure difference between the high and low pressure sides of the membrane is denoted as AP the osmotic pressure difference across the membrane is defined as Att the net driving force for water transport across the membrane is AP — (tAtt, where O is the Staverman reflection coefficient and a = 1 means 100% solute rejection. The standardized terminology recommended for use to describe pressure-driven membrane processes, including that for reverse osmosis, has been reviewed (24). 

In considering the effect of mass transfer on the boiling of a multicomponent mixture, both the boiling mechanism and the driving force for transport must be examined (17—20). Moreover, the process is strongly influenced by the effects of convective flow on the boundary layer. In Reference 20 both effects have been taken into consideration to obtain a general correlation based on mechanistic reasoning that fits all available data within 15%. 

All criteria proposed here are constructed such that if absolutely no gradient of a particular type exists, then the value of the corresponding criterion is zero. For fast catalytic processes this is not reasonable to expect and therefore a value judgment must be made for how much deviation from zero can be ignored. For the dimensionless expressions the Damkdhler numbers are used as these are applied to each particular condition. The approach is that the Damkdhler numbers can be calculated from known system values, which are related to the unknown driving forces for the transport processes. 

The basic mechanism of passivation is easy to understand. When the metal atoms of a fresh metal surface are oxidised (under a suitable driving force) two alternative processes occur. They may enter the solution phase as solvated metal ions, passing across the electrical double layer, or they may remain on the surface to form a new solid phase, the passivating film. The former case is active corrosion, with metal ions passing freely into solution via adsorbed intermediates. In many real corrosion cases, the metal ions, despite dissolving, are in fact not very soluble, or are not transported away from the vicinity of the surface very quickly, and may consequently still... 

The rate of extraction depends on the mass transport coefficient (f), the phase contact area (F) and the difference between the equilibrium concentration and the initial concentration of the dissolved component, which is usually expressed as the driving force of the process (a). The rate of extraction (V) can be calculated as shown in Equation (135) ... 

A CVD reaction is governed by thermodynamics, that is the driving force which indicates the direction the reaction is going to proceed (if at all), and hykinetics, which defines the transport process and determines the rate-control mechanism, in other words, how fast it is going. 

A CVD reaction can occur in one of two basic systems the closed reactor or the open reactor (also known as close or open tube). The closed-reactor system, also known as chemical transport, was the first typetobeusedforthe purification of metals. It is a hybrid process which combines vapor-phase transfer with solid-state diffusion. As the name implies, the chemicals are loaded in a container which is then tightly closed. A temperature differential is then applied which provides the driving force for the reaction. 

In many epithelia Cl is transported transcellularly. Cl is taken up by secondary or tertiary active processes such as Na 2Cl K -cotransport, Na Cl -cotransport, HCOJ-Cl -exchange and other systems across one cell membrane and leaves the epithelial cell across the other membrane via Cl -channels. The driving force for Cl -exit is provided by the Cl -uptake mechanism. The Cl -activity, unlike that in excitable cells, is clearly above the Nernst potential [15,16], and the driving force for Cl -exit amounts to some 2(f-40mV. 

Separations in membrane processes result from differences in the transport rates of analytes or solvent molecules through a membrane interface. The transport rate is usually determined by the existence of a driving force, such as a concentration, pressure- or temperature gradient and the mobility and concentration of analytes within the Interface. The most useful membrane processes for sampld preparation are dialysis. 

This result shows that the most likely rate of change of the moment due to internal processes is linearly proportional to the imposed temperature gradient. This is a particular form of the linear transport law, Eq. (54), with the imposed temperature gradient providing the thermodynamic driving force for the flux. Note that for driven transport x is taken to be positive because it is assumed that the system has been in a steady state for some time already (i.e., the system is not time reversible). 

Some of the elements of thermodynamics of irreversible processes were described in Sections 2.1 and 2.3. Consider the system represented by n fluxes of thermodynamic quantities and n driving forces it follows from Eqs (2.1.3) and (2.1.4) that n(n +1) independent experiments are needed for determination of all phenomenological coefficients (e.g. by gradual elimination of all the driving forces except one, by gradual elimination of all the fluxes except one, etc.). Suitable selection of the driving forces restricted by relationship (2.3.4) leads to considerable simplification in the determination of the phenomenological coefficients and thus to a complete description of the transport process. 

This device has not reached commercialization, no doubt in part because bulk electrochemical transport of major gaseous components will rarely be economical compared with more standard separation processes. It is in the transport of minority species from low partial pressure to high (e.g. 02 from seawater, C02 from air) where the benefits of the electrochemical driving force, as detailed at the outset of this chapter can best be exploited. Two final examples of contaminant control of great commercial interest demonstrate this principle. 

The relative contribution of each driving force (X) generated by component j to the flux of solute i (./,) is expressed by coefficients Li in this phenomenological description of parallel transport processes. 

---