Transport driving force

The mode of transport through a membrane may be passive, active, or facilitated type. In passive transport, the membrane acts as a barrier and permeation of the components is determined by their diffusivity and concentration in the membrane or just by their size. In facilitated transport along with the chemical potential gradient, the mass transport is coupled to specific carrier components in the membrane. In active transport driving force for transport is achieved by a chemical reaction in the membrane phase. 

Carrier-mediated transport involves cotransport of the absorbable species with a proton. The required proton gradient is hypothesized to be maintained by a Na+-H+ exchanger. The lumen of the intestine is acidic relative to the epithelial cell cytosol. The low cytosolic sodium concentration, required to produce the transporter driving force, is maintained by the Na K ATPase in the basolateral membrane. The sodium/proton exchanger working in concert with the sodium/potassium ATPase, therefore, results in a transport mechanism for the uptake of di- and tripeptides into the intestinal wall (Ganapthy and Leibach, 1985). 

Also, the increase in N2 dilution causes a decrease in the hydrogen concentration on the anode channel, thus reducing the concentration gradient for the mass transport driving force, reducing the macroscopic parameter anode limiting current... 

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... 

Nonporous Dense Membranes. Nonporous, dense membranes consist of a dense film through which permeants are transported by diffusion under the driving force of a pressure, concentration, or electrical potential gradient. The separation of various components of a solution is related directiy to their relative transport rate within the membrane, which is determined by their diffusivity and solubiUty ia the membrane material. An important property of nonporous, dense membranes is that even permeants of similar size may be separated when their concentration ia the membrane material (ie, their solubiUty) differs significantly. Most gas separation, pervaporation, and reverse osmosis membranes use dense membranes to perform the separation. However, these membranes usually have an asymmetric stmcture to improve the flux. 

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). 

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 ... 

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%. 

If there is a significant resistance to transport of the reactant in the pores, a concentration gradient will exist at steady state, whereby the concentration of the reactant is a maximum at the particle periphery and a minimum at the particle center. The product concentration will be higher at the particle center than at the periphery. The concentration gradients provide the driving force for the transport. 

The primary driviag force for material transport comes from the chemical potential difference that exists between surfaces of dissimilar curvature within the system. The greater the curvature, ie, the finer the particle size, the greater the driving force for material transport and sintering. 

Figure 16-9 depicts porous adsorbent particles in an adsorption bed with sufficient generality to illustrate the nature and location of individual transport and dispersion mechanisms. Each mechanism involves a different driving force and, in general, gives rise to a different form of mathematical result. 

Intraparticle convection can also occur in packed beds when the adsorbent particles have very large and well-connected pores. Although, in general, bulk flow through the pores of the adsorbent particles is only a small frac tion of the total flow, intraparticle convection can affec t the transport of veiy slowly diffusing species such as macromolecules. The driving force for convec tion, in this case, is the... 

Safer Storage Conditions The hazards associated with storage facihties can often be reduced significantly by changing storage con(i-tions. The primary objective is to reduce the driving force available to transport the hazardous material into the atmosphere in case of a leak (Hendershot, 1988). Some methods to accomplish this follow. 

The values of m given above conform to Hemng s scaling law (1950) which states that since the driving force for sintering, the transport length, the area over which uansport occurs and the volume of matter to be transported are proportional to a, and respectively, the times for equivalent change in two powder samples of initial particle size ai q and 2,0 are... 

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