Transport effects concentration gradients

In the bnlk, to the contrary, concentration gradients are leveled only as a result of convection, and diffnsion has practically no effect. In the transition region we find both diffnsional and convective transport. The concentration gradient gradnally falls to zero with increasing distance from the surface. 

Concentration gradient for the analyte showing the effects of diffusion and convection as methods of mass transport. 

It must be pointed out that in a diffusion layer where the ions are transported not only by migration but also by diffusion, the effective transport numbers t of the ions (the ratios between partial currents ij and total current t) will differ from the parameter tj [defined by Eq. (1.13)], which is the transport number of ion j in the bulk electrolyte, where concentration gradients and diffusional transport of substances are absent. In fact, in our case the effective transport number of the reacting ions in the diffusion layer is unity and that of the nonreacting ions is zero. 

It follows that convection of the hqnid has a twofold influence It levels the concentrations in the bnlk liquid, and it influences the diffusional transport by governing the diffusion-layer thickness. Shght convection is sufficient for the first effect, but the second effect is related in a qnantitative way to the convective flow velocity The higher this velocity is, the thinner will be the diffusion layer and the larger the concentration gradients and diffusional fluxes. 

In eukaryotes there is also evidence that Met(O) is actively transported. It has been reported that Met(O) is transported into purified rabbit intestinal and renal brush border membrane vesicles by a Met-dependent mechanism and accumulates inside the vesicles against a concentration gradient . In both types of vesicles the rate of transport is increased with increasing concentrations of Na" in the incubation medium. The effect of the Na" is to increase the affinity of Met(O) for the carrier. Similar to that found in the bacterial system, the presence of Met and other amino acids in the incubation medium decreased the transport of Met(O). These results suggest that Met(O) is not transported by a unique carrier. 

A stagnant diffusion layer is often assumed to approximate the effect of aqueous transport resistance. Figure 4 shows a membrane with a diffusion layer on each side. The bulk solutions are assumed to be well mixed and therefore of uniform concentrations cM and cb2. Adjacent to the membrane is a stagnant diffusion layer in which a concentration gradient of the solute may exist between the well-mixed bulk solution and the membrane surface the concentrations change from Cm to c,i for solution 1 and from cb2 to cs2 for solution 2. The membrane surface concentrations are cml and cm2. The membrane has thickness hm, and the aqueous diffusion layers have thickness ht and h2. 

Diffusion provides an effective basis for net migration of solute molecules over the short distances encountered at cellular and subcellular levels. Since the diffu-sional flux is linearly related to the solute concentration gradient across a transport barrier [Eq. (5)], a mean diffusion time constant (reciprocal first-order rate constant) can be obtained as the ratio of the mean squared migration distance (L) to the effective diffusivity in the transport region of interest. 

Various diffusion coefficients have appeared in the polymer literature. The diffusion coefficient D that appears in Eq. (3) is termed the mutual diffusion coefficient in the mixture. By its very nature, it is a measure of the ability of the system to dissipate a concentration gradient rather than a measure of the intrinsic mobility of the diffusing molecules. In fact, it has been demonstrated that there is a bulk flow of the more slowly diffusing component during the diffusion process [4], The mutual diffusion coefficient thus includes the effect of this bulk flow. An intrinsic diffusion coefficient, Df, also has been defined in terms of the rate of transport across a section where no bulk flow occurs. It can be shown that these quantities are related to the mutual diffusion coefficient by... 

The starting points for the continuity and energy equations are again 21.5-1 and 21.5-6 (adiabatic operation), respectively, but the rate quantity7 (—rA) must be properly interpreted. In 21.5-1 and 21.5-6, the implication is that the rate is the intrinsic surface reaction rate, ( rA)int. For a heterogeneous model, we interpret it as an overall observed rate, (—rA)obs, incorporating the transport effects responsible for the gradients in concentration and temperature. As developed in Section 8.5, these effects are lumped into a particle effectiveness factor, 77, or an overall effectiveness factor, r]0. Thus, equations 21.5-1 and 21.5-6 are rewritten as... 

Reaction rates of nonconservative chemicals in marine sediments can be estimated from porewater concentration profiles using a mathematical model similar to the onedimensional advection-diffusion model for the water column presented in Section 4.3.4. As with the water column, horizontal concentration gradients are assumed to be negligible as compared to the vertical gradients. In contrast to the water column, solute transport in the pore waters is controlled by molecular diffusion and advection, with the effects of turbulent mixing being negligible. 

---