Concentration gradient-dependent

In first-order reactions, the concentration gradient depends on the local concentration at time t ... 

The relationship between the flux and the concentration gradient depends on an experimental observation A one-dimensional gradient in the particle concentration is set up in a fluid by fixing the concentration at two parallel planes. The fluid is isothermal and stationary. It is observed that the rate at which particles are transported from the high to the low concentration (particlcs/cm- sec) is proportional to the local concentration gradient, Bn/dx ... 

Diffusive surfactant fluxes are functions of the intensity of the concentration gradient and the diffusion coefficient of the surfactant. The intensity of the concentration gradient depends upon the overall surfactant concentration. At low or high concentrations, these gradients are relatively weak. At intermediate concentrations, they are quite strong. 

Cao, L. X. Guo, W Wang, Y. G. Jiang, L. Concentration-gradient-dependent ion current rectification in charged conical nanopores. Langmuir 2012, 28, 2194—2199. 

Often, advective and diffusive process act together, in series, in parallel, or in opposition. Solute and colloid bound chemicals diffuse in the open pores of bed-sediment driven by concentration gradients. Depending on the relative positions of the hydraulic heads in ground water compared to the water body, a positive or negative Darcian velocity exists in the bed, resulting in an in-or-out advective chemical transport superimposed on the diffusive transport. Both transport processes must be appropriately combined for assessing the overall chemical mobility (see Section 4.4). 

Diffusion may be defined as the movement of a species due to a concentration gradient, which seeks to maximize entropy by overcoming inhomogeneities within a system. The rate of diffusion of a species, the flux, at a given point in solution is dependent upon the concentration gradient at that particular point and was first described by Pick in 1855, who considered the simple case of linear difflision to a planar surface ... 

In general, therefore, the surface flux of each substance is linearly related Co all the concentration gradients in the adjacent bulk phase. The coefficients in this linear relation depend on the bulk phase concentrations,... 

Concentration gradients for the analyte in the absence of convection, showing the time-dependent change in diffusion as a method of mass transport. 

Back-diffusion is the transport of co-ions, and an equivalent number of counterions, under the influence of the concentration gradients developed between enriched and depleted compartments during ED. Such back-diffusion counteracts the electrical transport of ions and hence causes a decrease in process efficiency. Back-diffusion depends on the concentration difference across the membrane and the selectivity of the membrane the greater the concentration difference and the lower the selectivity, the greater the back-diffusion. Designers of ED apparatus, therefore, try to minimize concentration differences across membranes and utilize highly selective membranes. Back-diffusion between sodium chloride solutions of zero and one normal is generally [Pg.173]

Mass is transferred in drying as a hquid and vapor within the solid and as vapor from the exposed surfaces. Movement within the solid results from a concentration gradient which is dependent on the characteristics of the solid. A solid to be dried may be porous or non-porous. It can also be hygroscopic or nonhygroscopic. Many solids fail intermediately between these two extremes, but it is generally convenient to consider the solid to be one or the other. 

FIG. 22-81 Permeant -concentration profile in a pervaporation membrane. 1— Upstream side (swollen). 2—Convex curvature due to concentration-dependent permeant diffiisivity. 3—Downstream concentration gradient. 4—Exit surface of membrane, depleted of permeant, thus unswollen. (Couttesy Elseoier )... 

Effectiveness As a reac tant diffuses into a pore, it undergoes a falling concentration gradient and a falling rate of reaction. The concentration depends on the radial position in the pores of a spherical pellet according to... 

HONO the mean flux was an emission of 1 ng Nm s but this includes periods both of emission and deposition. On several occasions, no concentration gradients were detected. The direction of the flux was dependent on NOj concentration, with emission observed only when NOj concentration was less than 10 ppb. The process of HONO exchange appears to be regulated by the net result of small deposition flux to the surface and a surface chemistry production of HONO from NOj. Fluxes of PAN deposition were measured using a chamber technique " and were small (less than 0.5ng Nm s ). 

The transparency and refractive power of the lenses of our eyes depend on a smooth gradient of refractive index for visible light. This is achieved partly by a regular packing arrangement of the cells in the lens and partly by a smoothly changing concentration gradient of lens-specific proteins, the crystallins. 

Airborne contaminant movement in the building depends upon the type of heat and contaminant sources, which can be classified as (1) buoyant (e.g., heat) sources, (2) nonbuoyant (diffusion) sources, and (d) dynamic sources.- With the first type of sources, contaminants move in the space primarily due to the heat energy as buoyant plumes over the heated surfaces. The second type of sources is characterized by cimtaminant diffusion in the room in all directions due to the concentration gradient in all directions (e.g., in the case of emission from painted surfaces). The emission rare in this case is significantly affected by the intensity of the ambient air turbulence and air velocity, dhe third type of sources is characterized by contaminant movement in the space with an air jet (e.g., linear jet over the tank with a push-pull ventilation), or particle flow (e.g., from a grinding wheel). In some cases, the above factors influencing contaminant distribution in the room are combined. 

We expect more insight from simulations in the future, particularly in situations where these multicomponent systems show effects of coupling between the different degrees of freedom, surface tensions depending on temperature and concentration, hydrodynamic flow induced by concentration gradients in addition to thermal buoyancy. 

With respect to general corrosion, once a surface film is formed the rate of corrosion is essentially determined by the ionic concentration gradient across the film. Consequently the corrosion rate tends to be independent of water flow rate across the corroding surface. However, under impingement conditions where the surface film is unable to form or is removed due to the shear stress created by the flow, the corrosion rate is theoretically velocity (10 dependent and is proportional to the power for laminar flow and... 

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