Diffusion concentration gradient

In the interruption test (Kressman and Kitchener, 1949), the ion exchanger is temporarily separated from the liquid. If the rate is controlled by mass transfer in the liquid, the rate upon reimmersion is the same as at the time of separation, the quasi-stationary state in the film is very quickly re-established. If the rate is controlled by intraparticle diffusion, concentration gradients within the particle have time to relax, and the rate is faster upon reimmersion. This comparison is independent of specific mechanisms and algebraic forms of rate laws. 

Infinite dilution diffusivity Concentration gradient Shear rate... 

Diffusion dialysis Composite Nonporous Diffusion Concentration gradient... 

The existence of a microdomain interphase due to the diffuse concentration gradient across the boundary has been predicted by statistical thermodynamic theories based on the mean-field approach. The results of several experimental works (e.g., the systematic deviation of SAXS intensity profiles from the behavior of sharp-boundary systems described by Porod s law and the modeling of rheological behavior measured by DMA ) support the view of a segmentally mixed diffuse interphase. However, various other models, such as a coarse interface with a sharp boundary, may also account for some of the observed results from SAXS data. The ambiguity... 

Diffusivity measures the tendency for a concentration gradient to dissipate to form a molar flux. The proportionality constant between the flux and the potential is called the diffusivity and is expressed in m /s. If a binary mixture of components A and B is considered, the molar flux of component A with respect to a reference plane through which the exchange is equimolar, is expressed as a function of the diffusivity and of the concentration gradient with respect to aji axis Ox perpendicular to the reference plane by the fpllqvving relatipn 6 /... 

The coefficients, L., are characteristic of the phenomenon of thermal diffusion, i.e. the flow of matter caused by a temperature gradient. In liquids, this is called the Soret effect [12]. A reciprocal effect associated with the coefficient L. is called the Dufour effect [12] and describes heat flow caused by concentration gradients. The... 

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 ... 

Most of our ideas about carrier transport in semiconductors are based on tire assumption of diffusive motion. Wlren tire electron concentration in a semiconductor is not unifonn, tire electrons move diffuse) under tire influence of concentration gradients, giving rise to an additional contribution to tire current. In tliis motion, electrons also undergo collisions and tlieir temporal and spatial distributions are described by the diffusion equation. The... 

Though a porous medium may be described adequately under non-reactive conditions by a smooth field type of diffusion model, such as one of the Feng and Stewart models, it does not necessarily follow that this will still be the case when a chemical reaction is catalysed at the solid surface. In these circumstances the smooth field assumption may not lead to appropriate expressions for concentration gradients, particularly in the smaller pores. Though the reason for this is quite simple, it appears to have been largely overlooked,... 

It arises solely because we continue Co describe micropore diffusion in terms of smooch macropore concentration fields and their gradients, even under reactive conditions where these no longer adequately describe Che actual concentration gradients in the micropores. 

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

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

When a sample is injected into the carrier stream it has the rectangular flow profile (of width w) shown in Figure 13.17a. As the sample is carried through the mixing and reaction zone, the width of the flow profile increases as the sample disperses into the carrier stream. Dispersion results from two processes convection due to the flow of the carrier stream and diffusion due to a concentration gradient between the sample and the carrier stream. Convection of the sample occurs by laminar flow, in which the linear velocity of the sample at the tube s walls is zero, while the sample at the center of the tube moves with a linear velocity twice that of the carrier stream. The result is the parabolic flow profile shown in Figure 13.7b. Convection is the primary means of dispersion in the first 100 ms following the sample s injection. 

This shows that Schlieren optics provide a means for directly monitoring concentration gradients. The value of the diffusion coefficient which is consistent with the variation of dn/dx with x and t can be determined from the normal distribution function. Methods that avoid the difficulty associated with locating the inflection point have been developed, and it can be shown that the area under a Schlieren peak divided by its maximum height equals (47rDt). Since there are no unknown proportionality factors in this expression, D can be determined from Schlieren spectra measured at known times. 

If a sedimentation experiment is carried out long enough, a state of equilibrium is eventually reached between sedimentation and diffusion. Under these conditions material will pass through a cross section perpendicular to the radius in both directions at equal rates downward owing to the centrifugal field, and upward owing to the concentration gradient. It is easy to write expressions for the two fluxes which describe this situation ... 

Calcium is absorbed from the intestine by facilitated diffusion and active transport. In the former, Ca " moves from the mucosal to the serosal compartments along a concentration gradient. The active transport system requires a cation pump. In both processes, a calcium-binding protein (CaBP) is thought to be required for the transport. Synthesis of CaBP is activated by 1,25-DHCC. In the active transport, release of Ca " from the mucosal cell into... 

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