Transverse diffusion

Certain microbes synthesize small organic molecules, ionophores, that function as shuttles for the movement of ions across membranes. These ionophores contain hy-drophihc centers that bind specific ions and are surrounded by peripheral hydrophobic regions this arrangement allows the molecules to dissolve effectively in the membrane and diffuse transversely therein. Others, Hke the well-smdied polypeptide gramicidin, form channels. 

The lack of hydrodynamic definition was recognized by Eucken (E7), who considered convective diffusion transverse to a parallel flow, and obtained an expression analogous to the Leveque equation of heat transfer (L5b, B4c, p. 404). Experiments with Couette flow between a rotating inner cylinder and a stationary outer cylinder did not confirm his predictions (see also Section VI,D). At very low rotation rates laminar flow is stable, and does not contribute to the diffusion process since there is no velocity component in the radial direction. At higher rotation rates, secondary flow patterns form (Taylor vortices), and finally the flow becomes turbulent. Neither of the two flow regimes satisfies the conditions of the Leveque equation. 

Figure 9.8 Isolated-boundary (Type-B) self-diffusion associated with a stationary grain boundary, (a) Grain boundary of width 6 extending downward from the free surface at y = 0. The surface feeds tracer atoms into the grain boundary and maintains the diffusant concentration at the grain boundary s intersection with the surface at the value cB(y = 0, t) = 1. Diffusant penetrates the boundary along y and simultaneously diffuses transversely into the grain interiors along x. (b) Diffusant distribution as a function of scaled transverse distance, xi, from the boundary at scaled depth, yx, from the surface. Penetration distance in grains is assumed large relative to 5.

Self-diffusion along the boundary in Exercise 9.6 is highly anisotropic because diffusion along the tilt axis (parallel to the dislocations) is much greater than diffusion transverse to it (i.e., perpendicular to the dislocations but still in the boundary plane). Find an expression for the anisotropy factor,... 

Now, it is possible to calculate the marker velocity, vK. The accumulation rate of mass provoked by the net diffusion, transversely to the marker plane, may be related to the marker speed as follows ... 

Very high dosages of PAN will produce bifacial necrosis. A diffuse, transverse band across the leaf blade first appears water-soaked, then dries to produce a white to tan-colored necrotic band. Injury usually develops at the tip of week-old leaves at the base of the third or fourth older leaf and as a diffuse band across intermediate-aged leaves. The tip and base of the intermediate-aged leaf will remain free of injury. 

Eddy diffusion, which relates to a variety of flow states, should always be considered in conjunction with transverse diffusion. Transverse diffusion takes place in a radial direction, in other words, in the cross-sectional plane of the column. The flow threads, which play the major role in eddy diffusion, are interlinked by transverse diffusion. Let us consider an extreme case, in which sample molecules enter a stationary flow thread, a "dead end", i.e. cease to flow. These molecules would have to remain permanently in the column if they were not able to jump into a "moving" flow thread by a lateral diffusion step. On the other hand, a molecule which is about to diffuse to a point in the column packing which does not favour transport may be prevented from so doing by being carried further on by the flow. To some extent, then, transverse diffusion and eddy diffusion cancel each other out. 

A cell membrane is illustrated in Fig. 6.1. It is built from a bilayer of lipids, usually phospholipids, associated with which are membrane proteins and polysaccharides. The antiparallel orientation of lipid layers in the bilayer is maintained due to the extremely slow flip-flop rate, i.e. the rate of diffusion transverse to the bilayer. The lipid bilayer is the structural foundation and the proteins and polysaccharides provide chemical functionality. The protein to lipid ratio shows a large variation depending on the cell, but proteins make up at least half of most cell membranes. A prominent exception is mammalian nerve cells which contain only 18 % protein (here also the lipids are sphingomyelins rather than phospholipids). Here, the primary requirement is that the cell membrane should be effective as an electrical... 

If the diffusion coefficient of species A is less tlian tliat of B (D < D ) tlie propagating front will be planar. However, if is sufficiently greater than tire planar front will become unstable to transverse perturbations and chaotic front motion will ensue. To understand tire origin of tire mechanism of tire planar front destabilization consider tire following suppose tire interface is slightly non-planar. We would like to know if tire dynamics will tend to eliminate this non-planarity or accentuate it. LetZ)g The situation is depicted schematically in figure... 

Because both spins are in the transverse plane and transition energy levels are matched, energy can be transferred from the protons to the nuclei. In this manner the rate of repolarization is controlled by rather than by Because the protons can interchange energy by spin-diffusion only a single-proton exists and its value is usually on the order of 1 s. As a result the preparation delay can be reduced from 10 s to about 5 s increasing the number of transients, which can be acquired by two or more orders of magnitude. 

The resulting overall energy balance for the plant at nominal load conditions is shown in Table 3. The primary combustor operates at 760 kPa (7.5 atm) pressure the equivalence ratio is 0.9 the heat loss is about 3.5%. The channel operates in the subsonic mode, in a peak magnetic field of 6 T. AH critical electrical and gas dynamic operating parameters of the channel are within prescribed constraints the magnetic field and electrical loading are tailored to limit the maximum axial electrical field to 2 kV/m, the transverse current density to 0.9 A/cm , and the Hall parameter to 4. The diffuser pressure recovery factor is 0.6. 

The Gaussian Plume Model is the most well-known and simplest scheme to estimate atmospheric dispersion. This is a mathematical model which has been formulated on the assumption that horizontal advection is balanced by vertical and transverse turbulent diffusion and terms arising from creation of depletion of species i by various internal sources or sinks. In the wind-oriented coordinate system, the conservation of species mass equation takes the following form ... 

Lipids also undergo rapid lateral motion in membranes. A typical phospholipid can diffuse laterally in a membrane at a linear rate of several microns per second. At that rate, a phospholipid could travel from one end of a bacterial ceil to the other in less than a second or traverse a typical animal ceil in a few minutes. On the other hand, transverse movement of lipids (or proteins) from one face of the bilayer to the other is much slower (and much less likely). For example, it can take as long as several days for half the phospholipids in a bilayer vesicle to flip from one side of the bilayer to the other. 

W. R. Lieb and W. D. Stem, Non-stochesian nature of the transverse diffusion within hmnan red cell membranes. J. Membr. Biol. 1986, 92, 111-110. 

Diffusivities. Our results for the dlffuslvltles of both systems are summarized In Table I. The pore average transverse dlffuslvlty for the bulk fluid at equilibrium agrees very well with experimental and simulation values for the dlffuslvlty of Argon at the same density and temperature (18.12.5). 

As explained In Section 1 three dlffuslvltles were calculated for each system. These were the equilibrium transverse dlffuslvlty and the two nonequilibrium (flow) dlffuslvltles parallel and normal to the direction of flow. As we can see from Table I, they all agree with each other within the limits of statistical uncertainty. We conclude, therefore, that the flow has no effect on the diffusivity even at such high shear rates as the ones employed in our simulation. At even higher shear rates a significant dependence of the dlffuslvlty on the shear rate has been reported (Ifl.) but one should consider that our shear rate Is already orders of magnitude higher than the ones encountered In realistic flow situations. 

In these equations x and y denote independent spatial coordinates T, the temperature Tib, the mass fraction of the species p, the pressure u and v the tangential and the transverse components of the velocity, respectively p, the mass density Wk, the molecular weight of the species W, the mean molecular weight of the mixture R, the universal gas constant A, the thermal conductivity of the mixture Cp, the constant pressure heat capacity of the mixture Cp, the constant pressure heat capacity of the species Wk, the molar rate of production of the k species per unit volume hk, the speciflc enthalpy of the species p the viscosity of the mixture and the diffusion velocity of the A species in the y direction. The free stream tangential and transverse velocities at the edge of the boundaiy layer are given by = ax and Vg = —ay, respectively, where a is the strain rate. The strain rate is a measure of the stretch in the flame due to the imposed flow. The form of the chemical production rates and the diffusion velocities can be found in (7-8). 

As described earlier, the inside-outside asymmetry of membrane proteins is stable, and mobifity of proteins across (rather than in) the membrane is rare therefore, transverse mobility of specific carrier proteins is not likely to account for facilitated diffusion processes except in a few unusual cases. 

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