Diffusion effective diffusivity

All the aforementioned phenomena, which contribute jointly to spot broadening, are used to be described as the effective diffusion. Effective diffusion is a convenient notion, which, apart from being concise and informative, emphasizes that all the contributory phenomena occur simultaneously. 

Since the blocked gas inside of the capillary is dissolving in the liquid and then diffusing towards the exit of the channel, the meniscus of the liquid crosses the position l and goes deeper. This second stage of capillary filling with liquid is called diffusive imbibition and plays an important role in PT processes. The effect of diffusive imbibition upon PT sensitivity has been studied in [7]. 

Perez Quintian, M.A.Rebollo, N.G. Gaggioli y C.A. Raffo, The non refractive effect in translucent diffusers A geometrical model . Aprobado para su publicacion en Journal of Modem Opties. 

It was determined, for example, that the surface tension of water relaxes to its equilibrium value with a relaxation time of 0.6 msec [104]. The oscillating jet method has been useful in studying the surface tension of surfactant solutions. Figure 11-21 illustrates the usual observation that at small times the jet appears to have the surface tension of pure water. The slowness in attaining the equilibrium value may partly be due to the times required for surfactant to diffuse to the surface and partly due to chemical rate processes at the interface. See Ref. 105 for similar studies with heptanoic acid and Ref. 106 for some anomalous effects. 

The quantity 1 /k is thus the distance at which the potential has reached the 1 je fraction of its value at the surface and coincides with the center of action of the space charge. The plane at a = l//c is therefore taken as the effective thickness of the diffuse double layer. As an example, 1/x = 30 A in the case of 0.01 M uni-univalent electrolyte at 25°C. 

The effect known either as electroosmosis or electroendosmosis is a complement to that of electrophoresis. In the latter case, when a field F is applied, the surface or particle is mobile and moves relative to the solvent, which is fixed (in laboratory coordinates). If, however, the surface is fixed, it is the mobile diffuse layer that moves under an applied field, carrying solution with it. If one has a tube of radius r whose walls possess a certain potential and charge density, then Eqs. V-35 and V-36 again apply, with v now being the velocity of the diffuse layer. For water at 25°C, a field of about 1500 V/cm is needed to produce a velocity of 1 cm/sec if f is 100 mV (see Problem V-14). 

It is necessary that the mercury or other metallic surface be polarized, that is, that there be essentially no current flow across the interface. In this way no chemical changes occur, and the electrocapillary effect is entirely associated with potential changes at the interface and corresponding changes in the adsorbed layer and diffuse layer. 

Surface active electrolytes produce charged micelles whose effective charge can be measured by electrophoretic mobility [117,156]. The net charge is lower than the degree of aggregation, however, since some of the counterions remain associated with the micelle, presumably as part of a Stem layer (see Section V-3) [157]. Combination of self-diffusion with electrophoretic mobility measurements indicates that a typical micelle of a univalent surfactant contains about 1(X) monomer units and carries a net charge of 50-70. Additional colloidal characterization techniques are applicable to micelles such as ultrafiltration [158]. 

The repulsion between oil droplets will be more effective in preventing flocculation Ae greater the thickness of the diffuse layer and the greater the value of 0. the surface potential. These two quantities depend oppositely on the electrolyte concentration, however. The total surface potential should increase with electrolyte concentration, since the absolute excess of anions over cations in the oil phase should increase. On the other hand, the half-thickness of the double layer decreases with increasing electrolyte concentration. The plot of emulsion stability versus electrolyte concentration may thus go through a maximum. 

The rate of dissolving of a solid is determined by the rate of diffusion through a boundary layer of solution. Derive the equation for the net rate of dissolving. Take Co to be the saturation concentration and rf to be the effective thickness of the diffusion layer denote diffusion coefficient by . 

Bonig L, Liu S and Metiu FI 1996 An effective medium theory study of Au islands on the Au(IOO) surface reconstruction, adatom diffusion, and island formation Surf. Sot 365 87... 

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... 

Figure A3.6.13. Density dependence of die photolytic cage effect of iodine in compressed liquid n-pentane (circles), n-hexane (triangles), and n-heptane (squares) [38], The solid curves represent calculations using the diffusion model [37], the dotted and dashed curves are from static caging models using Camahan-Starling packing fractions and calculated radial distribution fiinctions, respectively [38],...

If a fluid is placed between two concentric cylinders, and the inner cylinder rotated, a complex fluid dynamical motion known as Taylor-Couette flow is established. Mass transport is then by exchange between eddy vortices which can, under some conditions, be imagmed as a substantially enlranced diflfiisivity (typically with effective diflfiision coefficients several orders of magnitude above molecular difhision coefficients) that can be altered by varying the rotation rate, and with all species having the same diffusivity. Studies of the BZ and CIMA/CDIMA systems in such a Couette reactor [45] have revealed bifiircation tlirough a complex sequence of front patterns, see figure A3.14.16. 

Hwang L-P and Freed J H 1975 Dynamic effects of pair correlation functions on spin relaxation by translational diffusion in liquids J. Chem. Rhys. 63 4017-25... 

Carr H Y and Purcell E M 1954 Effects of diffusion on free precession in nuclear magnetic resonance experiments Rhys. Rev. 94 630-8... 

Ahn C B and Cho Z H 1989 A generalized formulation of diffusion effects in pm resolution nuclear magnetic-resonance imaging Med. Rhys. 16 22-8... 

Broadening of spots can result from themial diffuse scattering and island fomiation, among other causes. The themial effects arise from the disorder in atomic positions as they vibrate around their equilibrium sites the sites themselves may be perfectly crystalline. 

In most practical cases (and at moderate voltages) the high-field growth law can control film growth, say up to only a maximum of 10 nm, as at this thickness the field strength effects become even less important than film growth due to diffusion of vacancies or ions. 

Caldin E F, de Forest L and Queen A 1990 Steric and repeated collision effects in diffusion-controlled reactions in solution J. Chem. See. Faraday Trans. 86 1549-54... 

C3.6.13 where large diffusion fluxes are indicated by —> and smaller diffusion fluxes by —+. For tire part of tire B front tliat protmdes into tire A region, fast diffusion of B leads to dispersal of B and suppresses tire autocatalytic reaction tliat requires two molecules of B. The front will have difficulty advancing here. In tire region where A protmdes into B, A will react leading to advancement of tire front. The net effect is to remove any initial nonplanarity and give rise to a planar front. 

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