Diffusion of salts

Nernst-Haskell The theory of dilute diffusion of salts is well developed and has been experimentally verified. For dilute solutions of a single salt, the well-known Nernst-Haskell equation (Reid et al.) is applicable ... 

There is diffusion of salt away from both the solid-liquid interface and the vapor-liquid interface, in each case toward the brine. Water moves counterflow to the salt. Heat must transfer from solid to liquid to gas through stagnant films at the solid surface and through the turbulent liquid. An additional resistance to the formation of ice exists at the ice surface, where water molecules must orient themselves and find positions of low energy before being incorporated into the crystal lattice. When inadequate ice surface or foreign particles exist in the freezer, nucleation may control or affect the rate of ice production. 

At not too high concentrations of the outer solution, the amount of absorbed salt in the membrane in equilibrium is very low (y is very small). For this reason the diffusion of salt through a membrane is very small too. The membrane behaves as a barrier for salt diffusion. This is also favourable in electrodialysis, where high differences can occur in the salt concentrations of dialysate and concentrate. As the back-diffusion opposes the effect of the electrical desalting, its value must be as small as possible. 

Figure 4. Examples of process monitoring, (a) Change in effective conductivity at 200 MHz during the diffusion of salt through a soft kaolinite sediment and the hydration of a cemented paste backfill, (b) Change in the real relative permittivity at 1.3 GHz during the hydration of a cemented paste backfill (paste data from D. Simon).

The results of the concurrent EIS measurement are consistent with what were found with Prohesion test results shown in Figure 28.23. The earlier failure of the coating system due to partial delamination at the interface resulted in severe corrosion on the U-shaped scribed panels. The concurrent EIS measurement reveals the importance of the lateral diffusion of salts initiating from the damaged interface. This situation could be explained by Figure 28.26, which schematically depicts the pathways of electrolyte to the sampling site of EIS measurement. 

Second, for diffusion of salt, let the material of the dike have a conductivity factor or diflfusivity of 5 x 10 m sec. This is a value for the wet sand en masse regardless of the geometry of the tiny water pathways that permeate it. The salt content of seawater is about 3 g per 100 g or 3 kg per 100 kg a cubic meter of seawater has a mass of about 1100 kg so the salt content is about 33 kg/m if the concentration changes linearly from the salty side to the freshwater side, the change is 8.3 kg/m then the diffusion rate for salt is 4 X 10 kg/m -sec. A year is about 3 x 10 sec, so that this equals 1.2 kg or nearly 3 lb of salt crossing per square meter per year. 

Figure 3 shows the correlation function and the corresponding spectrum of relaxation times for a solution of sodium poly(styrenesulfonate) (NaPSS) in 3.7 M NaCl. Two modes can be clearly recognized. The slower mode corresponds to the diffusion of polyions, which will be discussed in the next section. The faster mode corresponds to the diffusion of salt (NaCl). As expected for a diffusive process, the inverse relaxation time of this mode Tvf (the subscript vf refers to very fast ) is q2 dependent (Figure 4). The diffusion coefficient of the salt small ions was calculated from the slope of the dependence Tvf = Dwfq2 in Figure 4 as Dvf = (1.7 0.1) X 10 5 cm2s The scattering amplitude of the very fast mode varies proportionally with the salt concentration and is q independent as expected. Figure 5 shows the correlation function and the corresponding spectrum of relaxation times for a pure solution of NaCl in water (no polymer added). Only one diffusive mode is present with the diffusion coefficient matching relatively closely the value of Dvf obtained in polyelectrolyte solution.

FIG. 4 Angular dependence of the inverse relaxation time = l/rvf of the very fast mode corresponding to the diffusion of salt (NaCl) in solution of sodium poly(styrenesulfonate) (NaPSS), = 5,400, in 3.7 M NaCl. Polymer concentration c = 1.9 g/L. 

In the research department of a food company, the diffusion of salt into meat products is studied. Large pieces are immersed in concentrated brine (salt concentration cj), and the salt uptake per unit surface area is determined as a function of brining time (t).As expected, it is proportional to t. By means of Eq. (5.19), the effective diffusion coefficient D is estimated. For lean pork a value of 2.2 10-10 m2 s-1 results, for back fat (untrimmed bacon) only 10 11 m2 s 1. As a check it is determined in a separate experiment what the salt content is at a distance of 1 cm from the outside after 5 days of brining. By using Eq. (5.21), it is expected that in the lean pork c (expressed per kg water) will equal nearly 0.5ci, whereas it... 

Permeability (see Section 5.3.1). Transport of liquid through the material can be greatly dependent on direction. The prime example is wood, which derives from vascular tissue that consists of long tubular cells (trachea), needed for transport of water. Some natural food materials also show this dependency. It finds its origin at a scale of, say, a micrometer. Anisotropy with respect to diffusion of small molecules is rarely encountered in foods. For instance, the rate of diffusion of salt into muscle tissue is not direction dependent (along or across the fibers). 

From consideration of the rate of diffusion of salt out of the fiber, as shown in Figs. 1-3, and the increase in rate accompanying an increase in... 

A phenomenon that can reduce the water flux through the membrane in RO is concentration polarization. The flux of water to the membrane carries with it salt by bulk flow. However, because the salt cannot readily penetrate the membrane, its concentration in the liquid adjacent to the membrane surface, csi, is higher than in the bulk of the feed, csF. This difference causes diffusion of salt from the membrane sur-... 

Consider steady-state transport of water with back-diffusion of salt. A salt balance at the upstream membrane surface gives... 

Fick s equation for the diffusion of salts in solutioh must be modified to allow for the decreasing diffusivity of the salt with increasing concentration and finally, van der Waals, Clausius, Rankine, Sarrau, etc., have attempted to correct the simple gas equation pv = BT, by making certain assumptions as to the internal structure of the gas. 

Dg is the diffusivity of salt through the membrane Kg is the partition coefficient of salt between the solution and the membrane... 

Albumin did not reduce the diffusion of salts. Diffusion in a jelly was nearly as fast as in water this was generally confirmed, but later workers (Reveil, 1868 Stefan, 1878, etc.) found that diffusion in jellies, especially with concentrated solutions, is somewhat slower. The theory of diffusion was first given by A. E. Fick, a physiologist. ... 

Diffusion of solutes in liquids is very important in many industrial processes, especially in such separation operations as liquid-liquid extraction or solvent extraction, gas absorption, and distillation. Diffusion in liquids also occurs in many situations in nature, such as oxygenation of rivers and lakes by the air and diffusion of salts in blood. 

For the situation where the voids are filled completely with liquid water, the concentration of salt in water at boundary 1 is c, and at point 2 isc j- The salt in diffusing through the water in the void volume takes a tortuous path which is unknown and greater than (zj — z,) by a factor t, called tortuosity. Diffusion does not occur in the inert solid. For a dilute solution using Eq. (6.3-5) for diffusion of salt in water at steady state,... 

When electrolytes are added to a solvent, they dissociate to a certain degree. It would appear that the solution contains at least three components solvent, anions, and cations. If the solution is to remain neutral in charge at each point, assuming the absence of any applied electric potential field, the anions and cations diffuse effectively as a single component, as with molecular diffusion. The diffusion of the anionic and cationic species in the solvent can thus be treated as a binary mixture. The theory of dilute diffusion of salts is well developed and has been experimentally verified. For dilute solutions of a single salt, the Nernst-Haskell equation is applicable ... 

If the water is containing salts, these sedts cannot be carried by the vapour and therefore build up at this position. This concentration effect causes back-diffusion of salt away from the wet-dry interface. If the salts concentration near the wet-dry interface ever exceeds the solubility of the salt compounds present, precipitation is likely to occur Pi-34]. The absorption-diffusion relationship can be described by the definition of the Peclet number... 

A large slab of salt is placed at the bottom of a tank containing water. The salt solid density is 2165 kg/m. The density of the solution at the surface is 380 kg/m. Diffusivity of salt water is 1.2 x 10 m /sec. Find the density distribution in the water and the rate of salt surface dissolution... 

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