Back-diffusion, phenomenon

The concentration polarization model, which is based on the stagnant fihn theory, was developed to describe the back-diffusion phenomenon during filtration of macromolecules. In this model, the rejection of particles gives rise to a thin fouling layer on the membrane surface, overlaid by a concentration polarization layer in which particles diffuse away from the membrane surface, where solute concentration is high, to the bulk phase, where the solute concentration is low [158]. At steady state, convection of particles toward the membrane surface is balanced by diffusion away from the membrane. Thus, integrating the onedimensional convective-diffusion equation across the concentration polarization layer gives... 

Residual current in polarography. In the pragmatic treatment of the theory of electrolysis (Section 3.1) we have explained the occurrence of a residual current on the basis of back-diffusion of the electrolysis product obtained. In conventional polarography the wave shows clearly the phenomenon of a residual current by a slow rise of the curve before the decomposition potential as well as beyond the potential where the limiting current has been reached. In order to establish the value one generally corrects the total current measured for the current of the blank solution in the manner illustrated in Fig. 3.16 (vertical distance between the two parallel lines CD and AB). However, this is an unreliable procedure especially in polarography because, apart from the troublesome saw-tooth character of the i versus E curve, the residual current exists not only with a faradaic part, which is caused by reduction (or oxidation)... 

IL3.3.I Using the Scheil solidification model Although it is realised that some back-diffusion will occur, results on the calculation of solidification using the Scheil simulation have proved to be successful in a number of cases. For Al-alloys it appears to be particularly successful, allowing not only very accurate predictions for fiaction solid transformed (/,) as a function of temperature but also for predicting the phases which appear during solidification, which in Al-alloys, is a complex phenomenon. 

Sample introduction is a major hardware problem for SFC. The sample solvent composition and the injection pressure and temperature can all affect sample introduction. The high solute diffusion and lower viscosity which favor supercritical fluids over liquid mobile phases can cause problems in injection. Back-diffusion can occur, causing broad solvent peaks and poor solute peak shape. There can also be a complex phase behavior as well as a solubility phenomenon taking place due to the fact that one may have combinations of supercritical fluid (neat or mixed with sample solvent), a subcritical liquified gas, sample solvents, and solute present simultaneously in the injector and column head [2]. All of these can contribute individually to reproducibility problems in SFC. Both dynamic and timed split modes are used for sample introduction in capillary SFC. Dynamic split injectors have a microvalve and splitter assembly. The amount of injection is based on the size of a fused silica restrictor. In the timed split mode, the SFC column is directly connected to the injection valve. Highspeed pneumatics and electronics are used along with a standard injection valve and actuator. Rapid actuation of the valve from the load to the inject position and back occurs in milliseconds. In this mode, one can program the time of injection on a computer and thus control the amount of injection. In packed-column SFC, an injector similar to HPLC is used and whole loop is injected on the column. The valve is switched either manually or automatically through a remote injector port. The injection is done under pressure. 

Back diffusion due to a non-zero value of the pressure at the permeate side is a very general phenomenon to decrease the value of a. The permeant gases at the permeate side of the membrane are removed by pumping or by a sweep gas. In the last case the total pressure is usually relatively large, but the partial pressure of the permeant is low. Using a sweep gas makes the mixture effectively a ternary system and ignoring the effect of the sweep gas (as is frequently done) is not always allowable as will be discussed in Sections 9.4 and 9.5. 

Concentration polarization Convective transport and retention of solutes by the membrane results in an accumulation of species at wall. Local concentrations, C , are higher than in the bulk, Cb, and a back-diffusion from near the wall into the bulk liquid phase takes place. This is the so-called "concentration polarization" phenomenon (Fig. 12.1). A simple mass balance leads to the classical equation ... 

The analysis procedure developed in the previous section for gas permeation forms the basis for analyzing RO. However, the RO analysis is more complicated because of 1) osmotic pressure, which is included in Eq. fl7-12T and 2) mass transfer rates are much lower in liquid systems. Since the mass transfer rates are relatively low, the wt frac of solute at the membrane wall x will be greater than the wt frac of solute in the bulk of the retentate x, . This buildup of solute at the membrane surface occurs because the movement of solvent through the membrane carries solute with it to the membrane wall. Since the solute does not pass through the semipermeable membrane, its concentration will build up at the wall and it must back diffuse from the wall to the bulk solution. This phenomenon, concentration polarization, is illustrated in Figure 17-10. Concentration polarization has a major effect on the separations obtained in RO and UF (see next section). Since concentration polarization causes x > Xp the osmotic pressure becomes higher on the retentate side and, following Eq. fl7-12). the flux declines. Concentration polarization will also increase Ax in Eq. tl7-13 and flux of solute may increase, which is also undesirable. In addition, since concentration polarization increases solute concentration, precipitation becomes more likely. 

Answer by author No attempt was made to determine the influence of the transient term in the differential equation. The basic differential equation governing the phenomenon studied by Schneider was of the form used in the present study, so the solutions are certainly analogous. Schneider was interested in a range of Peclet numbers somewhat higher than those which are shown in the present paper, but certainly the results demonstrate parallel trends with regard to the axial conduction of heat, or the back-diffusion of contaminants. 

If the surfaces are very smooth, for instance surfaces of high-polished metals, glass, crystals, and also liquids, the incident beam is not thrown back diffusely but is reflected in one direction of the same angle and in the same plane. Such a phenomenon is known as regular reflection, directed reflection, or specular reflection. The angle of the incident beam is - in relation to a perpendicular line - the same as that of the reflected beam, that is, = a,. (Fig. 4-50). 

A phenomenon that is particularly important in the design of reverse osmosis units is that of concentration polarization. This occurs on the feed-side (concentrated side) of the reverse osmosis membrane. Because the solute cannot permeate through the membrane, the concentration of the solute in the liquid adjacent to the surface of the membrane is greater than that in the bulk of the fluid. This difference causes mass transfer of solute by diffusion from the membrane surface back to the bulk liquid. The rate of diffusion back into the bulk fluid depends on the mass transfer coefficient for the boundary layer on feed-side. Concentration polarization is the ratio of the solute concentration at the membrane surface to the solute concentration in the bulk stream. Concentration polarization causes the flux of solvent to decrease since the osmotic pressure increases as the boundary layer concentration increases and the overall driving force (AP - An) decreases. 

As described above, the initial cause of membrane fouling is concentration polarization, which results in deposition of a layer of material on the membrane surface. The phenomenon of concentration polarization is described in detail in Chapter 4. In ultrafiltration, solvent and macromolecular or colloidal solutes are carried towards the membrane surface by the solution permeating the membrane. Solvent molecules permeate the membrane, but the larger solutes accumulate at the membrane surface. Because of their size, the rate at which the rejected solute molecules can diffuse from the membrane surface back to the bulk solution is relatively low. Thus their concentration at the membrane surface is typically 20-50 times higher than the feed solution concentration. These solutes become so concentrated at the membrane surface that a gel layer is formed and becomes a secondary barrier to flow through the membrane. The formation of this gel layer on the membrane surface is illustrated in Figure 6.6. The gel layer model was developed at the Amicon Corporation in the 1960s [8],... 

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