Concentration polarization geometry

These relations can be used as rough estimates of steric rejection, if the solute and membrane pore dimensions are known. The derivation is based on a strictly model situation (see Figure 1) and a long list of necessary assumptions can be written. Apart from the simplified geometry (hard sphere in a cylindrical pore), it was also assumed that the solute travels at the same velocity as the surrounding liquid, that the solute concentration in the accessible parts of the pore is uniform and equal to the concentration in the feed, that the flow pattern is laminar, the liquid is Newtonian, diffusional contribution to solute transport is negligible (pore Peclet number is sufficiently high), concentration polarization and membrane-solute interactions are absent, etc. 

As a consequence of the passage of solvent, say water, through the membrane, solute is carried to the membrane surface, and the concentration at the membrane surface tends to be higher than in the bulk of the liquid. This phenomenon is called concentration polarization. Several deleterious effects arise from concentration polarization, one of which is the local increase in osmotic pressure due to the increased solute concentration at the membrane. The result is that the solvent flux is decreased because the effective driving pressure is reduced. Another effect is an increase in the solute concentration in the product, for with real leaky membranes the flux of solute across the membrane is proportional to the difference in solute concentration on both sides. The extent of concentration polarization depends on the hydrodynamics and geometry of the system, with increased flow speed of the solution past the membrane tending to reduce the effect. 

The degree of concentration polarization depends on the hydrodynamics of the flow before the membrane and on the geometry of the membrane surface. Therefore, if we want to reduce negative consequences of concentration polarization, we should be looking at possible ways to change the flow hydrodynamics or the surface geometry. Thus, an increase of flow velocity along the membrane surface, in particular, turbulization of the flow, promotes transfer of dissolved substance from the wall and weakens the effect of polarization. 

For effective ultrafiltration, equipment must be optimized to promote the highest transmembrane flow and selectivity. A major problem which must be overcome is concentration polarization, the accumulation of a gradient of retained macrosolute above the membrane. The extent of polarization is determined by the macrosolute concentration and diffusivity, temperature effects on solution viscosity and system geometry. If left undisturbed, concentration polarization restricts solvent and solute transport through the membrane and can even alter membrane selectivity by forming a gel layer on the membrane surface—in effect, a secondary membrane — increasing rejection of normally permeating species. 

Within its working window, an electrode can be depolarized by electroactive substances which are dissolved in the electrolyte. The electrochemical reaction on the electrode surface causes concentration gradients perpendicular to the electrode surface. The current is proportional to these concentration gradients. This relationship depends on the electrode geometry, on the hydrodynamic conditions in the solution (whether it is stirred, or not) and on the voltammetric technique. However, in all cases, the current reaches a maximum, or a limiting value, which is proportional to the bulk concentration of the reactant. This is called the concentration polarization of the working electrode. It is the basis of all analytical applications of voltammetry. 

Activation and concentration polarization data presented are generally only valid for that particular cell and operating geometry. 

Geometry. The geometry of fluid flow and the design of the cell (horizontal or vertical) affects concentration polarization. 

In filtration processes for the extracorporeal treatment of renal failure, partially rejeeted proteins accumulate at the membrane separation layer [i.e., concentration polarization (CP) phenomena occur] to an extent that depends on protein eoncentralion in the bulk blood, and the fluid dynamics of the blood compartment. Higher protein concentrations at the membrane surface cause the membrane sieving coefficient to be higher than that expeeted, based on the intrinsic membrane separation properties. However, once the latter are known, the actual sieving coefficient can be estimated from the operating conditions and module geometry as follows (Klein et al., 1978) ... 

In addition to optimization of module design, which aims at improving flow geometry, and suppressing temperature and concentration polarization phenomaia, the properties of the membrane material and membrane morphology are cracial for the process performance. Membranes for MD should have the following characteristics [135-137] ... 

Adsorption Kinetics. In zeoHte adsorption processes the adsorbates migrate into the zeoHte crystals. First, transport must occur between crystals contained in a compact or peUet, and second, diffusion must occur within the crystals. Diffusion coefficients are measured by various methods, including the measurement of adsorption rates and the deterniination of jump times as derived from nmr results. Factors affecting kinetics and diffusion include channel geometry and dimensions molecular size, shape, and polarity zeoHte cation distribution and charge temperature adsorbate concentration impurity molecules and crystal-surface defects. 

Cell geometry, such as tab/terminal positioning and battery configuration, strongly influence primary current distribution. The monopolar constmction is most common. Several electrodes of the same polarity may be connected in parallel to increase capacity. The current production concentrates near the tab connections unless special care is exercised in designing the current collector. Bipolar constmction, wherein the terminal or collector of one cell serves as the anode and cathode of the next cell in pile formation, leads to gready improved uniformity of current distribution. Several representations are available to calculate the current distribution across the geometric electrode surface (46—50). 

Any fundamental study of the rheology of concentrated suspensions necessitates the use of simple systems of well-defined geometry and where the surface characteristics of the particles are well established. For that purpose well-characterized polymer particles of narrow size distribution are used in aqueous or non-aqueous systems. For interpretation of the rheological results, the inter-particle pair-potential must be well-defined and theories must be available for its calculation. The simplest system to consider is that where the pair potential may be represented by a hard sphere model. This, for example, is the case for polystyrene latex dispersions in organic solvents such as benzyl alcohol or cresol, whereby electrostatic interactions are well screened (1). Concentrated dispersions in non-polar media in which the particles are stabilized by a "built-in" stabilizer layer, may also be used, since the pair-potential can be represented by a hard-sphere interaction, where the hard sphere radius is given by the particles radius plus the adsorbed layer thickness. Systems of this type have been recently studied by Croucher and coworkers. (10,11) and Strivens (12). 

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