Water solute diffusion

As outlined earlier, hemodialysis and hemofiltration require the removal of solutes smaller than albumin from blood. Solute mass transfer rates across hemodialysis membranes cannot exceed the diffusivity of the solute In water. Solute diffusivity decreases with Increasing molecular diameter (Stokes-Einstein relationship) consequently, solute mass transfer rates for hemodlalyzers intrinsically decrease with increasing molecular size. In addition to limitations Imposed by diffusion In solution, mass transfer is further limited by diffusion resistance in the membrane as well as boundary layer effects resulting from laminar flow both of these effects are also functions of molecular size. The quantitation of mass transfer In hemodlalyzers has been reviewed extensively (22). 

In membranes with pore sizes of >2nm, the separation is based on size exclusion, and thus, these membranes are suited for separation of components with sufficient size difference, for example, in dialysis, waste water treatment, and functional clothing. " For separation of components with comparable sizes or the separation of ions from water, solution-diffusion membranes are used. ... 

At very low concentrations of water, or in foods held below the free2ing point of water, physical conditions may be such that the available water may not be free to react. Under these conditions, the water may be physically immobi1i2ed as a glassy or plastic material or it may be bound to proteins (qv) and carbohydrates (qv). The water may diffuse with difficulty and thus may inhibit the diffusion of solutes. Changes in the stmcture of carbohydrates and proteins from amorphous to crystalline forms, or the reverse, that result from water migration or diffusion, may take place only very slowly. 

Hydrothermal crystallisation processes occur widely in nature and are responsible for the formation of many crystalline minerals. The most widely used commercial appHcation of hydrothermal crystallization is for the production of synthetic quartz (see Silica, synthetic quartz crystals). Piezoelectric quartz crystals weighing up to several pounds can be produced for use in electronic equipment. Hydrothermal crystallization takes place in near- or supercritical water solutions (see Supercritical fluids). Near and above the critical point of water, the viscosity (300-1400 mPa s(=cP) at 374°C) decreases significantly, allowing for relatively rapid diffusion and growth processes to occur. 

Solution—Diffusion Model. In the solution—diffusion model, it is assumed that (/) the RO membrane has a homogeneous, nonporous surface layer (2) both the solute and solvent dissolve in this layer and then each diffuses across it (J) solute and solvent diffusion is uncoupled and each is the result of the particular material s chemical potential gradient across the membrane and (4) the gradients are the result of concentration and pressure differences across the membrane (26,30). The driving force for water transport is primarily a result of the net transmembrane pressure difference and can be represented by equation 5 ... 

Equation 7 shows that as AP — oo, P — 1. The principal advantage of the solution—diffusion (SD) model is that only two parameters are needed to characterize the membrane system. As a result, this model has been widely appHed to both inorganic salt and organic solute systems. However, it has been indicated (26) that the SD model is limited to membranes having low water content. Also, for many RO membranes and solutes, particularly organics, the SD model does not adequately describe water or solute flux (27). Possible causes for these deviations include imperfections in the membrane barrier layer, pore flow (convection effects), and solute—solvent—membrane interactions. 

Example 8 Estimation of Rate Coejficient Estimate the rate coefficient for flow of a 0.01-M water solution of NaCl through a bed of cation exchange particles in hydrogen form with e = 0.4. The superficial velocity is 0.2 cm/s and the temperature is 25 C. The particles are 600 im in diameter, and the diffusion coefficient of sodium ion is 1.2 X 10 cmVs in solution and 9.4 X 10 cmVs inside the particles (of. Table 16-8). The bulk density is 0.7 g dry resin/cnd of bed, and the capacity of the resin is 4.9 mequiv/g dry resin. The mass action eqiiihbrium constant is 1.5. 

Here / is the number of ink molecules diffusing down the concentration gradient per second per unit area it is called the flux of molecules (Fig. 18.3). The quantity c is the concentration of ink molecules in the water, defined as the number of ink molecules per unit volume of the ink-water solution and D is the diffusion coefficient for ink in water - it has units of m s . ... 

Complete and Incomplete Ionic Dissociation. Brownian Motion in Liquids. The Mechanism of Electrical Conduction. Electrolytic Conduction. The Structure of Ice and Water. The Mutual Potential Energy of Dipoles. Substitutional and Interstitial Solutions. Diffusion in Liquids. 

When a polymer film is exposed to a gas or vapour at one side and to vacuum or low pressure at the other, the mechanism generally accepted for the penetrant transport is an activated solution-diffusion model. The gas dissolved in the film surface diffuses through the film by a series of activated steps and evaporates at the lower pressure side. It is clear that both solubility and diffusivity are involved and that the polymer molecular and morphological features will affect the penetrant transport behaviour. Some of the chemical and morphological modification that have been observed for some epoxy-water systems to induce changes of the solubility and diffusivity will be briefly reviewed. 

Hadden, DA, Master of Science Thesis, Florida State University, Tallahassee, FL, 1999. Hadden, D Rill, RL McFadden, L Locke, BR, Oligonucleotide and Water Self-Diffusion in Pluronic Triblock Copolymer Gels and Solutions by Pulsed Field Gradient Nuclear Magnetic Resonance, Macromolecules 33, 4235, 2000. 

Malmsten, M Lindman, B, Water Self-Diffusion in Aqueous Block Copolymer Solutions, Macromolecules 25, 5446, 1992. 

In reversed-phase TLC, mobile phases with high eontent of water do not wet alkyl-bonded siliea layers unless partially modified silica plates are used. It is well known that high-viscosity solvents do not generate the same plate number as low-viscosity solvents because of the solute diffusion coefficient and slow mass transfer [21]. 

Winters and Lee134 describe a physically based model for adsorption kinetics for hydrophobic organic chemicals to and from suspended sediment and soil particles. The model requires determination of a single effective dififusivity parameter, which is predictable from compound solution diffusivity, the octanol-water partition coefficient, and the adsorbent organic content, density, and porosity. 

Diffusion is the process by which solute molecules are transported from one part of a system to another as a result of random molecular motion [2], It can be observed with the naked eye when a drop of dye is carefully and slowly placed at the bottom of a beaker filled with water. At first the colored part is separated from the clear by a sharp, well-defined boundary. Later the upper part turns colored, and the color becomes fainter toward the top while the lower part becomes correspondingly less intensely colored. After sufficient time, the whole solution has a uniform color. There is evidently, therefore, a net transfer of dye molecules from the lower part to the upper part of the beaker. The dye molecules have diffused into the water. This diffusion process is primarily due to random molecular motion. 

For hydrophilic and ionic solutes, diffusion mainly takes place via a pore mechanism in the solvent-filled pores. In a simplistic view, the polymer chains in a highly swollen gel can be viewed as obstacles to solute transport. Applying this obstruction model to the diffusion of small ions in a water-swollen resin, Mackie and Meares [56] considered that the effect of the obstruction is to increase the diffusion path length by a tortuosity factor, 0. The diffusion coefficient in the gel, )3,i2, normalized by the diffusivity in free water, DX1, is related to 0 by... 

Increased concentrations give increased moisture and decreased solute diffusivities. Dehydration efficiency (water loss/solid gain) increases with concentration but decreases or remains constant with temperature. 

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