Diffusivities of solutes

Diffusion and Mass Transfer During Leaching. Rates of extraction from individual particles are difficult to assess because it is impossible to define the shapes of the pores or channels through which mass transfer (qv) has to take place. However, the nature of the diffusional process in a porous soHd could be illustrated by considering the diffusion of solute through a pore. This is described mathematically by the diffusion equation, the solutions of which indicate that the concentration in the pore would be expected to decrease according to an exponential decay function. 

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. 

R is rate of reaction per unit area, a is interfacial area per unit volume, S is solubiHty of solute in continuous phase, D is diffusivity of solute, k is rate constant, kj is mass-transfer coefficient, is concentration of reactive species, and Z is stoichiometric coefficient. When Dk is considerably greater (10 times) than Ra = aS Dk. 

The diffusivity of solute 1 in the mixture is related to the binary infinite dilution diffiisivities for each of the other components calculated from Eq. (2-155) or the Umesi method. The viscosities are calculated by the methods in the previous section. Errors are not quantifiable, as little experimental data exist, although these errors would be related to those assumed for the binaiy pairs. 

Thorough displacement washing is possible in a nutsche if the wash solvent is added before the cake begins to be exposed to air displacement of filtrate. If washing needs to oe more effective, an agitator can be provided in the nutsche vessel to reslurry the cake to allow adequate diffusion of solute from the solids. 

There have been many modifications of this idealized model to account for variables such as the freezing rate and the degree of mix-ingin the liquid phase. For example, Burton et al. [J. Chem. Phy.s., 21, 1987 (1953)] reasoned that the solid rejects solute faster than it can diffuse into the bulk liquid. They proposed that the effect of the freezing rate and stirring could be explained hy the diffusion of solute through a stagnant film next to the solid interface. Their theoiy resulted in an expression for an effective distribution coefficient k f which could be used in Eq. (22-2) instead of k. 

Whilst the diffusion of solution in a liquid is governed by the same equations as for the gas phase, the diffusion coefficient D is about two orders of magnitude smaller for a liquid than for a gas. Furthermore, the diffusion coefficient is a much more complex function of the molecular properties. 

The diffusion of solute A away from the interface (K-direction) is thus given by equation 10.66 ... 

The diffusion of solutes in water is an important event in many biological processes. The influences of water temperature and hydropathic states of the solute are expected to be of importance in this process. A study modeling diffusion using CA was reported by Kier et al. [6]. The study revealed increases in diffusion rates with higher temperatures and higher solute hydrophobicity. More recent studies indicate that the diffusion rate may be maximum at an intermediate level of hydrophobicity and temperature [7]. 

Subsequent work by Johansson and Lofroth [183] compared this result with those obtained from Brownian dynamics simulation of hard-sphere diffusion in polymer networks of wormlike chains. They concluded that their theory gave excellent agreement for small particles. For larger particles, the theory predicted a faster diffusion than was observed. They have also compared the diffusion coefficients from Eq. (73) to the experimental values [182] for diffusion of poly(ethylene glycol) in k-carrageenan gels and solutions. It was found that their theory can successfully predict the diffusion of solutes in both flexible and stiff polymer systems. Equation (73) is an example of the so-called stretched exponential function discussed further later. 

To describe the diffusion of solutes in the rhizosphere, where concentration gradients change with time, /, as well as space, mass conservation is invoked with the spatial geometry appropriate for the cylindrical root (8) ... 

The in vitro system we have been using to study the transepithelial transport is cultured Madin-Darby canine kidney (MDCK) epithelial cells (11). When cultured on microporous polycarbonate filters (Transwell, Costar, Cambridge, MA), MDCK cells will develop into monolayers mimicking the mucosal epithelium (11). When these cells reach confluence, tight junctions will be established between the cells, and free diffusion of solutes across the cell monolayer will be markedly inhibited. Tight junction formation can be monitored by measuring the transepithelial electrical resistance (TEER) across the cell monolayers. In Figure 1, MDCK cells were seeded at 2 X 104 cells per well in Transwells (0.4 p pore size) as described previously. TEER and 14C-sucrose transport were measured daily. To determine 14C-sucrose... 

Diffusion of solutions containing zinc chloride and crown ethers can give solid state structure where the zinc ion is coordinated to the crown ether oxygens.718 A five-coordinate zinc is observed with distorted trigonal-bipyramidal geometry bound to a chloride, a water molecule,... 

M Palasis. The influence of interactions on the diffusion of solutes in responsive gels. PhD Dissertation, University of Cincinnati, Cincinnati, OH, 1994. 

Fig. 2.4p shows three types of post-column reactor. In the open tubular reactor, after the solutes have been separated on the column, reagent is pumped into the column effluent via a suitable mixing tee. The reactor, which may be a coil of stainless steel or ptfe tube, provides the desired holdup time for the reaction. Finally, the combined streams are passed through the detector. This type of reactor is commonly used in cases where the derivatisation reaction is fairly fast. For slower reactions, segmented stream tubular reactors can be used. With this type, gas bubbles are introduced into the stream at fixed time intervals. The object of this is to reduce axial diffusion of solute zones, and thus to reduce extra-column dispersion. For intermediate reactions, packed bed reactors have been used, in which the reactor may be a column packed with small glass beads. 

The diffusion layer theory, illustrated in Fig. 15B, is the most useful and best-known model for transport-controlled dissolution. The dissolution rate here is controlled by the rate of diffusion of solute molecules across a diffusion layer of thickness h, so that kT kR in Eq. (40), which simplifies to kx = kT. With increasing distance, x, from the surface of the solid, the concentration, c, decreases from cs at x = 0 to cb at x = h. In general, c is a nonlinear function of x, and the concentration gradient dddx becomes less steep as x increases. The hyrodynamics of the dissolution process has been fully discussed by Levich [104]. In a stirred solution, the flow velocity of the liquid dissolution medium increases from zero at x = 0 to the bulk value at x = h. 

B/Si is the molecular diffusion term and relates to diffusion of solute molecules within the mobile phase caused by local concentration gradients. Diffusion within the stationary phase also contributes to this term, which is significant only at low flow rates and increases with column length. As B is proportional to the diffusion coefficient in the mobile phase, the order of efficiency at low flow rates is liquids > heavy gases > light gases. 

De Pinto [90] measured the rate at which available phosphorus is released from various types of particulates suspended in lake water. The equipment consists of two culture vessels separated by a thin membrane filter, thus facilitating the separation of two particulate suspensions, while at the same time permitting their interaction by diffusion of solutes through the membrane. 

The most popular and versatile bonded phase is octadecylsilane (ODS), n-C18H37, a grouping that is non-polar and used for reverse phase separations. Octylsilane, with its shorter chain length, permits faster diffusion of solutes and this results in improved peak symmetry. Other groups are attached to provide polar phases and hence perform normal phase separations. These include cyano, ether, amine and diol groups, which offer a wide range of polarities. When bonded stationary phases are used, the clear distinction between adsorption and partition chromatography is lost and the principles of separation are far more complex. 

Wagner, C. Theoretical analysis of diffusion of solutes during the solidifi-... 

Bogar, R.G., Thomas, J.C., and Callis, J.B., Lateral diffusion of solutes bound to the alkyl surface of Cl8 reversed phase liquid chromatographic packings. Anal. Chem., 56, 1080, 1984. 

---