Osmotic diffusion coefficient

As usual, the osmotic diffusion coefficient is linked to the bulk osmotic modulus and to the effective mobility per monomer p = p x K/C. The quantity p can be measured through the sedimentation coefficient S = p(1- vp). Comb ing the experimental results for K and S, we obtain >c = 1.13 X 10"° X in agreement with the result presented above. This result confirms that the hydrodynamic screening length is proportional to that of the concentration fluctuations. Actually the scaling law is well verified (see Fig. 6) where is the diffusion coefficient of the isolated polymer chain, is only a function of CIC, ... 

All the thermodynamic and hydrodynamic quantities, which are sensitive to 5, such as osmotic bulk modulus, sedimentation coefficient, and the osmotic diffusion coefficient obey the scaling law in C/C. ... 

Rastogi, N.K. and Raghavarao, K.S.M.S. 1997. Water and solute diffusion coefficients of carrot as a function of temperature and concentration during osmotic dehydration. J. Food Engineer. 34, 429-440. 

The thermodynamic approach does not make explicit the effects of concentration at the membrane. A good deal of the analysis of concentration polarisation given for ultrafiltration also applies to reverse osmosis. The control of the boundary layer is just as important. The main effects of concentration polarisation in this case are, however, a reduced value of solvent permeation rate as a result of an increased osmotic pressure at the membrane surface given in equation 8.37, and a decrease in solute rejection given in equation 8.38. In many applications it is usual to pretreat feeds in order to remove colloidal material before reverse osmosis. The components which must then be retained by reverse osmosis have higher diffusion coefficients than those encountered in ultrafiltration. Hence, the polarisation modulus given in equation 8.14 is lower, and the concentration of solutes at the membrane seldom results in the formation of a gel. For the case of turbulent flow the Dittus-Boelter correlation may be used, as was the case for ultrafiltration giving a polarisation modulus of ... 

MeOH is transported through the membrane by two modes diffusion and electro-osmotic drag. ° When MeOH comes into contact with the membrane, it diffuses through the membrane from anode to cathode and is also dragged along with the hydrated protons under the influence of current flowing across the cell. Therefore, a correlation between the MeOH diffusion coefficient and proton conductivity is observed. The diffusive mode of MeOH transport dominates when the cell is idle, whereas the electro-osmotic drag... 

Nafion absorbs MeOH more selectively than water, and the MeOH diffusion flow is higher than the osmotic water flow in Nafion membranes. Diffusion coefficients of Nafion 117 determined by different techniques have been reported. Ren et al. measured MeOH diffusion coefficients in Nafion 117 membranes exposed to 1.0 M MeOH solutions using pulsed field gradient (PPG) NMR techniques. The MeOH self-diffusion coefficient was 6 x 10 cm S and roughly independent of concentration over the range of 0.5-8.0 M at 30°C. A similar diffusion coefficient was obtained for Nafion 117 at 22°C by Hietala, Maunu, and Sundholm with the same technique. Kauranen and Skou determined the MeOH diffusion coefficient of 4.9 x 10 cm for Nafion... 

There is no quantitative model yet describing the observed electro-osmotic drag coefficients as a function of the degree of hydration and temperature. However, the available data provide strong evidence for a mechanism that is (i) hydrodynamic in the high solvation limit, with the dimensions of the solvated hydrophilic domain and the solvent—polymer interaction as the major parameters and (ii) diffusive at low degrees of solvation, where the excess proton essentially drags its primary solvation shell (e.g., H3O+). 

Two other important electrolyte properties for the PEFC system are the water diffusion coefficient and electro-osmotic drag coefficient. These two param-... 

Figure 5. Electro-osmotic drag coefficient and water diffusivity as functions of water content in Nafion membranes.

In the above, D rn is the water diffusion coefficient through the membrane phase only. Note also that the water fluxes through the membrane phase, via electro-osmotic drag and molecular diffusion, represent a source/sink term for the gas mixture mass in the anode and cathode, respectively. 

This article reviews the following solution properties of liquid-crystalline stiff-chain polymers (1) osmotic pressure and osmotic compressibility, (2) phase behavior involving liquid crystal phasefs), (3) orientational order parameter, (4) translational and rotational diffusion coefficients, (5) zero-shear viscosity, and (6) rheological behavior in the liquid crystal state. Among the related theories, the scaled particle theory is chosen to compare with experimental results for properties (1H3), the fuzzy cylinder model theory for properties (4) and (5), and Doi s theory for property (6). In most cases the agreement between experiment and theory is satisfactory, enabling one to predict solution properties from basic molecular parameters. Procedures for data analysis are described in detail. 

The osmotic modulus, K, the frictional coefficient, f, and the diffusion coefficient, D, are related to density-density correlation function of the network, g(r), by [62]... 

Measurements of static light or neutron scattering and of the turbidity of liquid mixtures provide information on the osmotic compressibility x and the correlation length of the critical fluctuations and, thus, on the exponents y and v. Owing to the exponent equality y = v(2 — ti) a 2v, data about y and v are essentially equivalent. In the classical case, y = 2v holds exactly. Dynamic light scattering yields the time correlation function of the concentration fluctuations which decays as exp(—Dk t), where k is the wave vector and D is the diffusion coefficient. Kawasaki s theory [103] then allows us to extract the correlation length, and hence the exponent v. 

D = diffusion coefficient of the isotope. v = rate of osmotic flow. 

In semi-dilute solutions, the diffusion coefficient describing the thermal motion of the polymer chains that take part in an osmotic fluctuation in the surrounding solvent may be defined as follows... 

Analogous equations have been found for the osmotic pressure, the diffusion coefficient and the sedimentation coefficient (Chap. 16). b. Activated processes, i.e. phenomena that are controlled by an activation energy barrier. Here the equation takes the form ... 

In a binary mixture, diffusion coefficients are equal to each other for dissimilar molecules, and Fick s law can determine the molecular mass flows in an isotropic medium at isothermal and isobaric conditions. In a multicomponent diffusion, however, various interactions among the molecules may arise. Some of these interactions are (i) diffusion flows may vanish despite the nonvanishing driving force, which is known as the mass transfer barrier, (ii) diffusion of a component in a direction opposite to that indicated by its driving force leads to a phenomenon called the reverse mass flow, and (iii) diffusion of a component in the absence of its driving force, which is called the osmotic mass flow. 

For binary diffusion, there is only one independent flow, force or concentration gradient, and diffusion coefficient. On the other hand, multicomponent diffusion differs from binary diffusion because of the possibility of interactions among the species in mixtures of three or more species. Some of the possible interactions are (1) a flow may be zero although its zero driving force vanishes, which is known as the diffusion barrier (2) the flow of a species may be in a direction opposite to that indicated by its driving force, which is called reverse flow and (3) the flow of a species may occur in the absence of a driving force, which may be called osmotic flow. The theory of nonequilibrium thermodynamics indicates that the chemical potential arises as the proper driving force for diffusion. This is also consistent with the condition of fluid phase equilibrium, which is satisfied when the chemical potentials of a species are equal in each phase. 

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