Osmotic coupling coefficient

Thus, the osmotic coupling coefficient is the ratio of the actual volume flow observed with equal bathing media relative to the virtual volume flow that would be necessary for reabsorption to be isotonic. In the models we shall consider, 0 < y < 1. For tight couphng, Y 1 in an uncoupled system y = 0. y has also been termed the efficiency of osmotic transport [16]. 

These might be used, for example, to define the coupling of salt flux or water flux to a metabolic reaction. Our aim, however, in the introduction of the osmotic coupling coefficient, was to define a parameter that would reflect the relation between metabolically coupled salt flux and volume flow. 

To compute the osmotic coupling coefficient for this model one evaluates Eqn. 57 when Cj =C = 0, so that... 

We may now compute the osmotic coupling coefficient of this model by rewriting Eqn. 61 as... 

The study of the dynamical behavior of water molecules and protons as a function of the state of hydration is of great importance for understanding the mechanisms of proton and water transport and their coupling. Such studies can rationalize the influence of the random self-organized polymer morphology and water uptake on effective physicochemical properties (i.e., proton conductivity, water permeation rates, and electro-osmotic drag coefficients). 

There are actually no experimental measurements of protonic streaming currents (Lu) and coupled water and methanol transport (L23 = L32) however, the first may be related to the hydrodynamic component of the electro-osmotic drag L /Ln, Lis/Lu) (see discussion in Section 3.2.1.1). The second is expected to be qualitatively related to the ratio of the electro-osmotic drag coefficient of water and methanol (L12/Z.13). In the following, the directly accessible transport coefficients o (Do), FH2O, MvieOH,... 

It is worth emphasis that the verification of isotonic transport for a particular model necessitates the solution of Eqns. 5 and 6. In general, the simple calculation of (Cr)o, the reabsorbate concentration with exactly equal bathing media, is not sufficient. Nevertheless, (Cr)q is an important theoretical aspect of a model and has been used to define the coupling coefficient of osmotic transport [ 15] by... 

In his early analysis of isotonic transport. Diamond [13] tried to use measured values of the whole epithelial water permeability, Lp, in place of the quantity Llb-The unacceptably large osmotic deviations from isotonicity that he computed caused him to reject the elementary compartment model of the lateral intercellular space. We should reconsider, therefore, the requirements imposed upon the elementary compartment model by the experimental data on rabbit gallbladder (Table 1). For N/Cq = 1.47-10 cm/s and C/Q = 0.27, Eqn. 84 requires = 5.5-10 cm/s. Eqn. 86 may be used to give a lower bound on the coupling coefficient. If mucosal equilibrium is within 2% of exact isotonicity then — C /Cq = 0.02 so that y = 0.95. Thus, if Lp = 1.7- lO"" cm/s.osm, Eqn. 85 implies L b is at least 34-10" cm/s.osm. It remains to consider these model predictions for and Llb i relation to the pertinent experimental data. 

The dimensionless conductivity 0/0 and coupling coefficients depend linearly upon C The conductivity and electro-osmotic coefficients 6- = (cr/a - l)/c ) and are plotted in Figs 4a and 4b. respectively, versus the solid volume concentrations ( ) for the three reduced surface potentials = -1,0, +1. For = 0, one can see that 6- tends to -3/2 as (j) 0. Moreover, for uncharged particles, the... 

The electro-osmotic coupling of proton and water transport depends on the molecular mechanism of proton transport. It is useful to distinguish a molecular and a hydro-dynamic contribution to the electro-osmotic drag coefficient. The latter contribution increases strongly with water uptake and temperature. 

The total electro-osmotic coefficient = Whydr + mo includes a contribution of hydrodynamic coupling (Whydr) and a molecular contribution related to the diffusion of mobile protonated complexes—namely, H3O. The relative importance, n ydr and depends on the prevailing mode of proton transport in pores. If structural diffusion of protons prevails (see Section 6.7.1), is expected to be small and Whydr- If/ ori the other hand, proton mobility is mainly due to the diffusion of protonated water clusters via the so-called "vehicle mechanism," a significant molecular contribution to n can be expected. The value of is thus closely tied to the relative contributions to proton mobility of structural diffusion and vehicle mechanism. ... 

Abstract A permeameter was developed for measurement of coupled flow phenomena in clayey materials. Results are presented on streaming potentials in a Na-bentonite induced by hydraulic flow of electrolyte solutions. Transport coefficients are derived from the experiments, assuming the theory of irreversible thermodynamics to be applicable. Hydraulic and electro-osmotic conductivities are consistent with data reported elsewhere. However the electrical conductivity of the clay is substantially lower. This is ascribed to the high compaction of the clay resulting in overlap of double layers... 

Integral equations theories are another approach to incorporate higher order correlations, and consequently also lead to lowered osmotic coefficients. There are numerous variants of these theories around which differ in their used closure relations and accuracy of the treatment of correlations [36]. They work normally very well at high electrostatic coupling and high densities, and are able to account for overcharging, which was first predicted by Lozada-Cassou et al. [36] and also describe excluded volume effects very well, see Refs. [37] for recent comparisons to MD simulations. 

Another attempt to go beyond the cell model proceeds with the Debye-Hiickel-Bjerrum theory [38]. The linearized PB equation is used as a starting point, however ion association is inserted by hand to correct for the non-linear couplings. This approach incorporates rod-rod interactions and should thus account for full solution properties. For the case of added salt the theory predicts an osmotic coefficient below the Manning limiting value, which is much too low. The same is true for a simplified version of the salt free case. 

If we consider a membrane having the same solute concentration on both sides, we have All 0 However, a hydrostatic pressure difference AP exists between the two sides, and we have a flow Jv that is a linear function of AP. The term Lp is called the mechanical filtration coefficient, which represents the velocity of the fluid per unit pressure difference between the two sides of the membrane. The cross-phenomenological coefficient Ldp is called the ultrafiltration coefficient, which is related to the coupled diffusion induced by a mechanical pressure of the solute with respect to the solvent. Osmotic pressure difference produces a diffusion flow characterized by the permeability coefficient, which indicates the movement of the solute with respect to the solvent due to the inequality of concentrations on both sides of the membrane. 

Up to now the following observation repeatedly turned up from the simulations. The nonlinear PB equation provides a fairly good description of the cell model, but it suffers from systematic deviations in strongly coupled or dense systems. It underestimates the extent of counterion condensation and at the same time overestimates the osmotic coefficient. As the common reason for both problems, the neglect of correlations has been proposed, basically for two reasons ... 

The total electro-osmotic coefficient nd = nhydr + nmoi includes terms due to hydrodynamic coupling nhydr, and a molecular coupling nmoi, that is related to the structural diffusion of protonic defects. The relative contributions of nhydr and nmol depend on the mechanism of proton transport in pores. 

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