Osmotic pressure kinetic process

In the case K > fi, the usual diffusion determines the kinetics for any gel shapes. Here the deviation of the stress tensor is nearly equal to — K(V u)8ij since the shear stress is small, so that V u should be held at a constant at the boundary from the zero osmotic pressure condition. Because -u obeys the diffusion equation (4.18), the problem is trivially reduced to that of heat conduction under a constant boundary temperature. The slowest relaxation rate fi0 is hence n2D/R2 for spheres with radius R, 6D/R2 for cylinders with radius R (see the sentences below Eq. (6.49)), and n2D/L2 for disks with thickness L. However, in the case K < [i, the process is more intriguing, where the macroscopic critical mode slows down as exp(- Q0t) with Q0 oc K. 

Water molecules are constantly in motion, even in ice. In fact, the translational and rotational mobility of water directly determines its availability. Water mobility can be measured by a number of physical methods, including NMR, dielectric relaxation, ESR, and thermal analysis (Chinachoti, 1993). The mobility of water molecules in biological systems may play an important role in a biochemical reaction s equilibrium and kinetics, formation and preservation of chemical gradients and osmotic pressure, and macromolecular conformation. In food systems, the mobility of water may influence the engineering processes — such as freezing, drying, and concentrating chemical and microbial activities, and textural attributes (Ruan and Chen, 1998). 

It now appears that the dissolution dynamics of glassy polymers is at the very least a complicated process and its kinetics depends on many parameters of the solvent, the polymer and the processing condition. We have also found that one of the dynamical processes that strongly affect the dissolution kinetics of polymers with high Tg is the diffusion rate of the solvent into the polymer matrix which primarily depend on at least 4 factors polymer free volume and segmental mobility, solvent size and the osmotic pressure (chemical potential difference between the polymer solution and pure solvent). We believe that the above finding has important implication in resist technology. Positive... 

According to statistical-kinetic conceptions, osmotic pressure and gas pressure have the same origin, namely the random molecular motion of the gas molecules on the one hand and of the dissolved particles on the other. The difference in the two cases lies, as mentioned before, in the different way in which the total volume of the system is made up. The gas, on expansion into a vacuum, has access to tree space, whereas the new places required for the calculation of probability, according to the theory of the mixing process, are offered to the molecules of the solute only by interchange with the particles of the solvent. 

While the Debye-Huckel derivation was based on a charging process which took into account the distance of closest approach, a, the kinetic effect of the hard core could not adequately be dealt with. In order to include these effects. Pitzer proposed using the osmotic pressure equation (PI) ... 

The sequence presented above also suggests the kinetics of the osmotic dehydration process. As long as the mass transfer processes are not strongly dependent on the symplasmic pathway, the water flux will predominate over the osmoactive substance flux. This is due to osmotic pressure flow, which will reduce the countercurrent diffusion of osmoactive substance but it will not strongly affect the diffusive flux of water as the self-diffusion of water in a solution is of the same order of magnitude as that for solute. When plasmolysis occurs and the hypertonic solution fills in the volume between cell walls and plasmalemma, the... 

The theoretical approach generally used "in electro-osmotic dewatering is an electrochemical one in which the Helmholtz-Smoluchowski relation is used to relate the electro-osmotic convective liquid velocity to such parameters as the viscosity and permittivity of the solution, the zeta potential of the clay surface, and the strength of the applied field. Also, electrode kinetic effects are taken into account where the data point to the involvement of electrochemical reactions at the electrodes during the EOD process. " In combined pressure-electro-osmotic dewatering (CPEOD), the effect of pressure is interpreted in an empirical, ad-hoc manner without any attempt to develop a comprehensive theoretical framework that combines the two driving forces, namely, the pressure and the electric field. 

Turning briefly to the nucleation of ice in undercooled aqueous solutions, we find that here too, the effect of the molal concentration is exactly analogous to that of the pressure, i.e. = 2AT. Once again, the reasons are not understood, since the phenomena underlying the two temperature depression effects are quite unrelated. ATm is the well-documented osmotic freezing point depression, whereas ATh is the manifestation of a kinetic rate process. It is also unclear why this process should be identical for equivalent molar concentrations of widely different types of solutes as illustrated in Figure 10. 

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