2 resultados para Diffusion Equation
em Duke University
Resumo:
While the Stokes-Einstein (SE) equation predicts that the diffusion coefficient of a solute will be inversely proportional to the viscosity of the solvent, this relation is commonly known to fail for solutes, which are the same size or smaller than the solvent. Multiple researchers have reported that for small solutes, the diffusion coefficient is inversely proportional to the viscosity to a fractional power, and that solutes actually diffuse faster than SE predicts. For other solvent systems, attractive solute-solvent interactions, such as hydrogen bonding, are known to retard the diffusion of a solute. Some researchers have interpreted the slower diffusion due to hydrogen bonding as resulting from the effective diffusion of a larger complex of a solute and solvent molecules. We have developed and used a novel micropipette technique, which can form and hold a single microdroplet of water while it dissolves in a diffusion controlled environment into the solvent. This method has been used to examine the diffusion of water in both n-alkanes and n-alcohols. It was found that the polar solute water, diffusing in a solvent with which it cannot hydrogen bond, closely resembles small nonpolar solutes such as xenon and krypton diffusing in n-alkanes, with diffusion coefficients ranging from 12.5x10(-5) cm(2)/s for water in n-pentane to 1.15x10(-5) cm(2)/s for water in hexadecane. Diffusion coefficients were found to be inversely proportional to viscosity to a fractional power, and diffusion coefficients were faster than SE predicts. For water diffusing in a solvent (n-alcohols) with which it can hydrogen bond, diffusion coefficient values ranged from 1.75x10(-5) cm(2)/s in n-methanol to 0.364x10(-5) cm(2)/s in n-octanol, and diffusion was slower than an alkane of corresponding viscosity. We find no evidence for solute-solvent complex diffusion. Rather, it is possible that the small solute water may be retarded by relatively longer residence times (compared to non-H-bonding solvents) as it moves through the liquid.
Resumo:
The time reversal of stochastic diffusion processes is revisited with emphasis on the physical meaning of the time-reversed drift and the noise prescription in the case of multiplicative noise. The local kinematics and mechanics of free diffusion are linked to the hydrodynamic description. These properties also provide an interpretation of the Pope-Ching formula for the steady-state probability density function along with a geometric interpretation of the fluctuation-dissipation relation. Finally, the statistics of the local entropy production rate of diffusion are discussed in the light of local diffusion properties, and a stochastic differential equation for entropy production is obtained using the Girsanov theorem for reversed diffusion. The results are illustrated for the Ornstein-Uhlenbeck process.