Translational diffusion hydrodynamic theory

Combining the above descriptions leads to a picture that describes the experimentally observed concentration dependence of the polymer diffusion coefficient. At low concentrations the decrease of the translational diffusion coefficient is due to hydrodynamic interactions that increase the friction coefficient and thereby slow down the motion of the polymer chain. At high concentrations the system becomes an entangled network. The cooperative diffusion of the chains becomes a cooperative process, and the diffusion of the chains increases with increasing polymer concentration. This description requires two different expressions in the two concentration regimes. A microscopic, hydrodynamic theory should be capable of explaining the observed behavior at all concentrations. 

Monteiro, C. Herve du Penhoat, C. Translational Diffusion of Dilute Aqueous Solutions of Sugars as Probed by NMR and Hydrodynamic Theory. J. Phys. Chan. A 2001, 105, 9827-9833. 

The theoretical description of translational diffusion in a lipid bilayer depends on the size of the diffusing particle. Theoretical descriptions based on fluid hydrodynamic theory (51, 52) have been shown to be applicable to particles whose radius in the plane of the bilayer is significantly larger than the radius of the lipid molecules that constitute the bilayer, in which case the diffusion coefficient may be given by ... 

The values of A, S, d and X obtained from experimental data on the kinetics of the Kerr effect agree qualitatively with those determined for the same polymers by translational diffusion and sedimentation (Table 3). The agreement between geometrical molecular characteristics obtained from the phenomena of rotattonal and translational friction indicates that the hydrodynamic and the oinformational models on which this theory is based are valid. This is an evidence of the kinetic r idity of the investigated chains. 

It is pertinent to point out here that a corresponding universal scaling relationship is found [Aral et al., 1995 Tominaga et al., 2002] between ur and an, the chain expansion parameter for the hydrodynamic radius determined from translational diffusion. However, the scaling observed deviates substantially from the QTP theory when the latter is constructed using the Barrett equation for an [Barrett, 1984] ... 

Based on this, DLS can provide the translational diffusion coefficient and hydrodynamic radius of the sample. DLS measurement requires knowledge of solvent viscosity, solvent refractive index, and sample temperature. A comprehensive review of the theory/application of SLS and DLS in polymer systems is given by Schartl [60]. 

The fundamental rate expression to be considered is the Smoluchowski relation k = 4n iVDAB AB (Equation (2.1)). The derived expression ART/r] (Equation (2.3a)), is a useful approximation, but deviations from it are observed, because the Stokes-Einstein equation which is involved is derived by hydrodynamic theory for spherical particles moving in a continuous fluid, and does not accurately represent the measured values of translational diffusion coefficients in real systems. Although the proportionality Da 1 /rj is indeed a reasonable approximation for many solutes in common solvents, the numeral coefficient 1 /4 is subject to uncertainty. In the first place, this theoretical value derives from the assumption that in translational motion there is no friction between a solute molecule and the first layer of solvent molecules surrounding it, i.e., that slip conditions hold. If, however, one assumes instead that there is no slipping ( stick conditions), so that momentum is... 

Diffusion coefficients measured by the spin-echo technique provide a means of investigating the translational motion of molecules under the extremes of temperature and pressure. There have been numerous smdies of the self-diffusion coefficients of high-pressure liquids and supercritical fluids by NMR. As an illustration of the potential of these physicochemical measurements, we will focus on CO2 (3,28,33,38,39). The availability of a wide range of diffusion coefficients and viscosities allows one to test the Stokes-Einstein equation at the molecular level. From hydrodynamic theory,... 

In this chapter we formulate the thermodynamic and stochastic theory of the simple transport phenomena diffusion, thermal conduction and viscous ffow (1) to present results parallel to those listed in points 1-7, Sect. 8.1, for chemical kinetics. We still assume local equilibrium with respect to translational and internal degrees of freedom. We do not assume conditions close to chemical or hydrodynamic equilibrium. For chemical reactions and diffusion the macroscopic equations for a given reaction mechanism provide sufficient detail, the fluxes in the forward and reverse direction, to write a birth-death master equation with a stationary solution given in terms of For thermal conduction and viscous flow we derive the excess work and then find Fokker-Planck equations with stationary solutions given in terms of that excess work. 

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