Diffusion useful equations
equation do not differ significantly from the radii obtained from molecular models of these compounds. The use of the Stokes-Einstein diffusion relationship shear velocity and, hence, the coefficient of internal friction or viscosity. Einstein. CONSTANTS AND THE CALCULATION OF THE RADIUS. AND WEIGHT OF coefficient is the only practical means of determining the molecular size or weight . . The quantity allowed to diffuse must be small enough so that the difference. to determine relationships between diffusion coefficient and solute particle of effective radius rH moving through a fluid with viscosity η, giving.
In a so-called NMR spin echo experiment this technique uses the nuclear spin precession phase, allowing to distinguish chemically and physically completely identical species e. The self-diffusion coefficient of water has been experimentally determined with high accuracy and thus serves often as a reference value for measurements on other liquids.
The self-diffusion coefficient of neat water is: This is the process described by the diffusion equation. This diffusion is always a non-equilibrium process, increases the system entropy, and brings the system closer to equilibrium. The diffusion coefficients for these two types of diffusion are generally different because the diffusion coefficient for chemical diffusion is binary and it includes the effects due to the correlation of the movement of the different diffusing species.
Non-equilibrium system[ edit ] Illustration of low entropy top and high entropy bottom Because chemical diffusion is a net transport process, the system in which it takes place is not an equilibrium system i.
Many results in classical thermodynamics are not easily applied to non-equilibrium systems. However, there sometimes occur so-called quasi-steady states, where the diffusion process does not change in time, where classical results may locally apply.
As the name suggests, this process is a not a true equilibrium since the system is still evolving. Non-equilibrium fluid systems can be successfully modeled with Landau-Lifshitz fluctuating hydrodynamics. In this theoretical framework, diffusion is due to fluctuations whose dimensions range from the molecular scale to the macroscopic scale. Particles can spread out by diffusion, but will not spontaneously re-order themselves absent changes to the system, assuming no creation of new chemical bonds, and absent external forces acting on the particle.
Concentration dependent "collective" diffusion[ edit ] Collective diffusion is the diffusion of a large number of particles, most often within a solvent.
Contrary to brownian motionwhich is the diffusion of a single particle, interactions between particles may have to be considered, unless the particles form an ideal mix with their solvent ideal mix conditions correspond to the case where the interactions between the solvent and particles are identical to the interactions between particles and the interactions between solvent molecules; in this case, the particles do not interact when inside the solvent.
In case of an ideal mix, the particle diffusion equation holds true and the diffusion coefficient D the speed of diffusion in the particle diffusion equation is independent of particle concentration. In other cases, resulting interactions between particles within the solvent will account for the following effects: For an attractive interaction between particles, the diffusion coefficient tends to decrease as concentration increases.
For a repulsive interaction between particles, the diffusion coefficient tends to increase as concentration increases. In the case of an attractive interaction between particles, particles exhibit a tendency to coalesce and form clusters if their concentration lies above a certain threshold.Measuring Size, Stability and Conformation of Biopolymers with Dynamic Light Scattering
This is equivalent to a precipitation chemical reaction and if the considered diffusing particles are chemical molecules in solution, then it is a precipitation.
If molecules of types A and B interact binary diffusionthen the interdiffusion coefficient is: The kinetic theory of gases makes it possible to determine the constant in Eq.
Sutherland has made a correction to Eq. Contemporary kinetic theory takes into account the intricate character of molecular interaction; molecules repel one another when they are close and attract one another at a distance.
For dilute gas mixtures, and assuming that the molecular collisions are only binary and elastic, that the motion of colliding molecules is in terms of classical mechanics, that quantum effects are absent, and, finally, intermolecular forces act only along the center line, the expression for the diffusion coefficient in a binary mixture is obtained by Bird, Hirshfelder and Curtiss.
Wilke and Lee noted the coefficient 1.
This accurate definition results in a better agreement between experimental and computed data. A correlation formula obtained by Fuller, Schetter and Gittings by means of computer-aided correlation of experimental points, expressed as: Diffusion volumes of atoms and simple molecules In order to calculate the diffusion coefficient in multicomponent systems, Wilke used the Maxwell-Stefan equation to derive the expression where D'A is the diffusion coefficient of the component A in the mixture with B, C, As has been noted, diffusion in liquids encounters greater resistance and the diffusion coefficients for liquids lower than to times.
Molecular diffusion - Wikipedia
The constant b depends on the size of diffusing molecules: Introduction of the association parameter into the formula is brought about by the fact that associated molecules behave like large-size molecules and diffuse at a lower rate; the degree of association varying with mixture composition and with molecule types.
Therefore, Wilke and Chang presented the values for most widespread solvents: A semiempirical formula suggested by Scheibel, is worthy of attention. Reddy and Doraiswamy have suggested the equation where KRS varies depending on the ratio of molar volumes: All formulas suggested above for calculating the diffusion coefficient hold true for low-viscosity liquids.
For a high-viscosity solvent, they are in great error and therefore inapplicable. The temperature effect on the diffusion coefficient has been poorly studied so far.