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In the ultrashort time limit, in the order of the diffusion time a 2 /D, where a is the particle radius, the diffusion is described by the Langevin equation. At a longer time, the Langevin equation merges into the Stokes–Einstein equation. The latter is appropriate for the condition of the diluted solution, where long-range diffusion is ...
The diffusion coefficient is the coefficient in the Fick's first law = /, where J is the diffusion flux (amount of substance) per unit area per unit time, n (for ideal mixtures) is the concentration, x is the position [length].
The diffusion distance at time between two points can be measured as the similarity of two points in the observation space with the connectivity between them. It is ...
Before this point in time, a gradual variation in the concentration of A occurs along an axis, designated x, which joins the original compartments. This variation, expressed mathematically as -dC A /dx, where C A is the concentration of A. The negative sign arises because the concentration of A decreases as the distance x increases.
Typically, a compound's diffusion coefficient is ~10,000× as great in air as in water. Carbon dioxide in air has a diffusion coefficient of 16 mm 2 /s, and in water its diffusion coefficient is 0.0016 mm 2 /s. [1] [2] Diffusivity has dimensions of length 2 / time, or m 2 /s in SI units and cm 2 /s in CGS units.
The time scale for diffusion characterizes the time needed for heat to diffuse over a distance, ... to show significant temperature change is the diffusion time, ...
The diffusion equation is a parabolic partial differential equation. ... where ϕ(r, t) is the density of the diffusing material at location r and time t and D ...
Another method to describe the motion of a Brownian particle was described by Langevin, now known for its namesake as the Langevin equation.) (,) = (,), given the initial condition (, =) = (); where () is the position of the particle at some given time, is the tagged particle's initial position, and is the diffusion constant with the S.I. units ...