diffusion/ Einstein-Smoluchowski diffusion equationBrownian motionconcentration-dependent diffusion coefficientMaxwell-Boltzmann displacement distributionsteady state diffusion process/ A0560 Transport processes
Gisladottir S, Loftsson T, Stefansson E (2009) Diffusion characteristics of vitreous humour and saline solution follow the Stokes-Einstein equation . Graefes Arch Clin Exp Ophthalmol 247 : 1677–1684Gisladottir S, Loftsson T, Stefansson E. Diffusion characteristics of vitreous humour and saline...
The equation which relates the mobilityµ (of electrons or holes) and the diffusion coefficient (of electrons Dnor holes Dp) is known as Einstein Relationship. The Einstein Relationship is expressed as Where, Dp= Diffusion coefficient of holes Dn= Diffusion coefficient of electrons µp= Mobilit...
For over 100 years, the Nernst–Einstein relation has linked a charged particle’s electrophoretic mobility and diffusion coefficient. Here we report experimental measurements of diffusion and electromigration of K+ ions in narrow 0.8-nm-diameter single-
Einstein and Smoluchowski's treatment of. the Brownian motion has been discussed. It is shown that although the diffusion equations derived from both treatments are mathematically identical, Smoluchowski's equation defines a somewhat concentration-dependent diffusion coefficient, while Einstein's equation de...
This paper aims to use the Einstein relation as a probe to investigate anomalous diffusion and weak ergodicity breaking. Firstly, an irreversible Langevin equation16,25 capable of describing aging dynamics is presented. The velocity correlation function (VCF) shows aging features, in which two-time ...
α = k ρcp , (7) is the diffusion coefficient in the thermal diffusion equation ∂T ∂t = α∇2T. (8) Here k = (4 − 6) × 104 W·m−1K−1 is the range of the thermal conductivity of isotopically pure diamond between 50 and 100 K, and ρ = 3.51 × 103 kg m...
We study the diffusion of electrons moving through a monatomic gas. The two-term Legendre approximation for solving the Boltzmann equation is used to obtain an analytical expression for the isotropic part of the distribution function for hard spheres. We then obtain explicit expressions for the drift...
Over half a century ago, Wert suggested that the diffusion coefficient in cubic lattices is directly proportional to the atomic frequency, assuming a simple interstitial diffusion in which an atom migrates to an adjacent unoccupied position [40]. The Einstein temperature (θE) of a bond is direc...
H. Kim, [25], that the validity of (1.3) on M yields, via a non-trivial consequence of the second Bianchi identities, the validity of the equation Δff−kλ=−βe2kffor some constant β∈R. Here Δf is the symmetric diffusion operator Δf=Δ−〈∇f,∇〉. A consequence ...