At equilibrium, there is no net flow of particles: the tendency of particles to get pulled towards lower , called the drift current, perfectly balances the tendency of particles to spread out due to diffusion, called the diffusion current (see drift-diffusion equation).

We demonstrate this by deriving the equation of motion of a Brownian particle that is under the influence of an external force in the fluid with a non-constant temperature.

Albert Einstein understood this and formulated a relation between ionic mobility (̅ ) and diffusion coefficient (D). Now, since the conduction, as well as the diffusion, are irreversible processes, they cannot be treated by equilibrium statistical mechanics or by the equilibrium thermodynamics.

2013年1月24日 · With the molecular theory in mind, Einstein derived the diffusion equation from a model of random molecular motion instead of from a continuity equation and Fick's Law. This chapter presents Einstein's derivation and examine its strengths and weaknesses.

thus, if we define a diffusion constant D = α (δ x)2 δ t and extend the same idea to 3 dimensions, we derive the diffusion equation ∂p ∂t = D ∇2p. (Einstein) (7) Of course this is the equation for the probability of a single particle being in the volume element dx …

For a particle with electrical charge q, its electrical mobility μq is related to its generalized mobility μ by the equation μ = μq/q. The parameter μq is the ratio of the particle's terminal drift velocity to an applied electric field. Hence, the equation in the case of a charged particle is given as.

Einstein-Stokes equation The diffusion constant can be determined analytically for a few specific situations. One case is the random motion of a sphere of radius R moving in a fluid of viscosity η, which Einstein solved using Stokes' Law: F = 6πηR v. We saw this formula for viscous drag back at the beginning of the course.

The diffusion constant expresses the activity of the Brownian motion, i.e. the greater the value of the diffusion constant, the greater the Brownian motion activity will be. The solution of the equation depends on the initial and boundary conditions. In his work, Albert Einstein assumes the initial condition f(x,0) = δ(x−x 0), (6)

Diffusion: movement of mass from region of high concentration to low concentration. J = -D (Flux of mass, D: diffusion coefficient) 2. Diffusion is an important process in chromatography in determining the mass transfer and band-broadening dN dz ΔS>0 3. Einstein diffusion equation: td= d2/(2D) Where, t d= average time required to diffuse a ...

Albert Einstein developed a modified approach to correlate the viscosity with the diffusion coefficient by suggesting that a driving force (− / ) operates on the particles during diffusion which can be formulated as given below. − =6 (61) Where is the steady-state velocity of the ion under consideration. The right-hand side of the above ...