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Fick's first law relates the diffusive flux to the gradient of the concentration. It postulates that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative), or in simplistic terms the concept that a solute will move from a region of high concentration to a region of low ...
Both species A and B will typically be diffusing but diffusiophoresis is distinct from simple diffusion: in simple diffusion a species A moves down a gradient in its own concentration. Diffusioosmosis , also referred to as capillary osmosis, is flow of a solution relative to a fixed wall or pore surface, where the flow is driven by a ...
The convection–diffusion equation can be derived in a straightforward way [4] from the continuity equation, which states that the rate of change for a scalar quantity in a differential control volume is given by flow and diffusion into and out of that part of the system along with any generation or consumption inside the control volume: + =, where j is the total flux and R is a net ...
The self-diffusion coefficient of neat water is: 2.299·10 −9 m 2 ·s −1 at 25 °C and 1.261·10 −9 m 2 ·s −1 at 4 °C. [2] Chemical diffusion occurs in a presence of concentration (or chemical potential) gradient and it results in net transport of mass. This is the process described by the diffusion equation.
Diffusion force caused by concentration gradient: = ( (/)). Electrostatic force caused by electric potential gradient: q ∇ φ {\displaystyle q\,\nabla \varphi } . Here R is the gas constant, T is the absolute temperature, n is the concentration, the equilibrium concentration is marked by a superscript "eq", q is the charge and φ is the ...
The diffusion equation can be obtained easily from this when combined with the phenomenological Fick's first law, which states that the flux of the diffusing material in any part of the system is proportional to the local density gradient: = (,) (,).
It is directly related to the concentration gradient of the permeate, a material's intrinsic permeability, and the materials' mass diffusivity. [1] Permeation is modeled by equations such as Fick's laws of diffusion, and can be measured using tools such as a minipermeameter.
The Nernst–Planck equation is a conservation of mass equation used to describe the motion of a charged chemical species in a fluid medium. It extends Fick's law of diffusion for the case where the diffusing particles are also moved with respect to the fluid by electrostatic forces. [1] [2] It is named after Walther Nernst and Max Planck.