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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 ...
If there is a change in the potential energy of a system; for example μ 1 >μ 2 (μ is Chemical potential) an energy flow will occur from S 1 to S 2, because nature always prefers low energy and maximum entropy. Molecular diffusion is typically described mathematically using Fick's laws of diffusion.
The diffusion equation is a parabolic partial differential equation.In physics, it describes the macroscopic behavior of many micro-particles in Brownian motion, resulting from the random movements and collisions of the particles (see Fick's laws of diffusion).
Fick's law describes diffusion of an admixture in a medium. The concentration of this admixture should be small and the gradient of this concentration should be also small. The driving force of diffusion in Fick's law is the antigradient of concentration, − ∇ n {\displaystyle -\nabla n} .
The flux or flow of mass of the permeate through the solid can be modeled by Fick's first law. J = − D ∂ φ ∂ x {\displaystyle {\bigg .}J=-D{\frac {\partial \varphi }{\partial x}}{\bigg .}} This equation can be modified to a very simple formula that can be used in basic problems to approximate permeation through a membrane.
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.
Reaction–diffusion systems are naturally applied in chemistry. However, the system can also describe dynamical processes of non-chemical nature. Examples are found in biology, geology and physics (neutron diffusion theory) and ecology. Mathematically, reaction–diffusion systems take the form of semi-linear parabolic partial differential ...
Momentum: the drag experienced by a rain drop as it falls in the atmosphere is an example of momentum diffusion (the rain drop loses momentum to the surrounding air through viscous stresses and decelerates). The molecular transfer equations of Newton's law for fluid momentum, Fourier's law for heat, and Fick's law for mass are