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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 ...
This relationship is expressed by Fick's law N A = − D A B d C A d x {\displaystyle N_{A}=-D_{AB}{\frac {dC_{A}}{dx}}} (only applicable for no bulk motion) where D is the diffusivity of A through B, proportional to the average molecular velocity and, therefore dependent on the temperature and pressure of gases.
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} .
It states that the difference between the diffusive flux Fick's laws of diffusion of through the east and west faces of some volume corresponds to the change in the quantity in that volume. The diffusive coefficient of ϕ {\displaystyle \phi } and d ϕ d x {\displaystyle {\frac {d\phi }{dx}}} are required in order to reach a useful conclusion.
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).
Mathematically, mass flux is defined as the limit =, where = = is the mass current (flow of mass m per unit time t) and A is the area through which the mass flows.. For mass flux as a vector j m, the surface integral of it over a surface S, followed by an integral over the time duration t 1 to t 2, gives the total amount of mass flowing through the surface in that time (t 2 − t 1): = ^.
Discovered and stated by Isaac Newton (1643–1727), they can be formulated, in modern terms, as follows: First law: A body remains at rest, or keeps moving in a straight line (at a constant velocity), unless acted upon by a net outside force. Second law: The acceleration of an object of constant mass is proportional to the net force acting ...
The first term corresponds to Fick's law of diffusion, which gives the flux due to diffusion down the concentration gradient, i.e., from high to low concentration. The constant D A is the diffusion constant of the ion A.