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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 ...
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 ).
Darken’s equations can be applied to almost any scenario involving the diffusion of two different components that have different diffusion coefficients. This holds true except in situations where there is an accompanying volume change in the material because this violates one of Darken’s critical assumptions that atomic volume is constant.
We obtain the distribution of the property i.e. a given two dimensional situation by writing discretized equations of the form of equation (3) at each grid node of the subdivided domain. At the boundaries where the temperature or fluxes are known the discretized equation are modified to incorporate the boundary conditions.
The convection–diffusion equation describes the flow of heat, particles, or other physical quantities in situations where there is both diffusion and convection or advection. For information about the equation, its derivation, and its conceptual importance and consequences, see the main article convection–diffusion equation. This article ...
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.
Solution of equation: 1. For solving the one- dimensional convection- diffusion problem we have to express equation (8) at all the grid nodes. 2. Now obtained set of algebraic equations is then solved to obtain the distribution of the transported property .