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The simplest reaction–diffusion equation is in one spatial dimension in plane geometry, = + (), is also referred to as the Kolmogorov–Petrovsky–Piskunov equation. [2] If the reaction term vanishes, then the equation represents a pure diffusion process.
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 ...
Diffusion is usually in the Knudsen regime when average pore radius is less than 100 nm. For a given effectiveness factor, η {\displaystyle \eta } , and reaction order , n, the quantity β {\displaystyle \beta } is defined by the equation:
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-controlled (or diffusion-limited) reactions are reactions in which the reaction rate is equal to the rate of transport of the reactants through the reaction medium (usually a solution). [1] The process of chemical reaction can be considered as involving the diffusion of reactants until they encounter each other in the right ...
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 ).
The problem of diffusion in the atmosphere is often reduced to that of solving the original gradient based diffusion equation under the appropriate boundary conditions. This theory is often called the K theory, where the name comes from the diffusivity coefficient K introduced in the gradient based theory.
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 ...