Reaction–diffusion–advection equation

From Wikipedia, the free encyclopedia
Jump to: navigation, search

The reaction–diffusion–advection equation is a partial differential equation that models the concentration of a chemical species in a classical reaction–diffusion–advection process. In that process, a chemical species undergoes a reaction, can diffuse in the solvent, and is transported by the bulk movement of the solvent (advection). The equation modeling the concentration u(\boldsymbol{x},t) (units: M),  \boldsymbol{x} \in \mathbb{R}^n of the chemical species u is:

 \frac{\partial u}{\partial t} + \nabla \cdot \left( \boldsymbol{v} u - D\nabla u \right) = f,

where D is the diffusion coefficient (units: length2 /time),  \boldsymbol{v} \in \mathbb{R}^n is the bulk velocity (units: length/time), and  f (units: M/s) is the reaction term that models the generation or decay of the species u. In general, each  f,D, and  \boldsymbol{v} may depend on space, time, or the concentration of u itself. The equation above is a conservation of mass in a continuum model, where accumulation at a point is the next flux (rate in minus rate out) of a point plus the generation at that point (see continuity equation).

See also[edit]