linguistic:translation
Definition of diffusion flux

Each model of diffusion expresses the diffusion flux with the use of concentrations, densities and their derivatives. Flux is a vector J {\displaystyle \mathbf {J} } representing the quantity and direction of transfer. Given a small area Δ S {\displaystyle \Delta S} with normal ν {\displaystyle {\boldsymbol {\nu }}}, the transfer of a physical quantity N {\displaystyle N} through the area Δ S {\displaystyle \Delta S} per time Δ t {\displaystyle \Delta t} is

where (J, ν) {\displaystyle (\mathbf {J},{\boldsymbol {\nu }})} is the inner product and o (⋯) {\displaystyle o(\cdots)} is the little-o notation. If we use the notation of vector area Δ S = ν Δ S {\displaystyle \Delta \mathbf {S} ={\boldsymbol {\nu }}\,\Delta S} then

The dimension of the diffusion flux is = /(·). The diffusing physical quantity N {\displaystyle N} may be the number of particles, mass, energy, electric charge, or any other scalar extensive quantity. For its density, n {\displaystyle n}, the diffusion equation has the form

where W {\displaystyle W} is intensity of any local source of this quantity (for example, the rate of a chemical reaction).For the diffusion equation, the no-flux boundary conditions can be formulated as (J (x), ν (x)) = 0 {\displaystyle (\mathbf {J} (x),{\boldsymbol {\nu }}(x))=0} on the boundary, where ν {\displaystyle {\boldsymbol {\nu }}} is the normal to the boundary at point x {\displaystyle x}.