Drift–diffusion equation
The convection–diffusion equation is a combination of the diffusion and convection (advection) equations, and describes physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes: diffusion and convection. Depending on context, the same equation can be called the advection–diffusion equation, drift–diffusion equation, or (generic) scalar transport equation.
The general equation is
where
The right-hand side of the equation is the sum of three contributions.
In a common situation, the diffusion coefficient is constant, there are no sources or sinks, and the velocity field describes an incompressible flow (i.e., it has zero divergence). Then the formula simplifies to:
In this form, the convection–diffusion equation combines both parabolic and hyperbolic partial differential equations.
The stationary convection–diffusion equation describes the steady-state behavior of a convective-diffusive system. In steady-state, , so the formula is:
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