Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
Concept
Convection–diffusion equation
Summary
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
c is the variable of interest (species concentration for mass transfer, temperature for heat transfer),
D is the diffusivity (also called diffusion coefficient), such as mass diffusivity for particle motion or thermal diffusivity for heat transport,
v is the velocity field that the quantity is moving with. It is a function of time and space. For example, in advection, c might be the concentration of salt in a river, and then v would be the velocity of the water flow as a function of time and location. Another example, c might be the concentration of small bubbles in a calm lake, and then v would be the velocity of bubbles rising towards the surface by buoyancy (see below) depending on time and location of the bubble. For multiphase flows and flows in porous media, v is the (hypothetical) superficial velocity.
R describes sources or sinks of the quantity c. For example, for a chemical species, R > 0 means that a chemical reaction is creating more of the species, and R < 0 means that a chemical reaction is destroying the species. For heat transport, R > 0 might occur if thermal energy is being generated by friction.
∇ represents gradient and ∇ ⋅ represents divergence. In this equation, ∇c represents concentration gradient.
The right-hand side of the equation is the sum of three contributions.
The first, ∇ ⋅ (D∇c), describes diffusion. Imagine that c is the concentration of a chemical. When concentration is low somewhere compared to the surrounding areas (e.g. a local minimum of concentration), the substance will diffuse in from the surroundings, so the concentration will increase.
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.