advektiondiffuusion

Advection diffusion describes the combined physical process of transport of a substance or property by bulk fluid motion and its dispersion due to random molecular motion. This phenomenon is fundamental in understanding how quantities like heat, chemical species, or momentum spread within a fluid. Advection refers to the movement of the substance along with the flow of the fluid itself. Imagine a dye released into a river; the advection term represents the dye being carried downstream by the river's current. Diffusion, on the other hand, accounts for the spreading of the substance due to the random, microscopic movements of its constituent particles. This occurs even in a stationary fluid and leads to a gradual homogenization of the substance's concentration over time.

In mathematical terms, the advection diffusion equation is a partial differential equation that models this combined process. It typically consists of two main terms: an advective term, which is proportional to the velocity of the fluid and the gradient of the substance's concentration, and a diffusive term, which is proportional to the diffusion coefficient and the Laplacian of the concentration. The interplay between advection and diffusion determines the overall spatial and temporal distribution of the substance. High advection rates tend to stretch and distort concentration gradients, while diffusion acts to smooth them out. This equation finds wide applications in fields such as fluid dynamics, meteorology, chemical engineering, and environmental science for simulating pollutant transport, heat transfer, and the spread of solutes.