Team:Valencia UPV/prueba

Diffusion

The diffusion equation is a partial differential equation which describes density dynamics in a material undergoing diffusion. It is also used to describe processes exhibiting diffusive-like behavior, like in our case.

The equation is usually written as:

where ϕ(r, t) is the density of the diffusing material at location r and time t and D(ϕ, r) is the collective diffusion coefficient for density ϕ at location r; and ∇ represents the vector differential operator del.

If the diffusion coefficient does not depend on the density then the equation is linear and D is constant.

Thus, the equation reduces to the following linear differential equation:

also called the heat equation.

Making use of this equation we can write pheromones chemicals diffusion equation with no wind effect consideration as:

Where C is the pheromone concentration, ∇ is the Laplacian operator, and D is the pheromone diffusion constant in air.

If we consider the wind, we face a diffusion system with drift and an advection term is added to the equation above.

v is the average velocity that the quantity is moving. Thus, v would be the velocity of the air flow.