What is D in the diffusion equation?

Statement. 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.

What is a reaction diffusion equation?

Reaction-diffusion equations describe the behaviour of a large range of chemical systems where diffusion of material competes with the production of that material by some form of chemical reaction. Many other kinds of systems are described by the same type of relation.

What is 2d diffusion equation?

The two-dimensional diffusion equation is ∂U∂t=D(∂2U∂x2+∂2U∂y2) where D is the diffusion coefficient. A simple numerical solution on the domain of the unit square 0≤x<1,0≤y<1 approximates U(x,y;t) by the discrete function u(n)i,j where x=iΔx, y=jΔy and t=nΔt.

What is the formula for Fick’s law?

It states that ‘the rate of diffusion is proportional to both the surface area and concentration difference and is inversely proportional to the thickness of the membrane’. Fick’s law can be written as: Rate of diffusion ∝ surface area × concentration difference thickness of membrane.

What is the dimension of d2c dx2?

5. What is the dimension of d2c/dx2? Explanation: The numerator has the dimension of cm-3 and the denominator has a dimension of cm2. Therefore, the quantity has a dimension of cm-3/cm2 which gives us cm-5 as the dimension.

What is a diffusive system?

In the strict sense of the term, reaction-diffusion systems are systems involving constituents locally transformed into each other by chemical reactions and transported in space by diffusion.

How do you find the diffusion equation?

Dividing by Δx and taking the limit Δx→0 results in the diffusion equation: ut=Duxx. We note that the diffusion equation is identical to the heat conduction equation, where u is temperature, and the constant D (commonly written as κ) is the thermal conductivity.

Is one-dimensional wave equation hyperbolic?

Yes, it is hyperbolic. If you think of ∂/∂x=X and ∂/∂t=T, the equation looks like (X2−T2)u=0, and this looks like the equation of a hyperbola.