How do you use the diffusion equation?
How do you use the diffusion equation?
- = ∇·(D(u(r,t),r)∇u(r,t)), (7.1)
- where u(r,t) is the density of the diffusing material at location r = (x,y,z) and time. t. D(u(r,t),r) denotes the collective diffusion coefficient for density u at location r.
- If the diffusion coefficient doesn’t depend on the density, i.e., D is constant, then. Eq. (
What is diffusion variable?
The rate of diffusion INCREASES as the concentration gradient (difference in concentrations of the two sides) INCREASES. The rate of diffusion INCREASES the larger the surface area of the exchange surface. The rate of diffusion INCREASES the thinner the exchange surface.
What is DuFort Frankel method?
— The Du Fort-Frankel scheme is studied as an itérative method to solve the linear System Au = f where A is a complex N xN matrix. Stability conditions are given in terms of the eigenvalues of A. An error estimate ispresented. In order to provide afaster convergence, the optimal choice of the parameters is analysed.
Is DuFort Frankel scheme consistent?
For h→0, we see that the DuFort-Frankel scheme is consistent with the hyperbolic equation ∂U∂t+r20∂2U∂t2=∂2U∂x2 and not with the original diffusion equation.
Why is the diffusion equation?
The diffusion equation is a parabolic partial differential equation. In physics, it describes the macroscopic behavior of many micro-particles in Brownian motion, resulting from the random movements and collisions of the particles (see Fick’s laws of diffusion).
What are the 3 variables in the numerator of Fick’s Law of diffusion?
Fick’s Law essentially states that the rate of diffusion of a gas across a permeable membrane is determined by the chemical nature of the membrane itself, the surface area of the membrane, the partial pressure gradient of the gas across the membrane, and the thickness of the membrane.
