Transport Phenomena Fundamentals, 4th Edition

7

Conservative Transport and Waves

7.1 Introduction

Diffusion as a process can be modeled by considering random walks of particles along a line. We can show that if we had a totally uncorrelated random walk (equal probability of a particle taking a step forward or backward) we could predict the location of the particle at any time by solving the diffusion equation (7.1). This is true even if we superimpose some background velocity on the particles.

∂Ψ∂t=−vx∂Ψ∂x+12Dab∂2Ψ∂x21-DDiffusionequation

(7.1)

Here Ψ represents the probability that the particle is located at x ± Δx at a time t ± Δt, v_x is some average background velocity ...