Revisiting Discrepancies in Diffusion Theory: The Solution to Milne’s Problem for B-particles

Table of Links

Abstract and 1 Introduction

2 Preliminary material

3 Comments elicited by the solution to Milne’s problem for B-particles

4 Flux to a spherical trap

5 Molecular motion in liquids

6 Concluding remarks and References

3 Comments elicited by the solution to Milne’s problem for B-particles

Far from the wall the density increases linearly with distance, as one expects from the diffusion equation. When this asymptotic solution is extrapolated across the boundary region it reaches zero not at the wall (as the solution of the diffusion equation with absorbing boundary would) but at some distance beyond it. The value we find for this “Milne extrapolation length” is, in the appropriate dimensionless units, approximately twice the value found in the radiative transfer problem. The density in the actual solution is everywhere lower than that of the extrapolated asymptotic solution, but of course it stays finite at the wall.

3.1 Length scales for Brownian moton and its inverse

3.2 Profiles of particle density