A slab of gel occupies and is sealed at both ends so that no dye can cross or (a…

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Partial differential equations and boundary-value problems · Partial differential equations and boundary-value problems

Computational Physics, Ch Rules on a lattice: diffusion, percolation and growth

Problem

A slab of gel occupies

0 \le x \le 0.20\,\mathrm{m}

and is sealed at both ends so that no dye can cross

x=0

x=0.20\,\mathrm{m}

(a zero-flux boundary at each end). At

t=0

the left half (

0 \le x < 0.10\,\mathrm{m}

) holds dye at concentration

8.0\,\mathrm{mol\,m^{-3}}

and the right half (

0.10\,\mathrm{m} \le x \le 0.20\,\mathrm{m}

) holds it at

2.0\,\mathrm{mol\,m^{-3}}

. Diffusion then proceeds with no other process acting. Predict the concentration profile once a very long time has passed, and state the physical quantity that is conserved by a zero-flux boundary and that fixes your answer.

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