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I don't know where to start with the following problem:

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Can anyone give me any pointers?

(For maximum assistance, please adapt your responses and solutions to be understood by a beginner, prefacing and explaining what you are doing so I can follow along.)

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    @r.e.s. If you feel up to it, perhaps you could kindly suggest a complete answer below?2011-11-27

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The left- and right-hand sides of the conservation-of-mass equation

$\frac{\partial c}{\partial t} = - \frac{\partial q}{\partial x}$

are assumed to be everywhere-continuous functions of spatial coordinate $x$ and time $t$, with $c$ being the solute mass concentration (density).

The equation expressing "Fick's Principle" can be derived by fixing $t$ and integrating both sides of the above equation with respect to $x$ over a finite interval, say $[x_1, x_2]$:

$\int_{x_1}^{x_2}\frac{\partial c}{\partial t}\, dx = - \int_{x_1}^{x_2}\frac{\partial q}{\partial x}\, dx$

$\frac{\partial}{\partial t} \int_{x_1}^{x_2}c\, dx = -(q(x_2,t) - q(x_1,t))$

$\frac{\partial }{\partial t}m = q_{in} - q_{out}$

where $m$ is the solute mass in the interval at time $t$.


For similar derivations in the rather more-complicated case of three spatial dimensions, see continuity equation.

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    As far as I'm concerned, it wasn't out of order at all; I'm glad you answered it rather than waiting around! For me it was purely a math problem, and since I know so little about physics it was best to treat it as such.2011-11-28