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Hi guys I'm totally stuck on the following question:

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We know the ionic flux between two chambers due to uneven concentration can be computed by the Nernst-Planck equation

$$j = -D_p \left(\nabla C + \frac{Z_pF}{RT}C \, \nabla\phi \right)$$

where $C$ is the concentration, $\phi$ is the potential in chambers and $Z_p$, $F$, $R$ and $T$ are constants. At equilibrium, $j = 0 $ and $$-\nabla C = \frac{Z_pF}{RT}C\, \nabla\phi$$

Can anyone solve for the Nernst Potential (equilibrium potential) $Vm$ = $\phi_i - \phi_o$, where $i$ denotes inside and $o$ denotes outside without reducing the question to one dimension? The main problem I have is taking the volume integration of $\nabla C/C$.

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  • $\begingroup$ LaTeX tips (see edit): When terms inside a set of brackets do not fit, use \left( ... \right) to ensure the brackets scale properly. In your case, some symbols may be too close to each other, or nearly touch, so use \, to add a tiny space. $\endgroup$
    – JamalS
    Commented Oct 7, 2014 at 9:02

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