0
$\begingroup$

I am trying to model transport of ions (calcium, potassium, chloride etc.) in water. The ions move because of the influence of diffusion and electric force and can be modeled by the Poisson-Nernst-Planck equation. My question is the following. Is the normal component of electric displacement field continuous inside the solvent? I know it is discontinuous whenever there is any surface charge density. Now at any time instant, at any point in the water, there can be an ion. So will that mean that the normal component of electric displacement field is discontinuous, since we have a surface charge density because of that ion?

Also if one assumes the electro-nutrality condition, then one would have no effective charge at any point at any time in the water. Then can we say that the continuity of the normal component of electric displacement field is achieved?

Improve this question
$\endgroup$

1 Answer 1

Reset to default
0
$\begingroup$

In these type of equations, point charges no longer exist. You calculate your species with densities, smeared out point charges over the domain. This is also true for the electromagnetic fields, but less obvious and is of course an approximation. Think of it as particle motions are now governed by external fields and internal averaged fields, smoothed in space and time. If you want to learn more about this type of averaging a good starting point is the argumentation for the Vlasov equation.

So to answer your question, the displacement field in this sense of averaging is continuous.

Improve this answer
$\endgroup$
1
  • $\begingroup$ Thanks for your comment. I think you mean in this case one assumes continuous charge distribution. But even in the case of continuous charge distribution why the electric field needs to be continuous? $\endgroup$
    – abir
    Commented Sep 24, 2020 at 12:08

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.