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Maxwell stress, fluid volume force, axisymmetric

The below post is related to an archived discussion


So I have seen variations of this question around, like in the post above, but I still cannot make out the right answer for my problem.

I am simulating two-phase flow in an electrostatic field in a 2D axisimmetric domain. The two fluids have a different permittivity Image may be NSFW.
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, so that dielectrophoretic body forces are expected. I hoped that there was a ready made Multiphysics coupling for that, but there seems to be none in 5.4 + my set of modules.

Ok, modelling then. In the laminar flow physics tree, I add a volume force node. My understanding is that the force is given by the divergence of the stress tensor, as Image may be NSFW.
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. In cylindrical coordinates, that amounts to, for the two components r, z (e.g. wikipedia):

Image may be NSFW.
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Image may be NSFW.
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The question is how to write this force term inside Comsol. I'm confused among three possibilities:

  1. like written above, translated in code:
epsilon0_const*( d(es.epsilonr_iso*(es.Er^2-es.Ez^2)/2,r) + d(es.epsilonr_iso*es.Er*es.Ez,z) + es.epsilonr_iso*(es.Er^2-es.Ez^2)/(2*r) )
epsilon0_const*( d(es.epsilonr_iso*es.Er*es.Ez,r) + d(es.epsilonr_iso*(es.Ez^2-es.Er^2)/2,z) + es.epsilonr_iso*es.Er*es.Ez/r) )

but this would be singular at the axis;

  1. removing the 1/r terms, "because in physics interfaces Comsol takes care":
epsilon0_const*( d(es.epsilonr_iso*(es.Er^2-es.Ez^2)/2,r) + d(es.epsilonr_iso*es.Er*es.Ez,z) )
epsilon0_const*( d(es.epsilonr_iso*es.Er*es.Ez,r) + d(es.epsilonr_iso*(es.Ez^2-es.Er^2)/2,z) )
  1. Multiply 1. by Image may be NSFW.
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    , which removes the singularity, because an integration over Image may be NSFW.
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    is assumed:
pi*epsilon0_const*( r*d(es.epsilonr_iso*(es.Er^2-es.Ez^2),r) + 2*r*d(es.epsilonr_iso*es.Er*es.Ez,z) + es.epsilonr_iso*(es.Er^2-es.Ez^2) )
pi*epsilon0_const*( 2*r*d(es.epsilonr_iso*es.Er*es.Ez,r) + r*d(es.epsilonr_iso*(es.Ez^2-es.Er^2),z) + 2*es.epsilonr_iso*es.Er*es.Ez) )

Anther possibility comes to mind, that is to include the diagonal contribution in the pressure and the nondiagonal contribution in the deviatoric tensor, but it doesn't seem available in the volume force interface.

Can someone clarify and advise?


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