 # Electric field strength modelling in a conductive liquid?

Hi All,

I’m looking for a user-friendly way of 3D modelling electric fields in a conductive medium such as an electrolyte solution. The field will always be steady-state DC and generated be a simple set of electrodes (usually only 2, perhaps more later). The electrodes will generally have a fairly straightforward geometrical shapes. We need to model the resulting field in order to determine the resulting field strength at any point in the liquid. The aim is to maximise field strength at specific locations by way of optimisation of electrode geometry and position.

Does anybody have any knowledge of any suitable plug-in for Rhino (preferably V5) which will achieve this?

I assume this is an engineering/science project so you need reasonably accurate results.

Steady state DC electrical fields are governed by Laplace’s equation so you may need a Laplace equation solver. Thermal conductivity is

How complicated is the geometry? If it is two (or more) electrodes in an “infinite” medium and the electrodes can be considered as “points” then an exact, simple mathematical solution for the field is available. Note that an electrode can be considered to be a “point” if it’s dimensions are small compared to it’s distance from locations of interest. “Infinite” means that any boundaries are sufficiently far from the electrodes and any locations of interest. If the electrodes can not be considered as “points” and/or the fluid is not “infinite” then the solution becomes more complicated. Depending on the geometry the solution my required a Laplace equation solver.

It seems like, possibly, Grasshopper might have some tools that could help.

-Pascal

This looks reasonable for point electrodes in a 2D situation. Anyone looking for accurate solutions in 3D should remember that 3D solutions are not simply a set of 2D solutions or a revolved 2D solution.

Thanks for the replies so far.

The application is in fact an industrial one. Unfortunately because of commercial confidentiality issies I can’t reveal too much about it at the moment.

The particular geometry of the systems of interest is such that fluid can indeed be considered to be infinite but the electrodes cannot be considered as point sources (we’re interested in relatively near-field voltage gradients).

I confess that I was rather hoping to avoid trying to use Grasshopper to do what we need to do. Although we do have some useful experience with Grasshopper, I don’t underestimate the complexity of the simulation required and I fear that we could spend far too much time in Grasshopper-land only to end up with uncertain results. Hence a ready-made simulator would be our preference. A Rhino plug-in would be our first choice as it would integrate nicely with the rest of our development activities but if this isn’t available then another (non-Rhino) simulation package would certainly be worth considering. I stress that we are able to spend money here and we’re not simply looking for a freebie.

Any further thoughts gratefully appeciated… Thanks.

Assuming the medium is uniform then two types of field solvers for Laplace’s equation should be available. One general type of solver starts with the differential form of the field equation, ie Laplace’s equation, uses finite difference/finite volume/finite element methods. It needs a mesh throughout the field. It solves for the solution everywhere in the field.

The other type of solver starts with the integral form of the field equation and uses a distribution of singularities on the boundaries. The mesh only needs to cover the boundaries, It solves for the strength of the boundary singularities and then calculates the field at the desired locations. This type of method is referred to as a “panel method” in aerodynamics and a “boundary element method” or “BEM” method in some other fields.

Thanks davidcockey.

Do you know of any likely software packages which would be worth looking at? Of course the budget isn’t unlimited but the complexity of problems to be solved is probably quite low (given what I would expect a high-end package to be capable of). That said, useability would be a factor, especially as the field theory lectures during my learning years (approximately 150 years ago) weren’t something that filled me with joy, so useability probably scores above being low-cost.

@davidcockey
Dang. This is why I love this forum. How come you know all this stuff anyway??

-Pascal