Simulation of 3D resistance problem

Hii,

I am an electrical engineer but I feel myself too weak when I try to solve the problem.

I am trying to simulate an artificial experiment which is:

Let's place a gold piece which is about 10x10x10cm. Let's place it to the bottom of a pool and fillet with a liquid with which the resistivity is well known.

Question is very simple. I wanna to apply a current flow from the system where a two electrodes placed any two position at the top surface of liquid. Lets imagine that we make voltage measurement at the liquid surface between two different position and record the value. Lets change the measurement probes a lot of different positions and record the results.

We have to repeat all experiment with changing the position of supply electrodes also.

Therefore we have alot of records. My question is how can we calculate exact size and position of the gold piece in the pool by using the experiment records?

general resistivity formula is R=resistivity x length / cross area at wire etc which we learned in past.

My second target is to find best measurement techniques by this simulation tool. I am not familiar with matlab and finite element techniques that we need to model and simulate that I believe.

I became really crazy because I can not formulate/imagine 3D resistance.

Would you help me please?
 

anorlunda

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Wow, that sounds difficult. If I understand correctly, you want a measurement scheme that somewhat resembles a CAT scan (computed tomography). That sounds plausible. But first you would need the support of much experimentation to determine how the signals you measure vary as you move the sources and the size/shape of the target.

I think that's far to big a question for an Internet forum.

Good luck.
 
Yes i understand the difficulty. But i believe we should able to develop-imagine this artificial test and find/create a model to simulate. But i could not yet.
 

berkeman

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But i believe we should able to develop-imagine this artificial test and find/create a model to simulate.
Sure, it's done all the time with tools like Ansys and Comsol. You can also make your own simulation using Excel. You can refine that Excel simulation by making your grid finer and finer...
 

anorlunda

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I would begin with experiments, rather than simulation.

You also have to ask yourself if this new resistance-based method would be better than sonar. Modern sonars do a very good job of making remote images of objects.
 
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I understand you want to do a simulation instead of actual measurements. I am assuming for purposes of simulation, the container of liquid has a bottom of defined depth but essentially no boundaries.

For purposes of understanding the problem better I'm going to propose another setup. Suppose there are two electrodes in the liquid more than 15 cm apart. If there is a potential between the electrodes and you use a high impedance probe immersed between them, you should see a voltage on the probe at some value between the values of the two electrodes similar the the wiper of a pot. If you plot the values of equal potential as measured by the probe, I believe they will follow hyperbolas with the electrodes at the foci. If you then draw contours connecting the hyperbolas, always crossing the hyperbolas perpendicularly, you should have a series of concentric ellipses with the electrodes at their foci. The ellipses would be contours of equal conductivity. Now if you add the gold piece (assuming the gold piece has much less resistivity than the liquid) the contours of equal conductivity will be pulled towards the gold piece which means the hyperbolic contours have also been altered.

With your setup you are measuring the conductivity directly. You will have concentric ellipses of equal conductivity between your two electrodes also. As a contour intersects the gold piece it will be short circuited by the gold meaning for that distance it will no longer be an ellipse but a straight line. if you know the conductivity between the electrodes without the gold piece in the liquid and assuming the conductivity of the gold piece is much, much higher, by noting the conductivity between the electrodes you should be able to deduce how much liquid there is between the electrodes and thus which conductivity ellipses are intersecting the gold piece. That can tell you the distance the electrodes are from the gold piece or if you plot the rate of change of the contour values as you move your electrodes in different directions, you may get a rough image of the gold piece.

It may be worth learning MatLab or some other computer language to do this simulation. It may even be possible to simulate it in Excel but it would be very cumbersome.
 
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placed any two position at the top surface of liquid. Lets imagine that we make voltage measurement at the liquid surface between two different position and record the value. Lets change the measurement probes a lot of different positions and record the results.

We have to repeat all experiment with changing the position of supply electrodes also.

Therefore we have alot of records. My question is how can we calculate exact size and position of the gold piece in the pool by using the experiment records?
in most cases, this technique will provide zero-valuable results..

1. for many cases, current will go through only liquid ambient == actually, any flow always goes through paths of minimal resistance.
2. if brick is put between two electrodes & current runs through it, it's very unlikely that moving brick closer towards anode or cathode will change the resistance of entire path/conductor (between electrodes).
3. Vortexes of liquid can change resistance of ambient.
 

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