User:Brian P. Josey/Notebook/2010/07/15

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Theoretical and Experimental Forces

After some trouble, I created a new working model in FEMM that better represents the way I have the magnet mounted on the microscope's stage. Up to this point most of my models have been best case scenario models, that focus on areas that would be unobservable in a microscope, like within a few fractions of millimeter of the cone-tip on the yoke. This new model instead focuses on what I can observe. Experimentally, the magnet is held flush to the flow cell at a 45o angle as close to the field of view without obstructing it. I would estimate this distance as being about 2.0 mm, and ran my experiment as such. After analyzing the data I gathered on the sixth, I was able to calculate the forces exerted on the ferritin. Here is the table including the forces:

View/Edit Spreadsheet

It would be more correct to say that the measured forces, Average Force on Ferritin in the table, is actually the average force ferritin exerts on the droplet, but I am assuming that they are the same. There is also the issue with the direction of the force. In the above calculation, I measured the force as the average over the whole displacement, while it would be more useful to measure the displacement along the y-axis, towards the magnet. It is also difficult to estimate the diameter of the droplets, and in turn the number of ferritin in each droplet, which could result in a miscalculation. I hope to resolve both of these issues in the coming days as I work on the LabVIEW program for this.

The model I created was a little simplified compared to the actual experiment. Since glass is non-magnetic, I substituted air for the glass as the material surrounding the flow cell. Not knowing details of the objective, I measured its outer dimensions, and ran several iterations of the problem. Each of these iterations was to test the addition of magnets and changing the properties of the objective. The iterations were:

  • Iteration 1- Only the cone was magnetized, and the objective was made from air.
  • Iteration 2- Only the cone was magnetized, and the objective was made of aluminum.
  • Iteration 3- Both the cone and longer magnet were magnetized, and the objective was made from air.
  • Iteration 4- Both the cone and longer magnet were magnetized, and the objective was made from aluminum. This iteration is the one that most closely represents the real experiment out of the six.
  • Iteration 5- Both the cone and longer magnet were magnetized, and the objective was made from a slightly magnetizable steel.
  • Iteration 6- Both the cone and longer magnet were magnetized, and the objective was made from pure iron.

The reason I created different iterations, with different number of magnets and materials was to demonstrate that neither variable has a real effect on the magnitude of the force. As can be seen in the table bellow, the average force in the field of view is unaffected by the addition of more magnets or even in the presence of an all iron objective.

View/Edit Spreadsheet

The second set of data points I acquired by altering the distance of the magnet from the field of view. I know from earlier that the field of view in the camera is about 0.12 mm in height, and in the above table the average forces are taken from the points in the first 0.1 mm of the simulation. By moving the magnet, I was able to gather data on how the distance between the tip and field of view affects the average force. As expected, as I moved the magnet farther away, the forces decrease, but all the forces remain in the 0.0001 fN to 0.02 fN range. It is clear that there is a great change in the force from even a move of 1.5 mm. The peak forces represent the points where there is the greatest calculated force and gives an average over a 0.1 mm range.

Comparison of Forces

Comparing the forces I calculated to the ones I measured reveals a marked difference between the experiment and theory. From the average forces in the experiment, I calculated an average force of 12.09 * 10-6 fN. This is much, much lower than the force I calculated from the FEMM model, even for the magnet being 2 mm away. There are a couple of possible reasons for this discrepancy. I could be estimating the distance I held the magnet at incorrectly, as 2 mm is a small size. It could also be the result from errors in how I gathered data. As I said, my estimates of droplet size was imperfect, and the force I measured wasn't directly towards the magnet. I will see if I can find some solutions to these problems, and implement them into my LabVIEW program that I am working on.

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