Marks Final Notes - Drop Pinch Off

The camera does not support autofocus. Autofocus is the last thing we would want anyway because it would focus on pretty much everything in the field of view except for the precise location on the drop we are interested in. Additionally, pushing a button to achieve focus means the students would never look at nor think about where the focus is, which is in direct opposition to the teaching goals of the lab.

Camera serial #01398 has a damaged frame advance dial. When functioning properly this dial allows you to advance a video frame by frame when rotated, or in 10 frame increments when pushed in while rotating. This camera will only advance one frame at a time. The “push in” to advance in 10 frame increments is broken. This could be due to ordinary wear and tear, or someone may have mashed it too hard.

The cameras are built with a cs lens mount. In my experience cs lenses are generally crap and very expensive, and I don't know if you can find a macro cs lens for a reasonable price. I bought a Nikon f-mount to cs mount adapter, the blue coupler. The Nikon f-mount has one of the largest arrays of lens options going back decades. The older, manual focus lenses are optically fantastic for what we are doing and can be found used for very little money.

The ring on the blue mount adapter can be rotated to change the aperture of the lans which controls how much light reaches the sensor. It also has a very small effect on the depth of field, basically negligible. In order for this ring to function properly, the aperture of the lens must be set as shown, with the yellow line aligned with the number 32. In camera terms you are setting the camera to f/32 which is the smallest possible aperture, the adapter works by changing the aperture between the limits of full open f/2.8 to whatever is set by the yellow line.

Students can do the whole lab using the Tokina 100mm macro lens. Closest focus (highest magnification) is achieved when the lens tube is fully extended. At closest focus the subject distance is somewhere around 9“ from the lens. In principle higher magnification can be achieved by pushing the lens further from the image sensor by inserting the Kenko extension tubes between the lens and the mount adapter. There are two sets of extension tubes, each set composed of three pieces that can be inserted individually or in combination. If you use all three pieces you increase the magnification of the lens by a factor of about 1.4.

In practice students do not really need this, though it can help get better spatial resolution of the neck radii for the glycerine sample.

This lens is really not needed, though if used correctly it gives really nice results. It can be set to magnifications between 2.5 and 5. I would only offer it to students who seem to be doing really well and who are interested. There is only one of these lenses.

This lens is challenging to use. With these high magnifications you lose a lot of light and the field of view is narrow. So getting adequate lighting and just finding the subject can be tough if you are not used to working with this type of camera.

The lens is fixed focus. The ring which seems to be acting like a focus is actually setting the magnification according the markings on the barrel. Once you set the magnification you have to move the whole camera (or the subject) back and forth to achieve focus.

The aperture of the lens is set by the ring at the end of the lens furthest from the body of the camera. Due to lighting considerations, the aperture should always be wide open f/2.8.

The above photo shows a complete setup.

• Camera with Tokina 100mm Macro lens on translation stages.
• Make sure the camera has a memory card.
• It is good practice to remove the power cable to ensure the system really starts up in its default configuration.
• 50ml fluid dropper with the medium (II) 0.25mm nozzle installed.
• Beaker to collect water.
• Lab Jack to allow beaker height from dropper to be varied.
• Diffuser screen. The last couple years I have used a photographic translucent paper, but a single sheet of white printer paper works just fine.
• Bright light source. The brighter the better as the camera.
• Sponge for cleaning up spills.

For the first task, playing with the camera, I usually set out some matches, balloons, a Bic lighter and tuning forks.

I strongly recommend not setting out the extension tubes or the ultra macro lens. Doing so results in the students using them “because the wiki said to”, which is what I do not want. The intent of the lab is that students should only go to higher magnifications when they can justify the need based on what they see in the data and the videos. If they want higher magnification than the Tokina lens gives them, ask why and how much extra magnification do they need. Thinking and understanding is the point.Going to higher magnification because it is possible is not thinking and poor practice.

FFmpeg is the program to convert the cameras video codec from mp4 into avi which imagej can work with. It needs to be on the lab computer. In principle it should be able to be installed in the applications folder with the path set so that it can be invoked from anywhere on the machine. However the app does not come with an installer, and I could not figure out how to get the path setup correctly. So I just put a copy of the FFmpeg executable on the desktop and the lab wiki tells the students to put a copy in the directory they create where they store their video files. In other words you run the app out of the same directory as your video files. Shortcuts do not seem to want to work.

The latest version of FFmpeg can be found at FFmpeg.org

FIJI is the most up to date version of ImageJ. It is a free download and can be found at imagej.net

Each of the two setups has its own set of 3 different size nozzles.

The nozzles themselves are just plastic hose connectors that we had lying around. All of the nozzles have a 0.7mm inner diameter opening on one end, this is the end which gets inserted into the rubber hosing at the bottom of the dropper. The other end of the nozzles varies in size as follows:

The measurements of the medium and large were made using a caliper with the inner diameter prongs. For the small nozzle I found a magnet wire that just fit inside the aperture, then used the calipers to measure the diameter of the wire.

Note that there is nothing quantitative that students have to do with these values, small medium and large are perfectly fine distinctions. There is also nothing to be gained by increasing the range of diameters, these three are enough to show a trend in the data from small to larger.

Note that the smallest diameter nozzle is the tip of one of the small disposable pipets that has been press fit into the larger nozzle. It works better than I expected.

Nozzle II should already be in use from day 1, all that is needed is to add nozzles I and III.

Swapping the nozzles is a simple matter of carefully sliding them into and out of the tygon tubing at the bottom of the dropper.

There is confusion by the students over the point of the Day 2 investigation of the effect of nozzle size on the development of the neck.

Simply stated, the power laws we get from dimensional analysis do not include the diameter of the nozzle. This is justified by saying the minimum neck size is much smaller than the nozzle size.

But observation of the early part of the drop pinch off profile clearly shows that the minimum neck size is on the same order of magnitude as the nozzle size. Furthermore as the process progresses the minimum neck size becomes increasingly smaller and at some point can be said to be much smaller than the nozzle size. So over some region of the data the assumption that the nozzle size can be neglected is not necessarily valid.

The point of investigating this is to determine if and when the nozzle size can be neglected. We are testing an assumption in the model.

Here are two images from the same drop.

Image #1 here shows the drop early in the pinch off process. The diameter of the neck is about 250 pixels and the minimum diameter of the neck is about 210 pixels. I would not consider 210 to be “significantly” smaller than 250.

Image #2 shows the same drop, but later in the process. Now the minimum diameter of the neck is about 35 pixels which is reasonable to consider being “significantly” smaller than 250 pixels.

Ideally this is exactly what I would like the students to be able to do in terms of articulating the problem. Take individual frames from the video, measure the relevant dimensions, then note that the assumption is less likely to hold for Image #1 but more likely to be good for Image #2.

Then they need to make a more detailed and scientifically plausible argument. This is where they proceed to record videos of the whole process for water, one video for each of the three nozzle sizes is good enough. Here is the result.

This plot clearly shows that the minimum neck radius follows basically the same power law behavior for all three nozzles once the time from pinch off gets below 0.01s.

For times from pinch off larger than 0.01s all three data sets diverge from the power law behavior. Some things which should be immediately obvious are:

1. The smaller the nozzle the more this part of the data diverges.
2. In this time range the behavior does not follow any fixed power law.
3. All three nozzles appear to begin diverging at about the same time relative to the moment of pinch off.

We can go a bit further however, and try fitting the data below 0.01s to one of the power law models. Doing this for a power of 2/3 gives this.

This makes it visually even more convincing that the assumption of being able to neglect the size of the nozzle begins to break down.

From this I think you can conclude that:

1. The approximation for neglecting nozzle size does not hold early in the process.
2. The power law behavior is essentially the same for all three nozzles beyond 0.01s.

For day 3 nozzle II is used, the other two can be put away.

The only other change is to have the glycerine samples prepared. Since Glycerine is so hygroscopic I mix up a fresh batch each quarter and check them. The recipe I use is 15ml tap water added to 75ml glycerine. This gives a viscosity that displays the very thin thread near pinch-off. Any solution remaining in the 150ml beaker I cover with a piece of wax paper with a rubber band to minimize contact with the air in the lab.

Note that if poured into a dropper, any water that is still inside the dropper will mix with and can change the viscosity of the solution by noticeable amounts. For this reason, it should be assumed that the viscosity of the samples changes from day to day. So it is important that the zoomed out view of the whole process and the close up view be recorded in the same lab period. If students need to come back to redo either part, zoomed out or zoomed in, they need to redo it all. Otherwise the data will not be compatible.

For day 2 students will continue to work with water.