• Experimental research can be exploratory or discovery based. As opposed to testing models or theoretical predictions, or making precise measurements of a specific quantity like the mass of the Higgs boson.
• The human eye brain combination is a valuable “tool” for experimental work, but it needs training.
• For extremely complex systems, such as fluid dynamics, it is often not practical to begin with a first principles approach to model building. In these cases you use experiment and observation to deduce the most important physical parameters involved and to learn something of their functional relationship to one another. This can then lead to deeper and more rigorous studies.
• Scaling laws are a powerful tool.

• Ask the students to say something about what, if any background they have in fluid dynamics. Then review with them the basic parameters of surface tension, viscosity, and density and how each contributes to the shapes you see in fluids.
• Ask the students what they observed in the videos and images of the drop pinch-off process. The goal is to get them tuned in to looking for and seeing the macroscopic behaviors which imply something about the physics. In particular:
  • How the shape of the profile of the drop takes on different characteristics at different times in the pinch off process.
  • How the different shapes provide information about what the important physical parameters are.
  • That there are regions where the characteristic shape of the fluid remains constant, and that this implies that the underlying physical processes in play are not changing.
• Outline the basic process of learning about such a system:
  • Start by observing drops pinching off in slow motion by recording and viewing videos of the process. Try to identify which parts of the video suggest that a particular set of physical parameters is dominant.
  • Now that you have some intuition about what you are seeing in the video, measure minimum neck radii as a function of time from the moment of pinch off.
  • Plot r_min vs. t_pinchoff on a log log scale and look for regions of the data that clearly (to your eye) show a fixed powerlaw relationship.
  • Look back at the video and ask yourself if these apparent power law regions make sense in terms of what you see happening.
  • Use dimensional analysis to try and find a combination of relevant physical parameters which produce a function with a power law exponent that matches the power laws you have uncovered in the data. Ask yourself if the combination of parameters in these functions make sense in terms of what you observe in the video.

Try to present this discussion in a way that emphasizes the fact that the “process” for this experiment is kind of backwards from what they are used to. Make sure they understand that they are not trying to get some number which they can compare to a prediction or any known value. The whole point of the experiment is to gain insight into a seemingly simple but actually very complex phenomena.

Note that they are expected to discover as many distinct power law regions as they can for glycerine/water mixtures ranging from pure water to pure glycerine and something in between those two extremes. For each region their goal is to determine what are the dominant physical parameters that are determining the shape of the drop.

A good “script” to give the students is to first learn how to use the camera to obtain a well focused video of the entire pinch off process for a mixture of glycerine and water. They should not worry about trying to get everything “right” with this first video, that is unrealistic as working with cameras and fluids takes practice.

Once they have their first video they should export it to the computer, convert it from MP4 to AVI format, read it into ImageJ, spend some time studying it by eye and then make measurements of the minimum neck radii.

Then plot this data and see what potential power laws might be present.

At this point they will have learned a lot about the experimental process as well as gained some intuition into what is happening. The next steps are determined by what they learn from taking, processing and analyzing this first video.

At a minimum each group of students should be able to get one movie of the whole drop pinch off process, export it to the computer, read it into ImageJ, measure neck radii and make a log-log plot of the data.

When they get to that point the students should find one of the lab staff to show them their preliminary results and we will help them figure out what the next steps should be.

A good goal for the end of the first two days in lab is to have recorded and analyzed videos of the drop pinch off process, including zoomed in videos, for three different solutions; 100% glycerine, mixture of glycerine and water, 100% water. They should have identified power law regions and constructed models for each solution, and have some understanding of what the data and models imply about the physics at play in the different regimens that that see.

At a minimum they should have done all of the above for at least one of the solutions.

After looking over the analysis which the students submit, you should be able to develop an idea where each group stands. Different groups will likely be at different places in terms of how far they have gotten, how good their data look, and how well they understand what they are doing. Based on where a particular group is after the first two days in lab there are two likely paths for day three.

1. Students have not completed collecting and analyzing data for all three solutions. Or they have significant amounts of work which may need to be redone such as poor movie quality. For these groups you should work with them to make sure that they understand where they need to improve their results and that work constitutes their day 3.
2. If the students have done the above completely and well, then they can move on to looking at the pinch off process at the top of the neck with the goal of determining if it is indeed the same as the process at the bottom.