;#; **Summer 2025 Drop Pinch Off Immersion** ;#; {{ :phylabs:lab_courses:phys-211-wiki-home:drop-pinch-off:dsc_5116.jpg?400 |}} ====== Components ====== The most important component of the experiment is the high speed camera and associate lens. Pretty much everything else can be assembled in many ways and usually from stuff you already have on hand. For this reason I will go into some detail on the camera and lenses, and what the important considerations are. A summary of the camera and lens options we use is provided at the end of this section. ===== Camera ===== The heart of the experiment is an affordable high speed camera made by Kron Technologies. I use their least expensive model which actually turns out to be the one which is best suited for this application. It has a 1240 x 1024 pixel sensor capable of up to 40k fps. Their more expensive models offer larger sensors but correspondingly lower FPS. I color is not needed so I recommend the B&W models which are less expensive. You can specify 8GB to 32GB of memory, we use 16GB which is more than enough for all of the experiments we do. In all cases you are only going to be saving and working with a small fraction of the total video. * Chronos 1.4 high speed camera, B&W, 16GB memory. https://www.krontech.ca/product/chronos-1-4-high-speed-camera/ For reasons listed below I do not recommend purchasing any of the lenses offered for the camera from Kron Tech. ===== Lenses ===== The Chronos camera takes interchangeable CS mount lenses. My experience with CS mount lenses for this application has been sub-optimal. I recommend using an older DSLR macro lens with an adapter to work with the CS mount. DSLR macro lenses are designed to perform optimally at close distances, can produce images with a 1:1 magnification factor, and work well in low light applications. There are a lot of older, but optically excellent lenses of type which are very affordable. I use a Tamron 90mm f/2.8 DI Macro lens with the Nikon F mount. These lenses can be found new for under \$500. And used but in excellent condition for under \$300. They are durable enough for use in a student lab. The adapter I use is a Fotodiox brand which costs \$50. Note that autofocus ability is not needed, whatever lens you choose will be used in manual focus mode. There are plenty of other brand options out there including Canon and Sony which have similar lenses, any of which will work equally well. Here are the important specs to consider: * Macro. The lens should carry the Macro designation indicating it is designed for very close up use. * I recommend a focal length of 90mm or 100mm, both of which are common. The focal length determines how far the front of the lens is from the subject at closest focus. These lenses have closest focus of about 9" which is desirable. There are macro lenses which with focal lengths of 60mm and shorter, but these need to be within 6" or less of the subject which can cause problems with lighting and are more likely to get wet from splashes. * A maximum aperture of f/2.8 or less is preferable. This determines how much light is able to reach the sensor and at high speeds you will need all the light gathering power you can get. Other lens attributes such as auto-focus, special lens coatings, etc. are not important for this application. Since the neck of the drop essentially becomes infinitely narrow as you approach the moment of pinch-off higher magnifications than 1:1 can be useful, though they are more difficult to work with. The least expensive option of achieving higher magnification is to use extension tubes. These are basically spacers that go between the camera and the lens to move the lens further away from the sensor which increases magnification at the expense of image quality. When used with the recommended lenses they can provide up to a factor of 2:1 magnification. I use a set from [[https://www.bhphotovideo.com/c/product/375238-REG/Kenko_AEXTUBEDGN_Auto_Extension_Tube_Set.html/?ap=y&ap=y&smp=y&smp=y&store=420&lsft=BI%3A514&gad_source=1&gad_campaignid=1413135038&gbraid=0AAAAAD7yMh1zhtmWM1fvkZEyBYBatvhtQ&gclid=Cj0KCQjwm93DBhD_ARIsADR_DjFHaI6H61C_Kg_L8Oip-ipydr8nwCnY4oG1ALnsRoHF5Phou-VnlgEaAmJMEALw_wcB|Kenko]] which cost about $130. ===== Camera And Lenses Used In This Immersion ===== ^ Part ^ Source ^ Cost ^ | Chronos 1.4 high speed camera, B&W, 16GB memory. | [[https://www.krontech.ca/product/chronos-1-4-high-speed-camera|KronTech]] | \$4,900 | | Used Tamron 90mm f/2.8 DI Macro (Nikon F-Mount) | [[https://www.bhphotovideo.com/c/product/803221625-USE/tamron_90mm_f_2_8_sp_af.html|Tamron 90mm Macro]] | \$219.95 | | Kenko Extension Tubes | [[https://www.bhphotovideo.com/c/product/375238-REG/Kenko_AEXTUBEDGN_Auto_Extension_Tube_Set.html/overview?ap=y&ap=y&smp=y&smp=y&store=420&lsft=BI%3A514&gad_source=1&gad_campaignid=1413135038&gbraid=0AAAAAD7yMh1zhtmWM1fvkZEyBYBatvhtQ&gclid=Cj0KCQjwm93DBhD_ARIsADR_DjFHaI6H61C_Kg_L8Oip-ipydr8nwCnY4oG1ALnsRoHF5Phou-VnlgEaAmJMEALw_wcB|Kenkop Extension Tubes]] | \$129.90 | | Photodiox CS to Nikon F-mount converter | [[https://www.amazon.com/Fotodiox-Adapter-Compatible-F-mount-C-mount/dp/B00T0QVLL2|Mount Adapter]] | \$41.36 | | Venus Optics Laowa 25mm f/2.8 2.5-5X Ultra Macro Lens | [[https://www.bhphotovideo.com/c/product/1399602-REG/venus_optics_ve2528n_laowa_25mm_f_2_8_2_5_5x.|Ultra Macro Lens]] | \$399.00 | ===== Other Components ===== You need something to create the drops and control their rate of formation. We currently use an EISCO Dropping Funnel (\$25) purchased from [[https://www.fishersci.com/shop/products/dropping-funnel-glass-key-stopcock-5/S89274|Fisher]] to generate and control the rate of drop formation. We have also used a plastic syringe we had on hand with a short piece of plastic tubing that we pinched off with a clamp whose tension could be adjusted to control the rate. To hold the dropping funnel in place and allow it to be raised and lowered we use a (\$20) [[https://www.amazon.com/veetalee-Aluminum-Photography-Compatible-Mirrorless/dp/B0D28Y8FS3/ref=asc_df_B0D28Y8FS3?mcid=f88e20e3f6a33458be808aa60863f52a&hvocijid=4412588927895571614-B0D28Y8FS3-&hvexpln=73&tag=hyprod-20&linkCode=df0&hvadid=721245378154&hvpos=&hvnetw=g&hvrand=4412588927895571614&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9021740&hvtargid=pla-2281435177858&psc=1| macro rail]] attached to a piece of scrap aluminum stock. The camera is attached to a pair of crossed [[https://www.thorlabs.com/thorproduct.cfm?partnumber=PT1B#ad-image-0 | linear translation stages]] to allow for precise focusing and centering of the drops. These translation stages cost about \$300 each. The camera and stage assembly is rigidly attached to a 12" x 24" ThorLabs [[https://www.thorlabs.com/thorproduct.cfm?partnumber=MB1224|optical breadboard]] which cost about \$300. An ordinary table lamp is used for a light source and photographic diffusion paper to diffuse its light. We have also used ordinary waxed paper from the grocery store as a diffuser with good results. ====== Investigations ====== Here are some high speed camera fluid dynamics investigations we have done or plan to do, and some ideas we have not yet tried but which should work. ===== Dimensional Analysis Models ===== As shown in our [[phylabs:lab_courses:phys-211-wiki-home:drop-pinch-off:start|Drop Pinch-Off]] lab wiki, dimensional analysis can be used to develop three power-law relationships between the minimum radius of the neck and the time from pinch-off. These relationships suggest the possibility of different regimes where different physical properties of the fluid dominate the behavior of the system. The [[phylabs:lab_courses:phys-211-wiki-home:drop-pinch-off:expected-powerlaws|development of the models]] introduces students to: * Some basic properties of fluids such as surface tension and viscosity. * Scaling phenomena. The idea that certain processes should behave the same over many order of magnitude if the underlying physics remains the same. The classic example is testing air plane models in a wind tunnel with the expectation that a full size aircraft will behave the same way. Undergraduates usually do not encounter scaling as an aspect of nature, but it is an important concept in fluid dynamics. * Dimensional analysis as a tool for developing functional relationships for phenomena which would be very difficult to approach more rigorously. These are concepts which many undergraduate physics majors typically do not see. These investigations can be conducted over a wide range of viscosities using mixtures of water and glycerine. Glycerine is safe and easy to work with and there are very clear and visually obvious differences in pinch-off behavior between pure water and pure glycerin. ===== Effects of Nozzle Size ===== In the development of the power-law relationships some possible parameters are excluded from consideration based on size considerations. For example the size of the nozzle which produces the drops is assumed to not be a factor due to the fact that its size scale is on the order of mm while the size scale on which the pinch-off occurs is on the order of microns. It is easy to provide multiple size nozzles and allow students to test whether or not this is a reasonable assumption. You can also investigate validity of the assumption that the nozzle should not effect the pinch off process when it is larger than the size of the neck. Early in the pinch off process the neck diameter is not small compared to the size of the nozzle. You can examine the data and the video during the early part of the development. Does the early development agree with any of the power law models which assume the nozzle should have no effect? How and when does the process transition into a regime where the nozzle size is unimportant. How much smaller than the nozzle does the neck have to get before this assumption holds, is this consistent across nozzle sizes. ===== Top vs Bottom Pinch Off ===== Most of the focus of these experiments is on the pinch-off of the bottom of the neck of liquid. But simple observation shows that for some viscosities the fluid in the neck pinches off at both ends. In principle there is nothing different about the physics so one would expect the process to proceed identically at both the top and bottom of the neck. This is easy to investigate for pure water. However it should be noted that when pure glycerine is used, a long thin neck develops and after the initial pinch-off occurs the neck continues to stretch and thin out, until it breaks apart at multiple locations. Each of these breaks is also a pinch-off process, and this can be seen in the videos but it would require considerable magnification to be able to analyze. ===== Establishing Repeatability ===== Intuitively students often assume that because it involves a fluid, a phenomena like drop pinch-off is kind of chaotic and each drop would look at least somewhat different from the others. For example, if multiple drops of the same fluid are examined at the same time before pinch-off occurs would the shape of each drop be exactly the same shape and size? Even more interesting is to watch the behavior of the rebounding fluid in the neck after pinch-off as it oscillates while rising, falling and possibly colliding with other small droplets formed by the process. Most students are surprised to find that if you examine the position, size and shape of the rebounding neck fluid what you see from drop to drop is remarkably consistent as a function of time from the pinch-off event. I find that this is a good opportunity to try to get students to focus their attention and thinking on what they are seeing with their eyes, rather than number and plots. ===== Splashing in a Vacuum ===== We have not tried this one, but in principle should not be too difficult. It may be more of a demonstration than a lab however. The idea is to investigate the question of how would you expect the splash of a water drop on a hard surface to be affected by the absence of Air. This is inspired by a study done by {{ :phylabs:lab_courses:phys-211-wiki-home:drop-pinch-off:physrevlett.94.184505.pdf |Lei Xu, Wendy Zhang and Sid Nagel}} where his initial though would be that the splash would be bigger with no air to oppose the motion of the water droplets. What they found however was that in vacuum there was no splashing effect at all. The falling water drop hit the surface and simply spread out in a thin film. ====== Data and Analysis ====== Some things I have looked into. ===== Top-Bottom Similarity ===== fps 31283238 ==== Bottom Data ==== Bottom Pinch Off Frame = 77 ^ Frame ^ Diameter (px) ^ | 1 | 109.3 | | 3 | 106.7 | | 7 | 103.33 | | 10 | 100 | | 13 | 97.67 | | 17 | 93.17 | | 20 | 89.58 | | 23 | 85.79 | | 27 | 81.56 | | 30 | 79.11 | | 33 | 75.56 | | 36 | 71.11 | | 40 | 66.89 | | 43 | 63.11 | | 46 | 59.56 | | 49 | 55.11 | | 52 | 50.56 | | 55 | 46.94 | | 58 | 44.14 | | 60 | 40.40 | | 63 | 36.87 | | 65 | 32.77 | | 67 | 28.38 | | 68 | 27.19 | | 69 | 24.93 | | 70 | 21.46 | | 71 | 19.73 | | 72 | 15.87 | | 73 | 13.93 | | 74 | 9.30 | | 75 | 4.98 | | 76 | 3.67 | | | | ==== Top Data ==== Top Pinch Off Frame = 92 ^ Frame ^ Diameter (px) ^ | 86 | 21.67 | | 87 | 19.17 | | 88 | 15.58 | | 89 | 13.12 | | 90 | 8.23 | | 91 | 2.45 | Here is a plot of the data. {{ :phylabs:lab_courses:phys-211-wiki-home:drop-pinch-off:bottom-v-top.png?600 |}} Here is what happens when I fit the data to a powerlaw with the exponent as a free parameter. $Y = aX^[\gamma]$ ^ ^ Bottom ^ Top ^ | $\gamma$ | 0.65 ± 0.02 | 0.64 ± 0.28 | | Red Chi-Sq | 0.06 | 0.01 | {{ :phylabs:lab_courses:phys-211-wiki-home:drop-pinch-off:bottom-v-top-fits.png?600 |}} ===== Effect of Nozzle Size ===== Investigated whether or not the diameter of the drop nozzle has an effect on the dynamics of the drop pinch off process. Scaling arguments suggest this should not be a factor. ==== Parameters ==== Assembled three different dropper nozzles with the following diameters. ^ Nozzel ^ Diameter (mm) ^ | I | 4.25mm +/- .1mm | | II | 2.75mm +/- .1mm | | III | 1.25mm +/- .1mm | For nozzles I and II ordinary calipers were used to measure the inner diameter of the tubing used. For III wires of various gauges were used to find the one which just barely fit in the nozzle and then the diameter of the wire was measured with the caliper. Tap water was used for the fluid. The camera was setup with the Tokina macro lens set to closest focus for all videos. The following videos were recorded. ^ Nozzle - ID# ^ FPS ^ Pinchoff Frame ^ | I-1 | 1069.6 | 103 | | I-2 | 7132.7 | 43 | | II-1 | 1069.6 | 121 | | II-2 | 7132.7 | 56 | | III-1 | 1069.6 | 130 | | III-2 | 8810.6 | 81 | | III-3 | 7132.7 | 70 | ==== Raw Data Plots ==== Plot of all the measured minimum neck radii vs. time from pinch off. {{ :phylabs:lab_courses:phys-211-wiki-home:drop-pinch-off:all-raw-data.png?600 |}} For clarity here are plots of the data for each nozzle size. {{ :phylabs:lab_courses:phys-211-wiki-home:drop-pinch-off:nozzle-i-data.png?600 |}} {{ :phylabs:lab_courses:phys-211-wiki-home:drop-pinch-off:nozzle-ii-data.png?600 |}} {{ :phylabs:lab_courses:phys-211-wiki-home:drop-pinch-off:nozzle-iii-data.png?600 |}} ==== Powerlaw Fits - Power Is A Free Paramater ==== Fit Function $a*\tau_{o}^{\gamma}$. ^ Data Set ^ a ^ $\gamma$ ^ R $\chi^{2}$ ^ | I-1 | 2000 ± 200 | 0.60 ± 0.03 | 0.33 | | I-2 | 2200 ± 200 | 0.61 ± 0.02 | 0.28 | | II - 1 | 1900 ± 150 | 0.57 ± 0.02 | 1.22 | | II - 2 | 2400 ± 200 | 0.64 ± 0.2 | 0.11 | | III - 1 | 1200 ± 200 | 0.50 ± 0.04 | 3.22 | | III - 2 | 1700 ± 100 | 0.58 ± 0.01 | 0.83 | | III - 3 | 1600 ± 90 | 0.58 ± 0.01 | 1.00 | === Powerlaw Fits To Data === Powerlaw fits to selected subsets of the data for each nozzle. Data subsets were determined by eye based on which portion of the data appeared linear on the log-log plots. Plots are shown with the appropriate subset of data used in each fit. The final plot shows the same fits but to the full data sets. {{ :phylabs:lab_courses:phys-211-wiki-home:drop-pinch-off:nozzle-i-fits.png?600 |}} {{ :phylabs:lab_courses:phys-211-wiki-home:drop-pinch-off:nozzle-ii-fits.png?600 |}} {{ :phylabs:lab_courses:phys-211-wiki-home:drop-pinch-off:nozzle-iii-fits.png?600 |}} {{ :phylabs:lab_courses:phys-211-wiki-home:drop-pinch-off:all-fits.png?600 |}} {{ :phylabs:lab_courses:phys-211-wiki-home:drop-pinch-off:fits-to-fulldata.png?600 |}} ==== Powerlaw Fits - Keim ==== A different fitting strategy which is suggested by Nathan Keim is to fit the data to the three power law exponents as predicted by the dimensional analysis. This results in a fit with only 1 free parameter but allows you to evaluate each of the predictions independently. {{ :phylabs:lab_courses:phys-211-wiki-home:drop-pinch-off:fits-keim-1.png?600 |}} {{ :phylabs:lab_courses:phys-211-wiki-home:drop-pinch-off:fits-keim-5.png?600 |}} {{ :phylabs:lab_courses:phys-211-wiki-home:drop-pinch-off:fits-keim-67.png?600 |}} ==== Note ==== The assumption is that the nozzle size can be neglected is not valid for the early part of the process where the size of the minimum neck width is in fact on the same order as the nozzle. I presume that this is why the data early in the process never seems to agree with any of the three power law predictions. ====== Drop Oscillations ======