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| - | ====== Drop Pinch-Off Winter 2022 ====== | ||
| - | The formation and pinch-off of a drop is governed by a myriad of fluid physics phenomena. With the help of high-speed photography, | ||
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| - | Before we get into the nuts and bolts of the experiment, spend some time watching the following videos and looking at the images of fluids undergoing drop pinchoff. | ||
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| - | ====== Preparation Meeting ====== | ||
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| - | Before your Preparation meeting with your TA, you and your lab partner(s) should do some background research. The purpose of this is so that you can go into your first meeting with the TA with a picture of what you will be studying and the technique you will be using. Then at your first meeting you can focus on the details of what you need to do to start getting data to work with. Remember that you are expected to come to this meeting prepared to participate and demonstrate your understanding of these concepts. | ||
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| - | This is a //Fluid Dynamics// experiment, you may not have had a course in fluid dynamics but that is ok. It is enough to familiarize yourself with the following terms; | ||
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| - | * Surface Tension | ||
| - | * Viscosity | ||
| - | * Capillary Length | ||
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| - | We will use the technique of //<color # | ||
| - | Examples of the Use of Symmetry// by Hans G. Hornung is a very good introduction to the subject if you find the subject particularly interesting. | ||
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| - | Also read through the following section titled Imagery, watch the videos and spend time studying the images. | ||
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| - | ===== Imagery ===== | ||
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| - | ==== Video Clips ==== | ||
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| - | //Two different video clips of the drop pinch off process recorded with a high speed camera running at several thousand frames per second. | ||
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| - | ==== Images captured one at a time using a digital camera. ==== | ||
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| - | Now that you have hopefully spent some time observing the phenomena lets ask a few questions to get the scientific process started. | ||
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| - | * The neck connecting the drop to the faucet exhibits at least two different characteristic shapes. | ||
| - | * There are different time scales apparent in the videos. | ||
| - | * After pinch-off the remaining strand of fluid from the long thin neck forms back into a drop. Did you notice that the shape of this drop oscillates with a characteristic frequency. | ||
| - | * The behavior of the water drop and the glycerin drop are markedly different in terms of how the next develops. | ||
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| - | Fluids are incredibly complicated systems to study in rigorous mathematical detail. | ||
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| - | How then do we study such phenomena if we cannot write down precise equations? | ||
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| - | By watching how the drop pinch-off process evolves using high speed photography and video techniques, and using our physics intuition we have identified that the physical properties of //surface tension//, // | ||
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| - | ====== Theory ====== | ||
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| - | In dimensional analysis one begins by identifying relevant physical parameters which would be expected to play a role in the phenomena under consideration. So what physical parameters might one expect would play a role in determining how a liquid dripping from a faucet stretches, thins and eventually breaks in two. Obviously gravity is pulling on the drop. The size of a water molecule might matter. The radius of the faucet might be expected to matter. The shape and flow of fluids are dependent on properties such as viscosity, surface tension and density. | ||
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| - | Each of these parameters is defined by a set of dimensions, mass (M), length (L), time (T), etc. The two parameters we are interested in studying are the radius of the neck at its narrowest point $r$ (dimension L) and the time $\tau$ (dimension T) which we will measure relative to the moment at which the drop breaks in two. Some of these parameters should be less important due to scaling considerations. For example in this experiment we will be using a high speed camera to record the pinchoff process. As you will see for yourself when you begin the experiment the radius of the neck that we will be able to observe with the camera will range from a scale of mm to tens of μm and the pinchoff process will occur on a time scale of thousandths of a second. | ||
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| - | The size of a molecule is many orders of magnitude smaller than the observable neck size so it can be neglected. The same consideration can be used to neglect the radius of the faucet which is ten times larger than the neck radii we will be measuring. This leaves us with Surface Tension, Density and Viscosity as a set of parameters which might reasonably be expected to influence the behavior of the fluid during the pinchoff process. | ||
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| - | In terms of dimensions our list of potential parameters looks like: | ||
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| - | | Parameter | ||
| - | | Minimum neck radius $r_{min}$ | ||
| - | | Time from pinch-off $\tau$ | ||
| - | | Fluid density $\rho$ | ||
| - | | Surface Tension $\gamma$ | ||
| - | | Viscosity $\eta$ | ||
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| - | Now that we have identified a set of parameters which might be involved in the pinch-off process all that is left is to find combinations of $\tau$, | ||
| - | $r_{min} = F(\rho, \gamma, \eta, \tau)$ | ||
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| - | You should be able to find three different combinations of parameters for which the units on the right hand side of the equation reduce to L which matches the left hand side. You can multiply and divide different combination of parameters as well as raise individual parameters to different powers in order to make the units work out. | ||
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| - | ====== Experimental procedure ====== | ||
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| - | As a lab in development, | ||
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| - | The apparatus is illustrated in Fig. 1. | ||
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| - | |**Figure 1**: The drop pinch-off apparatus| | ||
| - | ===== High-speed camera notes ===== | ||
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| - | The TA and laboratory staff will show you how to configure and use the high-speed camera. Below are some things you will need to take into consideration when setting up. To assist you here are some short videos showing how to use the camera. | ||
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| - | == Video on positioning the drop in the field of view of the camera and obtaining initial focus. == | ||
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| - | == Setting camera resolution and frame rate. == | ||
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| - | == Recording, reviewing and saving video clips. == | ||
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| - | == Setting up the camera focus assist function. == | ||
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| - | == Fine tuning the focus. == | ||
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| - | == Adding and removing the extension tubes to the camera. == | ||
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| - | ==== Camera resolution ==== | ||
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| - | In order to collect enough data at the moment when the pinch-off occurs, you need to run the camera at a frame rate of at least 10,000 frames per second (fps). (However, 20,000 fps is even better.) | ||
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| - | When setup to use the full resolution of the sensor, the maximum frame rate is about 1000 fps. As you reduce the resolution (thereby using fewer pixels) the maximum frame rate increases. To get an adequate frame rate you will need to make the resolution as small as possible. The question you need to answer is "How small can you go?" | ||
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| - | Your goal is to record a high speed movie of the moment the drop pinches off. You will be making measurements of the narrowest part of the neck of the drop, so the active area of the camera sensor has to be wide enough to see the full width of the neck throughout the whole pinch-off process. You also need enough vertical pixels to record the drop as it falls, right up to the point where it pinches off. Therefore, you will need to play with different camera resolution settings as well as the height of the syringe until you are satisfied that you are recording all of the features you need to see at a sufficiently high frame rate. | ||
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| - | ==== Lens aperture and drop illumination ==== | ||
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| - | A consequence of increasing the frame rate is that each frame is exposed for a shorter period of time. This results in dimmer images as frame rate increases. For this reason you need to get as much light into the camera as possible. There are two factors under your control that affect image brightness. | ||
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| - | First is the brightness of the lamp which illuminates the drop. Note that we are back-illuminating the drop so that we actually record its shadow. To provide more uniform illumination of the drop, it is best to place a diffusing material (such as wax paper) in front of the light source. Experiment with the placement of both the diffuser and the lamp to obtain the brightest and most uniform illumination of the drop. | ||
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| - | The second factor under you control is the aperture of the camera. Wikipedia has a nice explanation of how [[https:// | ||
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| - | ==== Distance from camera to drop ==== | ||
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| - | Filling the video frame without wasting space (thereby utilizing the full resolution of the camera) may require adjusting the position of the camera relative to the drop. | ||
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| - | ===== Video conversion ===== | ||
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| - | ==== Installing and configuring FFMPEG to convert mp4 movies to avi which can be read by imageJ ==== | ||
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| - | These instructions are specific to installation on the Windows 7 computers used in the lab. | ||
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| - | - Go [[https:// | ||
| - | - Unzip the downloaded file and rename the resulting folder " | ||
| - | - Move the folder " | ||
| - | - I could not get the system path updated to recognize the location of the binary, so invoke ffmpeg using its full path. | ||
| - | - Open a command terminal by typing cmd into the search box in the Start bar. | ||
| - | - Test the installation by executing the following command in the cmd prompt window: | ||
| - | '' | ||
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| - | ==== Converting an mp4 movie file into an avi file ==== | ||
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| - | - Create a folder where you will store your movie files. | ||
| - | - Open a command terminal by typing cmd into the search box in the Start bar. | ||
| - | - Use the dos " | ||
| - | - Enter the following command in the cmd window. ''" | ||
| - | ''" | ||
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| - | ====== Analysis ====== | ||
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| - | Your written analysis that you submit to be graded should be built around your final conclusions. | ||
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| - | You need to make clear things you did, decisions you made in the lab which are important to understanding how you arrived at your results and conclusions. | ||
| - | * Details on sample preparation if you made your own samples. | ||
| - | * A description of the different power law relationships you were able to come up with and an interpretation of why they seem like reasonable descriptions of the pinch off process. | ||
| - | * How you assessed, quantified and propagated uncertainties. | ||
| - | * Plots of the data showing different power law regimes. | ||
| - | * How you determined minimum neck radii. | ||
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| - | The above list is not intended to be complete, nor should it be treated as a checklist of what should go into your written analysis. | ||
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| - | For this quarter we are focusing on developing your skills in data analysis and drawing appropriate conclusions from your data. Your analysis should focus on these things. | ||
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| - | <WRAP download> | ||
| - | Don't spend too much time wrestling with this code; this is supposed to be a helpful tool, not an exercise in debugging. | ||
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| - | To get started, download the attached .zip file from Github | ||
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| - | [[https:// | ||
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| - | <iframe src=" | ||
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| - | You may also use the Python notebook online [[https:// | ||
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| - | ====== | ||
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| - | Your analysis is due 4 days after your second day in lab. The analysis is not a lab report, rather it is all of the data reduction, number crunching, calculations, | ||
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| - | Three days after your analysis submission your group will have a meeting with the TA to go over your analysis and make sure you are prepared to write your final report. | ||
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| - | The final report is due three days after the analysis meeting. | ||
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| - | Your graded analysis will be returned along with your graded final report. | ||
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| - | ===== Analysis Meeting ===== | ||
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| - | Three days after your analysis is due your group will meet with the TA to discuss the overall analysis and make clear what needs to go into your final report. | ||
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| - | ===== Analysis Rubric ===== | ||
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| - | Your analysis, like your reports, should be submitted as a single PDF. It is not expected that you will write narrative descriptions as you will in your final report. | ||
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| - | Each item below is graded on a 0-4 point scale: | ||
| - | * **(4) - Good (A):** Work is done correctly and covers everything in adequate detail. | ||
| - | * **(3) - Adequate (B):** Minor mistakes were made. Misses one or more minor elements. | ||
| - | * **(2) - Needs improvement (C):** Work is incomplete or incorrect in some significant way. | ||
| - | * **(1) - Inadequate (D):** Work is mostly incomplete or incorrect. | ||
| - | * **(0) - Missing (F):** omits all elements or makes no meaningful attempt. | ||
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| - | All rubric items carry the same weight. The final grade for the analysis will be assigned based on the average (on a 4.0 scale) over all rubric items. | ||
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| - | <div rubric four_section> | ||
| - | | Item | Good (4) | | ||
| - | | Data Reduction | ||
| - | | Calibration | ||
| - | | Error Propagation | ||
| - | | Comparison of Data to Model | Properly fitted plots of data in comparison with predictions of the model are provided along with relevant information such as fit function, best fit parameters, uncertainties and goodness of fit estimates. | ||
| - | | Physical Parameters to be Compared with Accepted Values | ||
| - | | Other specific items which may have been discussed with your TA. | Anything else which your TA has made clear they expect to see in your analysis. | ||
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| - | ===== Analysis ===== | ||
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| - | Your written analysis that you submit to be graded should be built around your final conclusions. | ||
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| - | You need to make clear things you did, decisions you made in the lab which are important to understanding how you arrived at your results and conclusions. | ||
| - | * How you calibrated the image scale. | ||
| - | * How you assessed, quantified and propagated uncertainties should be discussed and made clear including examples of how calculations were done where appropriate. | ||
| - | * How you arrived at the different power law relationships. | ||
| - | * How your observations of the behavior of the drop in each regime makes sense in terms of the dominant physical parameters in play. | ||
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| - | The above list is not intended to be complete, nor should it be treated as a checklist of what should go into your written analysis. | ||
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| - | For this quarter we are focusing on developing your skills in data analysis and drawing appropriate conclusions from your data. Your analysis should focus on these things. | ||
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| - | ==== Rubric ==== | ||
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| - | Your analysis will be evaluated based on the following rubric. The rubric is not a format for your analysis, you are not expected to have a specific section on //Data Handling// or // | ||
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| - | Each item below is graded on a 0-4 point scale: | ||
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| - | * **4 – Good (A):** completes all listed tasks and provides appropriate context; thinks carefully about data and analysis; addresses all concerns raised by the results (where appropriate). | ||
| - | * **3 – Adequate (B):** misses one or more minor element or lacks appropriate context; leaves a problem or ambiguity unaddressed; | ||
| - | * **2 – Needs improvement (C):** omits or mishandles one or more item which renders the analysis fundamentally incorrect or incomplete; presents results in an incorrect or unclear way. | ||
| - | * **1 – Inadequate (D):** omits or mishandles multiple items or treats them at an insufficient level; presentation is overall muddled or inaccurate; flaws in logic or process. | ||
| - | * **0 – Missing (F):** omits all elements or makes no meaningful attempt. | ||
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| - | All rubric items carry the same weight. The final grade for the analysis will be assigned based on the average (on a 4.0 scale) over all rubric items. | ||
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| - | <div rubric four_section> | ||
| - | | Item | Good (4) | | ||
| - | | Lab notebook | ||
| - | | Presentation of Data | Presents plots of data as needed and uses them to support the narrative of the report. Properly labels plots, and makes presentation clean and clear. Uses error bars where appropriate. Includes captions that provide appropriate context. Presents all numerical values with appropriate units and significant figures. Clearly formats numbers, equations, tables, etc. | | ||
| - | | Data Handling | ||
| - | | Discussion of Uncertainties | ||
| - | | Presentation of Results | ||
| - | | Conclusions | ||
| - | </ | ||