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Using Schlieren Optics to Visualize Ultrasonic Standing Waves in Acoustic Levitation

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Using Schlieren Optics to Visualize Ultrasonic Standing Waves in Acoustic Levitation Dickinson College Dickinson Scholar Student Honors Theses By Year Student Honors Theses Spring 5-17-2020 Using Schlieren Optics To Visualize Ultrasonic Standing Waves In Acoustic Levitation Ming-Hua Chang Dickinson College Follow this and additional works at: https://scholar.dickinson.edu/student_honors Part of the Atomic, Molecular and Optical Physics Commons, and the Other Physics Commons Recommended Citation Chang, Ming-Hua, "Using Schlieren Optics To Visualize Ultrasonic Standing Waves In Acoustic Levitation" (2020). Dickinson College Honors Theses. Paper 370. This Honors Thesis is brought to you for free and open access by Dickinson Scholar. It has been accepted for inclusion by an authorized administrator. For more information, please contact [email protected]. Using Schlieren Optics To Visualize Ultrasonic Standing Waves In Acoustic Levitation Submitted in partial fulfillment of honors requirements for the Department of Physics and Astronomy, Dickinson College, by Ming-Hua Chang Advisor: Professor David P. Jackson Reader: Professor Lars English Reader: Professor Brett Pearson Carlisle, PA May 18, 2020 i Great are the works of the LORD, studied by all who delight in them. Psalm 111:2 ii Abstract Acoustic levitation is the phenomenon wherein a standing sound pressure wave can be used to levitate small objects by exerting a force large enough to counter the force of gravity. In this paper we examine the theory of acoustic levitation using an analysis from first-principles, a ponderomotive analysis, and a fluid motion analysis. The first-principles approach involves using Newton’s second law to calculate the net force of an acoustic standing pressure wave on a small object. However, the rapid oscillation of the pressure wave results in a time averaged net force of zero, so we extend the analysis by separating out the rapid motion of the particle from the slow motion. Doing so leads to a ponderomotive force that has a promising form, since the force no longer averages to zero, but disagrees with the research literature. Hence, we consider the accepted analysis using the governing equations of fluid motion and find that the acoustic radiation force causes objects to rest at the pressure nodes of a standing sound pressure wave. The remainder of this paper describes a three-phase investigation into acoustic levitation and schlieren optics. Phase one consists of building a schlieren optics experiment. The schlieren apparatus consists of a point source of light, which is focused by a concave spherical mirror onto a light-block in front of a camera. Changes in refractive index in the path of the light rays will deflect the light rays around the light-block into the camera. This allows for the visualization of minute density gradients in air, allowing us to observe, for example, the airflow above a lit candle or the flow of air from a hair dryer. Phase two of the project involves experimentally producing acoustic levitation. To do this, we use an ultrasonic transducer driven with a 30.1 kHz sinusoidal signal and directed at a flat piece of glass. The resulting standing wave is capable of supporting several small Styrofoam balls. Finally, in phase three we determine the location of these levitating objects using three different analyses: a geometric comparison, direct measurements of the standing pressure wave, and a visual approach using the schlieren system. These three analyses are consistent and demonstrate that objects levitate just below the nodes of standing pressure waves. iii Acknowledgements This project has simultaneously been the most challenging and rewarding undertaking of my time at Dickinson College and I would not have been able to complete it without the help and guidance of several people. Firstly, I would like to thank my research advisor Professor David Jackson who, in the spring of 2019, took me on as an advisee for this year-long project. His work- ethic and high standards, together with his patient mentorship and guidance over the past year, stretched me and enabled me to bring all the aspects of the project together coherently, and honed the way I approach physics. During the thesis-writing process, his feedback and suggestions were of great help and significantly improved the final product. Secondly, I would like to thank Jonathan Barrick who built most of the equipment and taught me how to use the workshop tools. Jonathan was not only extremely creative in building everything needed, but he was also ever ready to help and teach. Professors Lars English and Brett Pearson, who were on my thesis committee, were ever willing to help by way of giving advice, troubleshooting the experimental process, and providing valuable feedback. Further, Professors English, Pearson, and Pfister were always ready to engage in thought-provoking discussions and were a great encouragement. Thank you, professors. The Dickinson Physics Department truly is a wonderful community, and I am grateful for the time I spent as part of this community. In the middle of the Spring 2020 semester, Dickinson was forced to transition online because of the global COVID-19 pandemic. This happened when the experimental process was not yet complete and would have severely restricted the scope of the project had it not been for several key people to whom I am most grateful. Firstly, the physics department for giving me permission to remove the entire experiment from Tome Hall, and Professor Catrina Hamilton- Drager who helped me petition to be given one-time access to Tome to do so. Secondly, the Provost and Dean of the college, Neil Weissman, for considering my petition and granting me permission. Thirdly, Amanda George and Amber Kelly in Residence Life for arranging another dorm room in Malcolm Hall for use as a temporary laboratory. Finally, I would like to thank Public Safety Officer Rob Stone for his help in moving the fragile components of the experiment across the Dickinson campus from Tome to Malcolm. I am grateful to my parents who, through personal sacrifice, have provided me the opportunity to attend Dickinson and supported me throughout this entire process. Several friends provided much-needed moral support during the long period of isolation in which I wrote this thesis. Sabrina Knapp for companionship, encouragement, and much-needed hiatuses. Daniel Friess and Natalie Cist for their prayers and support, which came in many and unexpected ways. Finally, I thank God for the opportunities and capacity He has blessed me with, and the relationships into which He has brought me. This past year has been like no other: memorable but bittersweet. It is in Him that I found the strength to finish this project and graduate amidst uncertain circumstances. iv Contents Abstract iii Acknowledgements iv List of Figures vi 1 Introduction 1 1.1 Refraction of Light ........................................................................................... 1 1.2 Schlieren Imaging ............................................................................................ 3 1.3 Standing Waves ............................................................................................... 5 1.4 Overview of the Project ................................................................................... 6 2 Acoustic Levitation 3 2.1 First-Principles Analysis .................................................................................. 7 2.2 Ponderomotive Force Analysis ........................................................................ 9 2.3 A More Detailed Analysis ................................................................................ 11 3 Apparatus 13 3.1 Schlieren Imaging ............................................................................................ 14 3.2 Acoustic Levitation .......................................................................................... 15 4 Experiment 16 4.1 White Light Illumination ................................................................................. 18 4.2 Density gradients ............................................................................................. 18 4.3 Acoustic Levitation .......................................................................................... 21 4.4 Examining Acoustic Levitation ....................................................................... 23 4.4.1 Geometric Analysis .............................................................................. 23 4.4.2 Pressure measurements ........................................................................ 24 4.4.3 Schlieren Analysis ............................................................................... 25 5 Conclusion 29 6 References 31 v List of Figures 1 Schlieren image by Hubert Hardin .............................................................................. 2 2 Ray diagram of a light ray ........................................................................................... 3 3 Layout of schlieren experiment ................................................................................... 4 4 Acoustic levitation of Styrofoam balls in an ultrasonic standing wave ...................... 6 5 Schematic of a cube in a standing wave ...................................................................... 7 6 Graph of net force on a cube according to the first-principles analysis ...................... 8 7 Graph of net force on a cube according to the ponderomotive analysis ..................... 10 8 Graph of net force on a cube according to the fluid motion analysis
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