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A Numerical Study for Liquid Bridge Based Microgripping And © 2007 SANTANU CHANDRA ALL RIGHTS RESERVED A NUMERICAL STUDY FOR LIQUID BRIDGE BASED MICROGRIPPING AND CONTACT ANGLE MANIPULATION BY ELECTROWETTING METHOD A Dissertation Presented to The Graduate Faculty of the University of Akron In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Santanu Chandra December, 2007 A NUMERICAL STUDY FOR LIQUID BRIDGE BASED MICROGRIPPING AND CONTACT ANGLE MANIPULATION BY ELECTROWETTING METHOD Santanu Chandra Dissertation Approved: Accepted: _________________________________ _________________________________ Advisor Department Chair Dr. Celal Batur Dr. Celal Batur _________________________________ _________________________________ Committee Member Dean of the College of Engineering Dr. Minel Braun Dr. George K. Haritos _________________________________ _________________________________ Committee Member Dean of the Graduate School Dr. Jiang “John” Zhe Dr. George R. Newkome _________________________________ _________________________________ Committee Member Date Dr. George G. Chase _________________________________ Committee Member Dr. Gerald Young ii ABSTRACT The last decade had witnessed some very outstanding research on Micro Electro Mechanical Systems (MEMS) that has vast impact on future technologies. However building a complete microsystem requires proper microassembly methods. But microassembly research is facing stiff resistance due to the presence of many dominant forces which appears due to the scaling law. Overcoming these forces has been found to be a major drawback in microgripper research. So the primary the challenge today researches face is the lack of proper manipulation schemes. Understanding the physical forces associated with micro-scale as well as devising techniques to control them is needed in order to design a proper micromanipulation scheme. The motivation of this study is to contribute to the microassembly research by studying the forces in microscale and propose a micromanipulation scheme to control these forces. A pick and place technique using a liquid bridge based microgripper is presented in this dissertation. Studies conducted on liquid bridge based single probe gripper have shown promise in picking up an object using strong capillary force and surface tension forces as the lifting forces. But a smooth release of the object has been a challenge. We have proposed a novel manipulation scheme by using electrowetting method to control the lifting forces. By changing the electrical field imposed on the iii gripper surface, one can change the contact angle of the liquid bridge and therefore can change the meniscus geometry. Change in curvature of the meniscus causes the lifting forces between the object and the gripper to change. The focus of this study is to explore the possibility of breaking a liquid bridge by increasing the contact angles for a smooth release of an object. A theoretical study was conducted to understand the effect of contact angle manipulation on the lifting forces. Young-Laplace equation, the non linear differential equation governing the liquid interface is numerically solved for a constant liquid volume and the specified contact angles as boundary conditions. Another set of numerical solution using commercial multi-physics software CFDACE+ has been used in parallel to validate the hypothesis. Results show that for a proper choice of liquid volume the contact angle manipulation is suitable for picking up and releasing of an object. iv DEDICATION I dedicate this dissertation to my parents Dr. Chirasukh Chandra Mrs. Indira Chandra v ACKNOWLEDEMENTS First and foremost I would like to express my sincere gratitude to my advisor Dr. Celal Batur, for providing me the opportunity to work under his supervision. Without his kind support and guidance this work would not have been possible. He has taught me how to approach a research problem from the basics, how to ask questions and be persistent to find the answers. I would like to thank my dissertation committee members Dr. Minel Brown, Dr. John Zhe, Dr. George Chase and Dr. Gerald Young for their intelligent questions and constructive criticisms and encouragement to complete successfully. I would like to extend my thanks to the Department of Mechanical Engineering and for providing me the teaching assistantships and their enriching instructions through their curriculum. I appreciate all the support I got from the staff members specially Stacy, Stephanie and Cliff for their friendly and helpful attitude. A special thanks goes to all my friends in Akron, for being there to share the good moments and bad moments of life. Last but not the least I am grateful to my parents Dr Chirasukh Chandra and Mrs Indira Chandra for their patience in me, their constant encouragement in pursuing my goals and being there for me when I needed most. I always appreciate my brother Shovan and my sister in law Monalisa for being there and motivating me when need. Thank you. vi TABLE OF CONTENTS Page LIST OF TABLES ……………………………………………………………………..xiii LIST OF FIGURES .…………………………………………………………………....xiv CHAPTER I. INTRODUCTION………………………………………………………………...1 1.1 Definition of The Problem………………………………………………...2 1.2 Synopsis…………………………………………………………………...6 II. MICROSYSTM AND MICROASSEMBLY……………………………………..8 2.1 What is Microsystem……………………………………………………...8 2.2 What is Microassembly?..............................................................................9 2.3 Why Microassembly is Important? ……………………………………...10 2.4 Main Challenges in Microassembly……………………………………...10 2.5 Micro Assembly Systems………………………………………………..12 2.6 Survey of Adhesion Forces………………………………………………13 2.6.1 Electrostatic Force……………………………………….………15 2.6.2 Van Der Waal’s Force…………………………………………...16 2.6.3 Surface Tension …………………………………………………18 2.6.4 Gravitational Force………………………………………………19 vii 2.7 Comparison of Adhesion Forces ………………………………………..19 2.8 Gripping And Releasing Techniques…………………………………….20 2.9 Gripping Using Physical Contact………………………………………...22 2.9.1 Mechanical Grippers……………………………………………..22 2.9.1 Adhesive Gripper………………………………………………...24 2.9.2 Vacuum Gripper………………………………………………….24 2.10 Noncontact Manipulation………………………………………………...25 III. THEORETICAL FRAMEWORK FOR SOLVING THE LIQUID BRIDGE MENISCUS GEOMETRY ……………………………………………………...27 3.1 Introduction……………………………..………………………………..27 3.2 Definition of Parameters…………………………………………………28 3.2.1 Curvature…………………………………………………………27 3.2.2 Principle Curvature of Surface…………………………………...30 3.2.3 Sign Convention of the Radius of Curvature…………………….32 3.2.4 Mean Curvature………………………………………………….33 3.2.5 Surface Tension …………………………………………………33 3.2.6 Contact Angle……………………………………………………34 3.2.7 Laplace Equation………………………………………………...36 3.2.8 Derivation of Laplace Equation………………………………….37 3.2.9 Kelvin Equation …………………………………………………38 3.3 Modeling the Meniscus Profile………...…….………………………….40 3.3.1 Analytical Solution of Young-Laplace Equation Using Elliptic Integrals…………………………………………………………………..40 3.3.2 Solving Young-Laplace Equation Using Iterative Method……...45 viii 3.3.3 Numerical Algorithm for Solution of Laplace Equation at Constant Volume …………………………………………………………….…….48 3.4 Characterization of Energies……………………………….…………….51 3.5 Formulation of Forces….………………………………………………...56 3.6 Validation of Numerical Scheme ………………………………………..58 3.7 Validation of Lifting Force………………………………………………59 3.8 Simulation Results……………………………………………………….60 3.7.1 Meniscus Profile for Change in Gap……………………………..60 3.7.2 Meniscus Profile for Change in Contact Angle………………….64 3.9 Circular Approximation of Meniscus Shape………..……………………69 3.10 Conclusion……………………………………………………………….76 IV. ELECTROWETTING…………………………………………………………...78 4.1 Introduction…............................................................................................78 4.2 Electrowetting............................................................................................75 4.2.1 History of Electrowetting...............................................................79 4.2.2 Electrowetting On Dielectric (EWOD)…………………………..80 4.2.3 Young Lippman’s Equation ………………………………..........81 4.3 Theoretical Background.............................................................................82 4.3.1 Classical Thermodynamics Approach...........................................84 4.3.2 Energy Minimization Approach……………………………........87 4.3.3 EletroMechanical Approach..........................................................88 4.4 Contact Angle Saturation...........................................................................90 4.4.1 Vallet’s Theory .............................................................................91 ix 4.4.2 Verheijen and Prins Theory ..........................................................92 4.4.3 Kang’s Theory...............................................................................93 4.4.4 Shapiro Theory...............................................................................95 4.4.5 Papathanasiou Theory....................................................................95 4.4.6 Summary of Saturation Theories...................................................96 4.5 Application of Electrowetting....................................................................98 4.5.1 Lab on a Chip.................................................................................98 4.5.2 Micro Lenses................................................................................100 4.5.3 Liquid Paper.................................................................................101 4.5.4 Single Plate
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