The Design and Analysis of a Micro Squeeze Flow Rheometer By David Cheneler A thesis submitted to The University of Birmingham for the degree of DOCTOR OF PHILOSOPHY Department of Mechanical Engineering College of Engineering and Physical Sciences The University of Birmingham September 2009 University of Birmingham Research Archive e-theses repository This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder. ABSTRACT This thesis describes the analysis and design of a micro squeeze flow rheometer. The need to analyse the rheology of complex liquids occurs regularly in industry and during research. However, frequently the amount of fluid available is too small, precluding the use of conventional rheometers. Conventional rheometers also tend to have the disadvantage of being too massive, preventing them from operating effectively at high frequencies. The investigation carried out in this thesis has revealed that current microrheometry techniques also have their own disadvantages. The proposed design is a stand-alone device capable of measuring the dynamic properties of nanolitre volumes of viscoelastic fluid at frequencies up to the kHz range, an order of magnitude greater than conventional rheometers. The device uses a single piezoelectric component to both actuate and sense its own position. Thorough analytical analysis of the microrheometer has been carried out. The capillary effects, including contact angle hysteresis, and viscoelasticity associated with the liquid has been combined with the dynamics and electrical response of the rheometer itself to form a complete and consistent model. The validity of the model has been proven through fabrication and testing of the rheometer. CONTENTS 1 INTRODUCTION .............................................................................................................. 1 1.1 The Need for Microrheology ....................................................................................... 1 1.2 Project Goal ................................................................................................................. 4 1.3 Review of Conventional Rheometric Experimental Techniques ................................ 5 1.3.1 Origins of Rheology ............................................................................................. 5 1.3.2 Conventional Rheometry ...................................................................................... 7 1.3.2.1 Sliding Plate Rheometry ................................................................................... 8 1.3.2.2 Cone and Plate .................................................................................................. 9 1.3.2.3 Rotational Coaxial Cylinder ........................................................................... 10 1.3.2.4 Capillary Tube Rheometer.............................................................................. 11 1.3.2.5 Acoustic Rheometer ....................................................................................... 12 1.3.3 Summary of Conventional Techniques .............................................................. 12 1.4 Review of Microrheometric Experimental Techniques ............................................. 13 1.4.1 Origins of Microrheology ................................................................................... 13 1.4.2 Interfacial Microrheometry ................................................................................ 15 1.4.3 ‗Passive‘ Microrheometers ................................................................................. 19 1.4.3.1 Optical Tweezers ............................................................................................ 19 1.4.3.2 Single/dual Particle Techniques ..................................................................... 21 1.4.3.3 Dynamic Light Scattering and Diffusing Wave Spectroscopy ....................... 22 1.4.4 ‗Active‘ Microrheometers .................................................................................. 24 1.4.4.1 μCaBER and FiSER ....................................................................................... 24 1.4.4.2 Atomic Force Microscope Extensional Flow ................................................. 25 1.4.4.3 Oscillating AFM Probes ................................................................................. 27 1.4.4.4 Squeeze Flow Rheometry ............................................................................... 28 1.4.5 Summary of Current Rheometric Techniques .................................................... 30 1.5 Review of Existing Squeeze Flow Theory ................................................................ 31 1.5.1 Origins of Squeeze Flow Theory ....................................................................... 31 1.5.2 The Development of Squeeze Flow Theory ....................................................... 32 1.5.2.1 Geometries Found in Squeeze Flow Theory .................................................. 32 1.5.2.2 Inertial Effects in Squeeze Flow ..................................................................... 35 1.5.2.3 Slip Effects in Squeeze Flow .......................................................................... 36 1.5.2.4 More Complex Constitutive Models .............................................................. 36 1.5.2.5 Free Surface Boundary Conditions ................................................................. 38 1.5.3 Summary of the Status of Squeeze Flow Theory ............................................... 39 1.6 Conclusion ................................................................................................................. 39 1.7 Structure of the Thesis ............................................................................................... 40 2 DESIGN OPTIONS ......................................................................................................... 41 2.1 Microsystems Technology ......................................................................................... 41 2.2 Actuation Methods .................................................................................................... 43 2.2.1 Electrostatics ...................................................................................................... 43 2.2.2 Magnetomotive Actuation .................................................................................. 46 2.2.3 Piezoelectricity ................................................................................................... 48 2.3 Proposed Rheometer Design ..................................................................................... 48 2.4 Conclusion ................................................................................................................. 49 3. COMPLETE SYSTEM MODEL ..................................................................................... 50 3.1. Specification .............................................................................................................. 50 3.2. Design ........................................................................................................................ 50 3.3. Dynamic model.......................................................................................................... 52 3.4. Device Parameters ..................................................................................................... 55 3.5. A Typical Experiment ............................................................................................... 56 3.6. Flow diagram of solution ........................................................................................... 59 3.7. Capabilities of the Rheometer ................................................................................... 60 3.8. Conclusion ................................................................................................................. 63 4. CAPILLARY EFFECTS .................................................................................................. 64 4.1. Surface Tension ......................................................................................................... 64 4.2. Contact Angles .......................................................................................................... 66 4.3. Contact Angle Hysteresis .......................................................................................... 67 4.4. The No-slip Condition ............................................................................................... 69 4.5. Modification of Surface Chemistry ........................................................................... 70 4.6. The Young-Laplace Equation .................................................................................... 71 4.7. Toroidal Approximation ............................................................................................ 76 4.8. Toroidal Approximation for Contact Angle Hysteresis ............................................ 80 4.9. Squeeze Flow ............................................................................................................