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Rheology of Complex Fluid Films for Biological and Mechanical Adhesive Locomotion by Randy H

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Rheology of Complex Fluid Films for Biological and Mechanical Adhesive Locomotion by Randy H Rheology of Complex Fluid Films for Biological and Mechanical Adhesive Locomotion by Randy H. Ewoldt B.S., Mechanical Engineering Iowa State University (2004) Submitted to the Department of Mechanical Engineering in partial ful¯llment of the requirements for the degree of Master of Science in Mechanical Engineering at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2006 °c Massachusetts Institute of Technology 2006. All rights reserved. Author.............................................................. Department of Mechanical Engineering May 12, 2006 Certi¯ed by. Anette Hosoi Assistant Professor, Mechanical Engineering Thesis Supervisor Certi¯ed by. Gareth H. McKinley Professor, Mechanical Engineering Thesis Supervisor Accepted by . Lallit Anand Chairman, Department Committee on Graduate Students 2 Rheology of Complex Fluid Films for Biological and Mechanical Adhesive Locomotion by Randy H. Ewoldt Submitted to the Department of Mechanical Engineering on May 12, 2006, in partial ful¯llment of the requirements for the degree of Master of Science in Mechanical Engineering Abstract Many gastropods, such as snails and slugs, crawl using adhesive locomotion, a tech- nique that allows the organisms to climb walls and walk across ceilings. These animals stick to the crawling surface by excreting a thin layer of biopolymer mucin gel, known as pedal mucus, and their acrobatic ability is due in large part to the rheological prop- erties of this slime. The primary application of the present research is to enable a mechanical crawler to climb walls and walk across ceilings using adhesive locomotion. A properly selected slime simulant will enable a mechanical crawler to optimally perform while climbing in the horizontal, inclined, and inverted positions. To this end, the rheology of gastropod pedal mucus is examined in greater detail than any previously published work. The linear rheological response of pedal mucus is examined with flow, oscillation, and creep tests. Nonlinear rheology is examined with large amplitude oscillatory shear (LAOS), and analyzed with Lissajous curves, Fourier transform rheology, and a new measure of non-linear elasticity. In addition, pedal mucus is examined with a flexure-based microgap rheometer, which can test the sample at the biologically relevant gap of 10-20¹m, the measured thickness of pedal mucus under a crawling slug. Adhesive locomotion of a mechanical crawler is modeled in order to ¯nd the cri- teria for an optimal slime simulant. After developing the selection criteria for the ideal simulant, a range of candidate materials are examined including polymeric gels, particulate gels, emulsions, composites, and ¯eld-responsive fluids. Two promising simulants are examined in detail and compared with native gastropod pedal mucus. Thesis Supervisor: Anette Hosoi Title: Assistant Professor, Mechanical Engineering Thesis Supervisor: Gareth H. McKinley Title: Professor, Mechanical Engineering Acknowledgments I would like to thank the National Science Foundation Graduate Research Fellowship Program for ¯nancial support and the freedom to pursue this research, Brian Chan for his original idea to pursue a robotic snail, and my advisors Prof. Anette Hosoi and Prof. Gareth H. McKinley for their enthusiasm, encouragement, and con¯dence in me. Furthermore, I would like to thank Dr. Christian Clasen for his help with microgap rheology, and my numerous lab mates, colleagues, and friends for their support. Finally, I am indebted to my wife Erin, who continues to be a constant source of wisdom, encouragement, and strength. A.M.D.G. R.H.E. Contents 1 Introduction and Background 19 1.1 Adhesive locomotion . 20 1.2 Mucus composition . 22 1.2.1 Vertebrate mucus . 22 1.2.2 Invertebrate mucus . 24 1.3 Prior work on the rheology of mucus . 24 1.3.1 Vertebrate mucus . 24 1.3.2 Invertebrate mucus . 26 2 Experimental Methods 29 2.1 Materials . 29 2.2 Linear viscoelasticity and steady-flow rheology . 30 2.3 Nonlinear oscillatory shear rheology . 32 2.3.1 Fourier transform rheology . 33 2.3.2 Lissajous curves . 34 2.3.3 Newly proposed quantitative measures for LAOS . 37 2.4 Microgap rheology . 41 2.4.1 Gap limits of bulk and microgap rheology . 42 2.4.2 FMR working principles . 44 2.4.3 FMR experimental range . 47 2.4.4 Theoretical models of LAOS rheology on the FMR . 47 7 3 Results and Discussion: Rheology of Pedal Mucus from Terrestrial Gastropods 55 3.1 Traditional rheology . 55 3.2 Nonlinear LAOS rheology . 64 3.2.1 Viscoelastic moduli . 64 3.2.2 Fourier transform rheology . 66 3.2.3 Lissajous curves . 67 3.2.4 Quantitative measure of sti®ening . 70 3.3 Microgap rheology . 73 3.4 Overview: the Pipkin diagram . 76 4 Modeling Adhesive Locomotion: Criteria for Optimizing a Slime Simulant 79 4.1 Adhesive locomotion model . 79 4.1.1 Velocity expression . 81 4.1.2 E±ciency expression . 83 4.2 Horizontal locomotion simulation . 85 4.3 Inclined locomotion model . 88 4.3.1 Generalized Newtonian fluid . 89 4.3.2 Idealized yield stress fluid . 90 4.3.3 Yield stress fluid with restructuring time . 93 5 Survey of Possible Slime Simulants 101 5.1 Polymeric gels . 103 5.1.1 Material preparation . 103 5.1.2 Results . 105 5.2 Particulate gels . 106 5.2.1 Material preparation . 107 5.2.2 Results . 108 5.3 Emulsions, foams, and composites . 109 5.3.1 Material preparation . 110 5.3.2 Results . 110 5.4 Field-responsive fluids . 113 5.4.1 Material preparation . 113 5.4.2 Results . 114 5.5 Conclusions . 114 6 Results: Detailed Rheology of Two Slime Simulants 115 6.1 Steady shear flow . 115 6.2 Creep . 118 6.3 Small amplitude oscillatory shear (SAOS) . 120 6.4 Nonlinear, large amplitude oscillation . 120 6.5 Time dependency of yield stress . 125 6.6 Summary . 129 7 Conclusions 131 A Biochemistry Reference 135 List of Figures 1-1 Bottom view of a crawling terrestrial slug Limax maximus, 1cm scale bar; i) compression wave, ii) interwave . 20 1-2 Chan's Robosnail mimics adhesive locomotion with ¯ve discrete pads which move forward sequentially while other pads remain stationary, 5cm scale bar. 21 1-3 Schematic representation of two well characterized human mucins (from [1]); MUC1 is a membrane-bound mucin and MUC2 is a secretory mucin. 23 1-4 The frequency dependent stress hardening and flow of native pig gastric mucus, as reported by [2] (A) 0.2 Hz and (B) 1 Hz. 26 1-5 A typical creep curve for the pedal mucus of the limpet Patella vulgata as reported by [3]. 27 1-6 A typical strain-controlled test performed by [4] to show the transi- tion to flow of the pedal mucus from the terrestrial slug Ariolimax columbianus................................. 28 1-7 Overshoot stress σy and flow stress σf depend on the imposed shear rate for pedal mucus from the terrestrial slug Ariolimax columbianus, as reported by [4]. The data points are from a representative sample, and the ruled areas show the total range observed in all samples tested. 28 2-1 A Pipkin diagram maps the phase-space of linear and nonlinear mate- rial responses. 32 2-2 Normalized Lissajous curves of linear viscoelastic materials with vary- ing phase angle ±.............................. 35 11 2-3 Normalized Lissajous curves of some nonlinear viscous fluids. 36 2-4 Sample Lissajous curves of some nonlinear purely-elastic solids. 37 2-5 Schematic de¯nitions for elastic material functions of a nonlinear vis- coelastic material; M: small strain elastic shear modulus; L: large strain elastic shear modulus; S = L=M: elastic sti®ening ratio. 41 2-6 Apparent bulk viscosity of a Newtonian oil deviates due to errors at decreasing gap sizes (AR1000, 4cm plate, 20±C). 42 2-7 Experimental limits of a typical bulk rheometer (AR1000, 4cm plate) and the Flexure-based Microgap Rheometer. 44 2-8 A schematic view of the Flexure-based Microgap Rheometer (image courtesy of Dr. Christian Clasen). 45 2-9 Experimental limits of the Flexure-based Microgap Rheometer. 46 2-10 Controlled strain input for FMR is a triangle wave. 48 2-11 Schematics of i) Maxwell model for a viscoelastic fluid and ii) Kelvin model for a viscoelastic solid. 48 2-12 Steady-state Maxwell model response to triangle wave strain input. 50 2-13 Kelvin model response to triangle wave strain input. 52 3-1 Steady state flow viscosity of native pedal mucus collected from two snails Helix aspera (D=0.8 cm plate with sandpaper, 20±C, Snail#1 on CSL2 500, 100¹m gap; Snail#2 on AR1000, 50¹m gap). 56 3-2 Creep compliance of native pedal mucus from the terrestrial snail Helix aspera (AR-G2, D=0.8 cm plate with sandpaper, 1000¹m gap, 22±C, ¿0 = 5 Pa < ¿y)............................... 57 3-3 Oscillatory stress sweep of native pedal mucus from the terrestrial slug Limax maximus (AR1000, 2cm plate with sandpaper, solvent trap, 200¹m gap, 22±C, ! = 1 rad.s¡1)..................... 58 3-4 Oscillatory frequency sweep of native pedal mucus from the terrestrial slug Limax maximus (AR1000, 2cm plate with sandpaper, solvent trap, ± 200¹m gap, 25 C, ¿0 = 5 Pa< ¿y)..................... 59 3-5 Kelvin and Je®reys models ¯t to inertio-elastic ringing during creep test of native pedal mucus from the terrestrial snail Helix aspera (AR- ± G2, D=0.8 cm plate with sandpaper, 1000¹m gap, 22 C, ¿0 = 5 Pa < ¿y). 61 3-6 Je®reys model for a viscoelastic fluid in series with the moment of inertia of the rheometer; if ´2 is not included a Kelvin model is retained. 62 3-7 Oscillatory stress sweep of native pedal mucus from the terrestrial slug Limax maximus (AR1000, 2cm plate with sandpaper, solvent trap, 180¹m gap, 22±C). Note these results are for a di®erent sample than Figures 3-3 and 3-4.
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