RHEOLOGY OF COLLOIDAL SUSPENSIONS: A COMPUTATIONAL STUDY by SEYEDSAFA JAMALI Submitted in partial fulfillment of the requirements For the degree of Doctor of Philosophy Thesis Advisor: Dr. Joao Maia Department of Macromolecular Science and Engineering Case Western Reserve University August, 2015 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the thesis/dissertation of Seyedsafa Jamali Candidate for the Ph.D. degree *. (Signed) Prof. Joao Maia (Chair of the committee) Prof. Gary Wnek Prof. Michael Hore Prof. Daniel Lacks (date) 05-12-2015 *We also certify that written approval has been obtained for any proprietary material contained therein. II Dedication To my wife, Shaghayegh, and to my parents, Saeed and Kobra. III Table of Contents Chapter 1 Introduction .......................................................................................... 19 1.1. Computer Simulations ............................................................................... 19 1.2. Dissipative Particle Dynamics ................................................................... 22 1.3. Rheology .................................................................................................... 24 1.4. Rheology of Suspensions ........................................................................... 26 1.5. Organization and Scope of Dissertation .................................................... 28 1.6. References .................................................................................................. 29 Chapter 2 Bridging Simulation to Experiment ..................................................... 31 2.1. Introduction ................................................................................................ 31 2.2. Formalism and Parametrization of DPD .................................................... 32 2.3. Formalism of MDPD ................................................................................. 36 2.4. Equation of State in MDPD ....................................................................... 39 2.5. Compressibility and Flory-Huggins χ parameter ....................................... 46 2.6. Interfacial Tension ..................................................................................... 52 2.7. Validation on polymer solutions ................................................................ 53 2.8. Transport properties and Dynamics ........................................................... 56 2.9. Conclusions ................................................................................................ 59 2.10. References ................................................................................................ 61 1 Chapter 3 DPD Rheometry ................................................................................... 64 3.1. Introduction ................................................................................................ 64 3.2. Boundary Conditions ................................................................................. 67 3.3. Steady Shear Flow ..................................................................................... 71 3.4. Zero Shear Viscosity .................................................................................. 77 3.5. Transient Shear and Poiseulle Flow ........................................................... 81 3.6. Conclusions ................................................................................................ 83 3.7. References .................................................................................................. 84 Chapter 4 Stabilizing Shear Flows in DPD........................................................... 87 4.1. Introduction ................................................................................................ 87 4.2. Temperature Measurements under Shear with DPD ................................. 90 4.3. GIANT, a new thermostat for DPD ........................................................... 95 4.4. Viscosity measurement using GIANT ..................................................... 102 4.5. Conclusions .............................................................................................. 104 4.6. References ................................................................................................ 105 Chapter 5 Rheology of Colloidal Suspensions ................................................... 108 5.1. Theoretical Background ........................................................................... 108 5.2. Prior DPD simulations on suspensions .................................................... 116 5.3. Modified DPD model ............................................................................... 120 2 5.4. Parameterization of colloidal forces ........................................................ 125 5.5. Suspensions at Rest (quasi-equilibrium conditions) ................................ 128 5.6. Crystallization of mono-sized suspensions .............................................. 136 5.7. Viscosity measurements........................................................................... 138 5.7.1. Effect of volume fraction .................................................................. 139 5.7.2. Effect of particle strength .................................................................. 141 5.7.3. Effect of lubrication interactions ...................................................... 146 5.8. Other rheological parameters ................................................................... 148 5.9. Microstructure under flow ....................................................................... 154 5.10. Rheology of bimodal suspensions ......................................................... 156 5.10.1. Effect of particle composition ......................................................... 157 5.10.2. Effect of size ratio ........................................................................... 158 5.11. Proposed mechanism ............................................................................. 160 5.11.1. Force Analysis ................................................................................ 160 5.11.2. Hydro-cluster formation.................................................................. 163 5.11.3. Contact network formation ............................................................. 167 5.12. Potential energy analysis........................................................................ 170 5.13. Colloidal Gels ........................................................................................ 177 5.13.1. Introduction ..................................................................................... 177 3 5.13.2. Equilibrium properties .................................................................... 180 5.13.3. Rate-dependent properties .............................................................. 188 5.13.4. Time-dependent properties ............................................................. 190 5.14. Conclusions ............................................................................................ 195 5.15. Refernces................................................................................................ 197 Chapter 6 Bibliography ....................................................................................... 204 4 Table of Figures FIGURE 1.1. DIFFERENT TIME AND LENGTH SCALES OF COMPUTER SIMULATIONS. ............. 21 FIGURE 1.2. TYPICAL COARSE-GRAINING AT DIFFERENT LEVELS, FROM THE MOLECULAR LEVEL TO BEADS. ............................................................................................................... 23 FIGURE 2.1. PRESSURE AS A FUNCTION OF: A) BIJ PARAMETER, AND B) PARTICLE DENSITY.40 FIGURE 2.2.PRESSURE DIVIDED BY REPULSIVE PARAMETER AS A FUNCTION OF: A) DENSITY, AND B) CUBIC DENSITY. ..................................................................................................... 41 FIGURE 2.3.PRESSURE VS. DENSITY FOR: A) BIJ =10, B) BIJ =30 AND, C) BIJ =50. ............... 41 FIGURE 2.4. ABSOLUTE VALUE OF THE TOTAL PRESSURE SUBTRACTED BY THE REPULSIVE PRESSURE AS A FUNCTION OF DENSITY FOR: A) BIJ =10, B) BIJ =30 AND, C) BIJ =50. ........... 42 FIGURE 2.5.ABSOLUTE VALUE OF THE ATTRACTIVE PRESSURE NORMALIZED BY AIJ PARAMETER FOR: A) BIJ =10, B) BIJ =30 AND, C) BIJ =50. THE DASH LINE SHOWS THE EXPRESSION PREDICTED FOR THE CONSERVATIVE PARAMETER DEPENDENCE IN STANDARD DPD BY GROOT AND WARREN. ......................................................................................... 43 FIGURE 2.6.MEASURED PRESSURE DIVIDED BY ITS PREDICTED VALUE FROM THE EQUATION 15 AS A FUNCTION OF DENSITY. .......................................................................................... 44 FIGURE 2.7. PRESSURE AS A FUNCTION OF AIJ, FOR A FLUID WITH COMPRESSIBILITY OF WATER. .............................................................................................................................. 47 FIGURE 2.8. BIJ AS A FUNCTION OF AIJ BASED ON EQUATION 16 AND 17. ............................ 48 FIGURE 2.9.FLORY-HUGGINS INTERACTION PARAMETER AS A FUNCTION OF ∆A. ............... 50 FIGURE 2.10. A) THE COLOR MAP OF THE INTERACTION PARAMETER FOR A RANGE OF AIJ AND ∆B CHOICES, AND B) INTERACTION PARAMETER AS A FUNCTION OF ∆B AT CONSTANT AIJ PARAMETER. ................................................................................................................. 51 5 FIGURE 2.11.A) THE DIFFERENCE BETWEEN THE NORMAL AND TANGENTIAL COMPONENTS