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1 A First Round of Brownian Motion |
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1 | (8) |
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1 | (2) |
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1.2 Stokes-Einstein Relations |
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3 | (1) |
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4 | (2) |
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6 | (3) |
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9 | (12) |
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2.1 Through a Small Grain of Glass |
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9 | (3) |
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12 | (1) |
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13 | (2) |
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2.4 Colloids Are Molecules |
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15 | (3) |
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18 | (3) |
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20 | (1) |
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21 | (26) |
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21 | (2) |
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3.2 Free Volumes and Collisions |
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23 | (4) |
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3.3 Pressure from Ideal Thermal Particles |
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27 | (4) |
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3.4 Velocity Distributions and Energy Equipartition |
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31 | (11) |
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42 | (5) |
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45 | (2) |
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4 A Tale of Ten Time Scales |
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47 | (14) |
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4.1 Brownian Versus Ballistic Motion |
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47 | (2) |
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4.2 Mass-Related Time Scales |
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49 | (6) |
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55 | (6) |
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60 | (1) |
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5 Continuity, Gradients and Fick's Diffusion Laws |
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61 | (10) |
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5.1 The Continuity Equation |
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61 | (3) |
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5.2 Constitutive Equations and Fick's Laws |
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64 | (3) |
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67 | (1) |
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5.4 Diffusion in a Dilute Gas |
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68 | (3) |
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70 | (1) |
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71 | (22) |
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6.1 Einstein for Chemists |
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71 | (6) |
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6.2 Translational Diffusion Coefficient from Equilibrium |
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77 | (3) |
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6.3 Quadratic Displacements via Einstein's Diffusion Approach |
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80 | (2) |
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6.4 Brownian Motion from Newtonian Mechanics |
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82 | (3) |
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6.5 Angular Displacements from a Diffusion Equation |
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85 | (3) |
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6.6 The Rotational Diffusion Coefficient |
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88 | (5) |
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91 | (2) |
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93 | (12) |
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7.1 Fluid Velocity Fields |
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94 | (2) |
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7.2 The Navier--Stokes Equation |
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96 | (4) |
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100 | (2) |
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102 | (3) |
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103 | (2) |
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8 Flow Past Spheres and Simple Geometries |
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105 | (16) |
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8.1 Slits and Tubes---and Darcy's Law |
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105 | (4) |
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8.2 Friction Factor of a Rotating Sphere |
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109 | (4) |
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8.3 The Translational Friction Factor |
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113 | (5) |
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8.4 Stick, Slip and the Lotus Sphere |
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118 | (3) |
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120 | (1) |
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9 Encounters of the Brownian Kind |
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121 | (12) |
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9.1 Diffusion Versus Convection |
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121 | (2) |
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9.2 Brownian Motion Towards a Spherical Absorber |
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123 | (4) |
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9.3 Diffusional Sphere Growth |
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127 | (1) |
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9.4 Birth and Growth of Brownian Clusters |
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127 | (6) |
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132 | (1) |
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10 Random Walks in External Fields |
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133 | (14) |
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10.1 One-Dimensional Diffusion |
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134 | (2) |
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10.2 Radial Brownian Motion and Colloidal Stability |
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136 | (2) |
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10.3 Brownian Motion in a Shear Flow |
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138 | (1) |
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10.4 Brownian Magnets in a Magnetic Field |
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139 | (3) |
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142 | (3) |
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145 | (2) |
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145 | (2) |
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11 Brownian Particles and Van't Hoff's Law |
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147 | (8) |
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11.1 Thermodynamics of Dilute Solutions |
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148 | (2) |
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11.2 Osmotic Pressure Gauged via the Solvent |
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150 | (1) |
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11.3 Osmotic Pressure from Brownian Motion; Vrij's Statistical Approach |
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151 | (4) |
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154 | (1) |
Appendix A Moments, Fluctuations and Gaussian Integrals |
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155 | (4) |
Appendix B Summary Vector Calculus |
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159 | (6) |
Appendix C Answers to Selected Exercises |
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165 | (10) |
Index |
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175 | |