(Publisher-supplied data) 1 Flow-induced deformation of two-dimensional biconcave capsules 1 C. Pozrikidis 1.1 Introduction 1 1.2 Mathematical framework4 1.2.1 Membrane mechanics 5 1.2.2 Boundary-integral formulation 7 1.3 Numerical method 9 1.3.1 Solution of the integral equation 10 1.3.2 MATLABR code rbc 2d 12 1.4 Cell shapes and dimensionless numbers 13 1.5 Capsule deformation in infinite shear flow 15 1.6 Capsule motion near a wall 25 1.7 Discussion 30 2 Flow-induced deformation of artificial capsules 35 D. Barthes-Biesel, J.Walter, A.-V. Salsac 2.1 Introduction 35 2.2 Membrane mechanics 38 2.2.1 Membrane deformation 38 2.2.2 Membrane constitutive laws and equilibrium 40 2.2.3 Osmotic effects and prestress 42 2.3 Capsule dynamics in flow 43 2.3.1 Instability due to compression 45 2.3.2 Numerical procedure 46 2.4 B-spline projection 46 2.4.1 Computation of boundary integrals 50 2.4.2 Two-grid method 51 2.5 Coupling finite elements and boundary integrals 52 2.5.1 Isoparametric interpolation 52 2.5.2 Mesh generation 53 2.5.3 Membrane finite-element formulation 54 2.5.4 Computation of boundary integrals . 57 2.6 Capsule deformation in linear shear flow 57 2.6.1 Simple shear flow 57 2.6.2 Plane hyperbolic flow 63 2.7 Discussion 65

3 A high-resolution fast boundary-integral method for multiple interacting blood cells 71 J. B. Freund, H. Zhao 3.1 Introduction 72 3.1.1 Fast summation methods 75 3.1.2 Boundary conditions 76 3.1.3 Membrane constitutive equations 76 3.1.4 Preamble 77 3.2 Mathematical framework . 77 3.2.1 Integral formulation 78 3.2.2 Time advancement 82 3.2.3 Flow specification 82 3.3 Fast summation in boundary-integral computations 83 3.3.1 Short-range component evaluation 84 3.3.2 Smooth component evaluation 84 3.3.3 Particle particle/particle mesh method (PPPM) 85 3.4 Membrane mechanics 87 3.4.1 Spectral basis functions 87 3.4.2 Constitutive equations 88 3.4.3 Equilibrium equations 89 3.5 Numerical fidelity 90 3.5.1 Truncation errors, convergence and resolution 90 3.5.2 Aliasing errors, nonlinear instability and dealiasing . 92 3.6 Simulations 96 3.6.1 Resolution and dealiasing 97 3.6.2 Effective viscosity 100 3.6.3 Leukocyte transport 101 3.6.4 Complex geometries 102 3.7 Summary and outlook 104 3.7.1 Pros 104 3.7.2 Cons 105 4 Simulating microscopic hemodynamics and hemorheology with the immersed-boundary lattice Boltzmann method 113 J. Zhang, P. C. Johnson, A. S. Popel 4.1 Introduction 114 4.2 The lattice Boltzmann method 116 4.2.1 General algorithm 116 4.2.2 Boundary conditions 119 4.3 The immersed-boundary method 121 4.4 Fluid property updating . 123 4.5 Models of RBC mechanics and aggregation 124 4.5.1 RBC geometry and fluid viscosity 124 4.6 Single cells and groups of cells 126 4.6.1 Deformation of a single cell in shear flow 127 4.6.2 Channel flow 129 4.6.3 Rouleaux formation 130 4.6.4 Rouleaux dissociation in shear flow . 130 4.7 Cell suspension flow in microvessels 134 4.7.1 Cell-free layers 136 4.7.2 RBC distribution and velocity profile 137 4.7.3 Effect of cell deformability and aggregation 139 4.7.4 Effect of the channel width 141 4.8 Summary and discussion 142

5 Front-tracking methods for capsules, vesicles and blood cells 149 P. Bagchi 5.1 Introduction . 149 5.2 Numerical method . . 153 5.2.1 Navier¿Stokes solver 154 5.2.2 Computation of the interfacial force 156 5.2.3 Membrane discretization 157 5.3 Capsule deformation in simple shear flow 157 5.3.1 Spherical capsules 158 5.3.2 Ellipsoidal capsules 159 5.3.3 Vesicles 162 5.3.4 Red blood cells 164 5.4 Capsule interception 164 5.5 Capsule motion near a wall 167 5.6 Suspension flow in a channel 168 5.7 Rolling on an adhesive substrate 170 5.8 Summary 173 6 Dissipative particle dynamics modeling of red blood cells 183 D. A. Fedosov, B. Caswell, G. E. Karniadakis 6.1 Introduction 184 6.2 Mathematical framework 185 6.2.1 Dissipative particle dynamics 185 6.2.2 Mesoscopic viscoelastic membrane model 187 6.2.3 Triangulation 189 6.3 Membrane mechanical properties 190 6.3.1 Shear modulus 191 6.3.2 Compression modulus 192 6.3.3 Bending rigidity 193 6.3.4 Membrane viscosity 194 6.4 Membrane-solvent interfacial conditions 196 6.5 Numerical and physical scaling 197 6.6 Membrane mechanics 198 6.6.1 Equilibrium shape and the stress-free model 199 6.7 Membrane rheology from twisting torque cytometry 202 6.8 Cell deformation in shear flow 204 6.9 Tube flow 209 6.10 Summary 212

7 Simulation of red blood cellmotion in microvessels and bifurcations 219 T.W. Secomb 7.1 Introduction 219 7.2 Axisymmetric models for single-file RBC motion 222 7.3 Two-dimensional models for RBC motion 225 7.3.1 Element cell model 226 7.3.2 Governing equations and numerical method 228 7.4 Tank-treading in simple shear flow 264 8.3.5 Oblate spheroids with aspect ratio 0.3 0.5 265 8.4 Brownian motion 266 8.4.1 Brownian motion near a wall in a quiescent fluid 267 8.4.2 Convective and diffusive transport 269 8.4.3 Influence on surface adhesive dynamics 272 8.5 Shape and wall effects on hydrodynamic collision 274 8.5.1 Collision mechanisms 275 8.5.2 Collision frequency 275 8.6 Transient aggregation of two platelets near a wall 283 8.6.1 Adhesive dynamics model 285 8.6.2 Binding efficiency for GPIba vWF kinetics 289 8.6.3 Effect of interplatelet binding on collision 290 8.6.4 Force mechanics of bond rupture 292 8.7 Conclusions and future directions 294.