Simulating deformable particle suspensions using a coupled lattice-Boltzmann and finite-element method

A novel method is developed to simulate suspensions of deformable particles by coupling the lattice-Boltzmann method (LBM) for the fluid phase to a linear finite-element analysis (FEA) describing particle deformation. The methodology addresses the need for an efficient method to simulate large numbers of three-dimensional and deformable particles at high volume fraction in order to capture suspension rheology, microstructure, and self-diffusion in a variety of applications. The robustness and accuracy of the LBM–FEA method is demonstrated by simulating an inflating thin-walled sphere, a deformable spherical capsule in shear flow, a settling sphere in a confined channel, two approaching spheres, spheres in shear flow, and red blood cell deformation in flow chambers. Additionally, simulations of suspensions of hundreds of biconcave red blood cells at 40% volume fraction produce continuum-scale physics and accurately predict suspension viscosity and the shear-thinning behaviour of blood. Simulations of fluid-filled spherical capsules which have red-blood-cell membrane properties also display deformation-induced shear-thinning behaviour at 40% volume fraction, although the suspension viscosity is significantly lower than blood.

[1]  Zhu Zeng,et al.  The measurement of shear modulus and membrane surface viscosity of RBC membrane with Ektacytometry: a new technique. , 2007, Mathematical biosciences.

[2]  Robert MacMeccan,et al.  Mechanistic Effects of Erythrocytes on Platelet Deposition in Coronary Thrombosis , 2007 .

[3]  M. Dupin,et al.  Modeling the flow of dense suspensions of deformable particles in three dimensions. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Yaling Liu,et al.  Rheology of red blood cell aggregation by computer simulation , 2006, J. Comput. Phys..

[5]  H. Kataoka,et al.  Dynamic deformation and recovery response of red blood cells to a cyclically reversing shear flow: Effects of frequency of cyclically reversing shear flow and shear stress level. , 2006, Biophysical journal.

[6]  Cyrus K Aidun,et al.  Cluster size distribution and scaling for spherical particles and red blood cells in pressure-driven flows at small Reynolds number. , 2006, Physical review letters.

[7]  John F. Brady,et al.  STOKESIAN DYNAMICS , 2006 .

[8]  Aleksander S Popel,et al.  Computational fluid dynamic simulation of aggregation of deformable cells in a shear flow. , 2005, Journal of biomechanical engineering.

[9]  Tomas Akenine-Möller,et al.  Fast, minimum storage ray/triangle intersection , 1997, J. Graphics, GPU, & Game Tools.

[10]  Anna C Balazs,et al.  Newtonian fluid meets an elastic solid: coupling lattice Boltzmann and lattice-spring models. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  C. Pozrikidis,et al.  Numerical Simulation of Cell Motion in Tube Flow , 2005, Annals of Biomedical Engineering.

[12]  Jeffrey F. Morris,et al.  Stationary shear flow around fixed and free bodies at finite Reynolds number , 2004, Journal of Fluid Mechanics.

[13]  Sehyun Shin,et al.  Measurement of red cell deformability and whole blood viscosity using laser-diffraction slit rheometer , 2004 .

[14]  Asimina Sierou,et al.  Shear-induced self-diffusion in non-colloidal suspensions , 2004, Journal of Fluid Mechanics.

[15]  C. Pozrikidis,et al.  Numerical Simulation of the Flow-Induced Deformation of Red Blood Cells , 2003, Annals of Biomedical Engineering.

[16]  Jason H. Haga,et al.  Quantification of the Passive Mechanical Properties of the Resting Platelet , 1998, Annals of Biomedical Engineering.

[17]  Cyrus K. Aidun,et al.  Extension of the Lattice-Boltzmann Method for Direct Simulation of Suspended Particles Near Contact , 2003 .

[18]  R. Pal Rheology of concentrated suspensions of deformable elastic particles such as human erythrocytes. , 2003, Journal of biomechanics.

[19]  L. Munn,et al.  Red blood cells initiate leukocyte rolling in postcapillary expansions: a lattice Boltzmann analysis. , 2003, Biophysical journal.

[20]  S. Suresha,et al.  Mechanics of the human red blood cell deformed by optical tweezers , 2003 .

[21]  John F. Brady,et al.  Rheology and microstructure in concentrated noncolloidal suspensions , 2002 .

[22]  Dominique Barthès-Biesel,et al.  Effect of constitutive laws for two-dimensional membranes on flow-induced capsule deformation , 2002, Journal of Fluid Mechanics.

[23]  Alexander Z. Zinchenko,et al.  Shear flow of highly concentrated emulsions of deformable drops by numerical simulations , 2002, Journal of Fluid Mechanics.

[24]  S. Chien,et al.  Low viscosity Ektacytometry and its validation tested by flow chamber. , 2001, Journal of biomechanics.

[25]  A. Ladd,et al.  Lattice-Boltzmann Simulations of Particle-Fluid Suspensions , 2001 .

[26]  Ignacio Pagonabarraga,et al.  Lees–Edwards Boundary Conditions for Lattice Boltzmann , 2001 .

[27]  A. Shabana,et al.  Performance of the Incremental and Non-Incremental Finite Element Formulations in Flexible Multibody Problems , 2000 .

[28]  Schram,et al.  Effective viscosity of dense colloidal crystals , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[29]  Cyrus K. Aidun,et al.  The dynamics and scaling law for particles suspended in shear flow with inertia , 2000, Journal of Fluid Mechanics.

[30]  Steven G. Johnson,et al.  Linear waveguides in photonic-crystal slabs , 2000 .

[31]  P. Lallemand,et al.  Theory of the lattice boltzmann method: dispersion, dissipation, isotropy, galilean invariance, and stability , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[32]  G. Breyiannis,et al.  Simple Shear Flow of Suspensions of Elastic Capsules , 2000 .

[33]  Dewei Qi,et al.  Lattice-Boltzmann simulations of particles in non-zero-Reynolds-number flows , 1999, Journal of Fluid Mechanics.

[34]  Shiyi Chen,et al.  LATTICE BOLTZMANN METHOD FOR FLUID FLOWS , 2001 .

[35]  C. Aidun,et al.  Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation , 1998, Journal of Fluid Mechanics.

[36]  L. McIntire,et al.  Biomechanics of cell interactions in shear fields. , 1998, Advanced drug delivery reviews.

[37]  A. Popel,et al.  Large deformation of red blood cell ghosts in a simple shear flow. , 1998, Physics of fluids.

[38]  W. C. Hwang,et al.  Energy of dissociation of lipid bilayer from the membrane skeleton of red blood cells. , 1997, Biophysical journal.

[39]  R K Jain,et al.  Role of erythrocytes in leukocyte-endothelial interactions: mathematical model and experimental validation. , 1996, Biophysical journal.

[40]  Richard L. Beissinger,et al.  Augmented Mass Transport of Macromolecules in Sheared Suspensions to Surfaces B. Bovine Serum Albumin , 1996 .

[41]  J. Moake,et al.  Platelets and shear stress. , 1996, Blood.

[42]  Cyrus K. Aidun,et al.  Lattice Boltzmann simulation of solid particles suspended in fluid , 1995 .

[43]  H. Goldsmith,et al.  Physical and chemical effects of red cells in the shear-induced aggregation of human platelets. , 1995, Biophysical journal.

[44]  A. Magnin,et al.  Rheometry of paints with regard to roll coating process , 1995 .

[45]  K. Bathe Finite Element Procedures , 1995 .

[46]  A. Ladd Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results , 1993, Journal of Fluid Mechanics.

[47]  A. Ladd Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation , 1993, Journal of Fluid Mechanics.

[48]  Augmented Mass Transport of Macromolecules in Sheared Suspensions to Surfaces , 1993 .

[49]  Zanetti,et al.  Use of the Boltzmann equation to simulate lattice gas automata. , 1988, Physical review letters.

[50]  C. Rankin,et al.  An element independent corotational procedure for the treatment of large rotations , 1986 .

[51]  M. Bitbol Red blood cell orientation in orbit C = 0. , 1986, Biophysical journal.

[52]  D. Barthes-Biesel,et al.  Role of membrane viscosity in the orientation and deformation of a spherical capsule suspended in shear flow , 1985, Journal of Fluid Mechanics.

[53]  Joseph B. Keller,et al.  Effective viscosity of a periodic suspension , 1984, Journal of Fluid Mechanics.

[54]  R. Grebe,et al.  A NEW MEMBRANE CONCEPT FOR VISCOUS RBC DEFORMATION IN SHEAR: SPECTRIN OLIGOMER COMPLEXES AS A BINGHAM‐FLUID IN SHEAR AND A DENSE PERIODIC COLLOIDAL SYSTEM IN BENDING a , 1983, Annals of the New York Academy of Sciences.

[55]  H. Brenner,et al.  Spatially periodic suspensions of convex particles in linear shear flows. III. Dilute arrays of spheres suspended in Newtonian fluids , 1983 .

[56]  T. Ishii,et al.  Experimental wall correction factors of single solid spheres in triangular and square cylinders, and parallel plates , 1981 .

[57]  C. Féo,et al.  Automated ektacytometry: a new method of measuring red cell deformability and red cell indices. , 1980, Blood cells.

[58]  R. Waugh,et al.  Thermoelasticity of red blood cell membrane. , 1979, Biophysical journal.

[59]  H Schmid-Schönbein,et al.  The red cell as a fluid droplet: tank tread-like motion of the human erythrocyte membrane in shear flow. , 1978, Science.

[60]  Marshall Sittig,et al.  Pulp and paper manufacture , 1977 .

[61]  J M Paulus,et al.  Platelet size in man. , 1975, Blood.

[62]  R. G. Cox The motion of suspended particles almost in contact , 1974 .

[63]  R. Skalak,et al.  Strain energy function of red blood cell membranes. , 1973, Biophysical journal.

[64]  W. R. Schowalter,et al.  Simple shear flow round a rigid sphere: inertial effects and suspension rheology , 1970, Journal of Fluid Mechanics.

[65]  G. Batchelor,et al.  The stress system in a suspension of force-free particles , 1970, Journal of Fluid Mechanics.

[66]  J. W. Goodwin,et al.  Interactions among erythrocytes under shear. , 1970, Journal of applied physiology.

[67]  R B Whittington,et al.  Blood-plasma viscosity: an approximate temperature-invariant arising from generalised concepts. , 1970, Biorheology.

[68]  J. Goddard,et al.  Nonlinear effects in the rheology of dilute suspensions , 1967, Journal of Fluid Mechanics.

[69]  E. Merrill,et al.  Non‐Newtonian Rheology of Human Blood ‐ Effect of Fibrinogen Deduced by “Subtraction” , 1963, Circulation research.