Moving boundaries in micro-scale biofluid dynamics

[+] Author and Article Information
W Shyy, M Francois, N N’dri, R Tran-Son-Tay

Department of Aerospace Engineering, Mechanics, and Engineering Science, University of Florida, Gainesville FL 32611

HS Udaykumar

Department of Mechanical Engineering, University of Iowa, Iowa City IA 52242

Appl. Mech. Rev 54(5), 405-454 (Sep 01, 2001) (50 pages) doi:10.1115/1.1403025 History:
Copyright © 2001 by ASME
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Crank J (1984), Free and Moving Boundary Problems, Oxford University Press, New York.
Floryan  JM and Rasmussen  H (1989), Numerical methods for viscous flows with moving boundaries, Appl. Mech. Rev. 42(12), 323–340.
Shyy W, Udaykumar HS, Rao MM, and Smith RW (1996), Computational Fluid Dynamics with Moving Boundaries, Taylor and Francis, Washington DC.
Harlow  FH and Welch  JE (1965), Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys. Fluids 8, 2182–2189.
Vicelli  JA (1969), A method for including arbitrary external boundaries in the MAC incompressible fluid computing technique, J. Comput. Phys. 4, 543–551.
Fukai  J, Zhao  Z, Poulikakos  D, Megaridis  CM, and Miyatake  O (1993), Modeling of the deformation of a liquid droplet impinging upon a flat surface, Phys. Fluids 5, 2588–2599.
Chen  S, Johnson  DB, and Raad  PE (1995), Velocity boundary conditions for the simulation of free surface fluid flow, J. Comput. Phys. 116, 262–276.
Liu  H and Kawachi  K (1998), A numerical study of insect flight, J. Comput. Phys. 146, 124–156.
Liu  H and Kawachi  K (1999), A numerical study of undulatory swimming, J. Comput. Phys. 155, 223–247.
Ashgriz  N and Poo  JY (1991), FLAIR: Flux line-segment model for an Advection and interface reconstruction, J. Comput. Phys. 93, 449–468.
Unverdi  SO and Tryggvason  G (1992), A front tracking method for viscous, incompressible, multi-fluid flows, J. Comput. Phys. 100, 25–37.
Udaykumar  HS, Mittal  R, and Shyy  W (1999), Computation of solid-liquid phase fronts in the sharp interface limit on fixed grids, J. Comput. Phys. 153, 535–574.
Shyy W (1994), Computational Modeling for Fluid Flow and Interfacial Transport, Elsevier Sci Publ, Amsterdam.
He X, Fuentes C, Shyy W, Lian Y, and Carroll B (2000), Computation of transitional flows around an airfoil with a movable flap, AIAA Fluids 2000 and Exhibit, Paper No AIAA-2000-2240, June 19–22, Denver CO.
Steger JL (1991), Thoughts on the Chimera grid method of simulation of three-dimensional viscous flow, Proc Computational Fluid Dynamics Symp on Aeropropulsion, NASA CP-3078, 1–10.
Johnson  RA and Belk  DM (1995), Multigrid approach to overset grid communication, AIAA J. 33, 2305–2308.
Venkatakrishnan  V (1996), Perspectives on unstructured grid flow solvers, AIAA J. 34, 533–547.
Camacho  GT and Ortiz  M (1996), Computational modeling of impact damage in brittle materials, Int. J. Solids Struct. 33, 2899–2938.
Camacho  GT and Ortiz  M (1997), Adaptive Lagrangian modeling of ballistic penetration of metallic targets, Comput. Methods Appl. Mech. Eng. 142, 269–301.
Fritz  MJ and Boris  JP (1979), The Lagrangian solution of transient problems in hydrodynamics using a triangular mesh, J. Comput. Phys. 31, 173–215.
Glimm  J, Grove  J, Lindquist  B, McBryan  OA, and Tryggvason  G (1988), The bifurcation of tracked scalar waves, SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 9, 61–79.
Rausch  RD, Batina  JT, and Yang  HTY (1993), Three-dimensional time-marching aeroelastic analyses using an unstructured-grid Euler method, AIAA J. 31(9), 1626–1633.
Lizska  TJ, Duarte  CAM, and Tworzydlo  WW (1996), Hp-meshless cloud method, Comput. Methods Appl. Mech. Eng. 139, 263–288.
Duarte  A and Oden  JT (1996), An h-p adaptive method using clouds, Comput. Methods Appl. Mech. Eng. 139, 237–262.
Randles  PW and Libersky  LD (1996), Smoothed particle hydrodynamics: some recent improvements and applications, Comput. Methods Appl. Mech. Eng. 139, 375–408.
Hirt  CW and Nichols  BD (1981), Volume of Fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys. 39, 201–225.
Brackbill  JU, Kothe  DB, and Zemach  C (1992), A continuum method for modeling surface tension, J. Comput. Phys. 100, 335–354.
Kothe  DB and Mjolsness  RC (1992), Ripple: A new model for incompressible flows with free surfaces, AIAA J. 30, 2694–2700.
Scardovelli  R and Zaleski  S (1999), Direct numerical simulation of free-surface and interfacial flow, Annu. Rev. Fluid Mech. 31, 567–603.
Osher  S and Sethian  JA (1988), Fronts propagating with curvature dependent speed: Algorithms based in Hamilton-Jacobi formulations, J. Comput. Phys. 79, 12–49.
Sethian JA (1996), Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision, and Materials Science, Cambridge Univ Press.
Kobayashi  R (1993), Modeling and numerical simulation of dendritic crystal growth, Physica D 63, 410–423.
Wheeler  AA, Boettinger  WJ, and McFadden  GB (1992), Phase field model for isothermal phase transitions in binary alloys, Phys. Rev. A 45, 7424–7439.
Voller  VR and Prakash  C (1987), A fixed grid numerical modeling methodology for convection-diffusion mushy region phase-change problems, Int. J. Heat Mass Transf. 30, 1709–1719.
Udaykumar  HS, Kan  H-C, Shyy  W, and Tran-Son-Tay  R (1997), Multiphase dynamics in arbitrary geometries on fixed Cartesian grids, J. Comput. Phys. 137, 366–405.
Zhang  H, Zheng  LL, Prasad  V, and Hou  TY (1998), A curvilinear level set formulation for highly deformable free surface problems with application to solidification, Numer. Heat Transfer, Part B 34, 1–20.
Sussman M, Almgren AS, Bell JB, Collela P, Howell LH, and Welcome ML (1997), An adaptive level set approach for incompressible two-phase flows, Lawrence Berkely Lab Report, LBNL-40327.
Barth  T and Sethian  JA (1998), Numerical schemes for the Hamilton-Jacobi and level-set equations on triangulated domains, J. Comput. Phys. 145, 1–40.
Ubbink  O and Issa  RI (1999), A method for capturing sharp fluid interfaces on arbitrary meshes, J. Comput. Phys. 153, 26–50.
Lafaurie  B, Nardone  C, Scardovelli  R, Zaleski  S, and Zanetti  G (1994), Modeling merging and fragmentation in multiphase flows with SURFER, J. Comput. Phys. 113, 134–147.
Xiao  F (1999), A computational model for suspended large rigid bodies in 3D unsteady viscous flows, J. Comput. Phys. 155, 348–379.
Colella  P and Woodward  PR (1984), The piecewise parabolic method (PPM) for gas-dynamical simulations, J. Comput. Phys. 54, 174–201.
Juric  D and Tryggvason  G (1996), A front tracking method for dendritic solidification, J. Comput. Phys. 123, 127–148.
Peskin  CS (1977), Numerical analysis of blood flow in the heart, J. Comput. Phys. 25, 220–252.
Fauci  LJ and Peskin  CS (1988), A computational model of aquatic animal locomotion, J. Comput. Phys. 77, 85–108.
Beyer  RP and LeVeque  RJ (1992), Analysis of a one-dimensional model for the immersed boundary method, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 29(2), 332–364.
Udaykumar  HS and Shyy  W (1995), A grid-supported marker particle scheme for interface tracking, Numer. Heat Transfer, Part B 27, 127–153.
Ye  Y, Mittal  R, Udaykumar  HS, and Shyy  W (1999), A Cartesian grid method for simulation of viscous incompressible flow with complex immersed boundaries, J. Comput. Phys. 156, 209–240.
Kwak  S and Pozrikidis  C (1998), Adaptive triangulation of evolving, closed, or open surfaces by the advancing-front method, J. Comput. Phys. 145, 61–88.
Yon  S and Pozrikidis  C (1998), A finite-volume/boundary-element method for flow past interfaces in the presence of surfactants, with application to shear flow past a viscous drop, Comput. Fluids 27, 879–902.
Liang  Py (1991), Numerical method for calculation of surface tension flows on arbitrary grids, AIAA J. 29, 161–167.
DeGregoria  AJ and Schwartz  LW (1985), Finger breakup in Hele-Shaw cells, Phys. Fluids 28, 2313–2314.
Glimm  J, McBryan  O, Melnikoff  R, and Sharp  DH (1986), Front tracking applied to Rayleigh-Taylor instability, SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 7, 230–251.
Miyata  H (1986), Finite difference simulation of breaking waves, J. Comput. Phys. 65, 179–214.
Wang  HP and McLay  RT (1986), Automatic remeshing scheme for modeling hot forming process, ASME J. Fluids Eng. 108, 465–469.
Thomas  PD and Lombard  CK (1979), Geometric conservation law and its application to flow computations on moving grids, AIAA J. 15, 226–243.
Thompson JF, Warsi ZUA, and Mastin CW (1985), Numerical Grid Generation, Elsevier, New York.
Demirdzic  I and Peric  M (1988), Space conservation law in finite volume calculations of fluid flow, Int. J. Numer. Methods Fluids 8, 1037–1050.
Demerdzic  I and Peric  M (1990), Finite volume method for prediction of fluid flow in arbitrary shaped domains with moving boundaries, Int. J. Numer. Methods Fluids 10, 771–790.
Shyy  W, Pal  S, Udaykumar  HS, and Choi  D (1998), Structured moving grid and geometric conservation laws for fluid flow computation, Numer. Heat Transfer, Part A 34, 369–397.
Kan  H-C, Udaykumar  HS, Shyy  W, and Tran-Son-Tay  R (1998), Hydrodynamics of a compound drop with application to leukocyte modeling, Phys. Fluids 10, 760–774.
Kan  H-C, Udaykumar  HS, Shyy  W, and Tran-Son-Tay  R (1999a), Numerical analysis of the deformation of an adherent drop under shear flow, ASME J. Biomech. Eng. 121, 160–169.
Kan  H-C, Udaykumar  HS, Shyy  W, Vigneron  P, and Tran-Son-Tay  R (1999b), Effects of nucleus on leukocyte recovery, Ann. Biomed. Eng. 27, 648–655.
Melton JE (1996), Automated three-dimensional cartesian grid generation and euler flow solutions for arbitrary geometries, PhD Thesis, Univ of California, Dept of Mech Eng, Davis CA.
Aftomis MJ, Berger MJ, and Adomavicius G (2000), A parallel multilevel method for adaptively refined Cartesian grids with embedded boundaries, AIAA 38th Aerospace Sciences Meeting and Exhibit, AIAA 2000-0808.
Agresar  G, Linderman  JJ, Tryggvason  G, and Powell  KG (1998), An adaptive, Cartesian, front tracking method for the motion, deformation and adhesion of circulating cells, J. Comput. Phys. 143, 346–380.
Udaykumar  HS, Shyy  W, and Rao  MM (1996), ELAFINT - A mixed Eulerian-Lagrangian method for fluid flows with complex and moving boundaries, Int. J. Numer. Methods Fluids 22, 691–704.
Hou  TY, Lowengrub  JS, and Shelley  MJ (1994), Removing the stiffness from interfacial flows with surface tension, J. Comput. Phys. 114, 312.
Fung YC (1993), Biomechanics: Mechanical Properties of Living Tissues, Second edition, Springer-Verlag, New York.
Schmid-Schönbein  GW, Sung  KLP, and Tözeren  H (1981), Passive mechanical properties of human leukocytes, Biophys. J. 6, 243–256.
Schmid-Schönbein  GW and Skalak  R (1984), Continuum mechanical model of leukocytes during protopod formation, ASME J. Biomech. Eng. 106, 10–18.
Marchesi  VT and Florey  HW (1960), Electron micrographic observations on the emigration of leukocytes, Q. J. Exp. Physiol. 45, 343–347.
Zigmond  SH (1978), Chemotaxis by polymorphonuclear leukocytes, J. Cell Biol. 77, 269–287.
Elsbach  P, Beckerdite  S, Pettis  P, and Franson  R (1974), Persistence of regulation of macromolecular synthesis by Escherichia coli during killing by disrupted rabbit granulocytes, Infect. Immun. 9, 663–668.
Waugh  R and Evans  E (1979), Thermoelasticity of red blood cells membrane, Biophys. J. 26, 115–131.
Evans EA and Skalak R (1980), in Mechanics and Thermodynamics of Biomembranes, CRC Press, Inc, Boca Raton, Florida.
Mohandas  N and Evans  E (1994), Mechanical properties of the red cell membrane in relation to molecular structure and genetic defects, Annu. Rev. Biophys. Biomol. Struct. 23, 787–818.
Waugh  R and Bauserman  RG (1995), Physical measurements of bilayer-skeletal separation forces, Ann. Biomed. Eng. 23, 308–321.
Discher  DE, Mohandas  N, and Evans  EA (1994), Molecular maps of red cell deformation: Hidden elasticity and in situ connectivity, Science 266, 1032–1035.
Discher  DE, Boal  DH, and Boey  SK (1997), Phase transitions and anisotropic responses of planar triangular nets under large deformation, Phys. Rev. E 55, 4762–4772.
Discher  DE, Boal  DH, and Boey  SK (1998), Simulations of the erythrocyte cytoskeleton at large deformation II Micropipette aspiration, Biophys. J. 75, 1584–1597.
Discher  DE (2000), New insights into erythrocyte membrane organization and microelasticity, Curr. Opin. Hematol. 7, 117–122.
Schmid-Schönbein  GW, Kosawada  T, Skalak  R and Chien  S (1995), Membrane model of endothelial cell leukocytes. A proposal for the origin of a cortical stress, ASME J. Biomech. Eng. 117, 171–178.
Dong  C, Skalak  R, Sung  KLP, Schmid-Schönbein  GW, and Chien  S (1988), Passive deformation analysis of human leukocytes, ASME J. Biomech. Eng. 110, 27–36.
Needham  D and Hochmuth  RM (1990), Rapid flow of passive neutrophils into a 4 μm pipet and measurement of cytoplasmic viscosity, ASME J. Biomech. Eng. 112, 269–275.
Tsaı̈  MA, Frank  RS, and Waugh  RE (1994), Passive mechanical behavior of human neutrophils: Effect of cytochalas-B, Biophys. J. 66, 2166–2172.
Tsaı̈  MA, Waugh  RE, and Keng  PC (1998), Passive mechanical behaviour of human neutrophils: Effect of colchicine and paclitaxel, Biophys. J. 74, 3282–3291.
Harris  AG and Skalak  TC (1993), Leukocyte cytoskeletal structure determines capillary plugging and network resistance, Am. J. Physiol. 265, H1670–1675.
Dong  C, Skalak  R, and Sung  KLP (1991), Cytoplasmic rheology of passive neutrophils, Biorheology 68, 557–567.
Zhelev  DV, Needham  D, and Hochmuth  RM (1994), Role of the membrane cortex in neutrophil deformation in small pipets, Biophys. J. 67, 696–705.
Tran-Son-Tay  R, Kan  H-C, Udaykumar  HS, Damay  E, and Shyy  W (1998), Rheological modeling of leukocytes, Med. Biol. Eng. Comput. 36, 246–250.
Schmid-Schönbein  GW, Shih  YY, and Chien  S (1980), Morphology of leukocytes, Blood 56, 866–875.
Bagge  U, Skalak  R, and Attefors  R (1977), Granulocyte rheology, Adv. Microcirc. 7, 29–48.
Evans  E and Kukan  B (1984), Passive material behavior of granulocytes based on large deformation and recovery after deformations tests, Blood 64, 1028–1035.
Usami  S, Wung  SL, Skierczyuski  BA, Skalak  R, and Chien  S (1992), Locomotion forces generated by a polymorphonuclear leukocyte, Biophys. J. 63, 1663–1666.
Skierczyuski  BA, Usami  S, Chien  S, and Skalak  R (1993), Active motion of polynuclear leukocytes in response to chemoattractant in a micropipette, ASME J. Biomech. Eng. 115, 503–509.
Tran-Son-Tay R, Ting-Beall HP, Zhelev DV, and Hochmuth RM (1994b), Viscous behavior of leukocytes, in Cell Mechanics and Cellular Engineering, VC Mow, F Guilak, R Tran-Son-Tay, and RM Hochmuth (eds), Springer-Verlag, NY, 22–32.
Moazzam  F, Delano  FA, Zweifach  BW, and Schmid-Schönbein  GW (1997), The leukocyte response to fluid stress, Proc. Natl. Acad. Sci. U.S.A. 94, 5338–5343.
Sung  KLP, Dong  C, Schmid-Shönbein  GW, Chien  S, and Skalak  R (1998), Leukocytes relaxation properties, Biophys. J. 54, 331–336.
Evans  E and Yeung  A (1989), Apparent viscosity and cortical tension of blood granulocytes by micropipet aspiration, Biophys. J. 56, 151–160.
Tran-Son-Tay  R, Needham  D, Yeung  A, and Hochmuth  RM (1991), Time-dependent recovery of passive neutrophils after large deformation, Biophys. J. 60, 856–866.
Hochmuth  RM, Ting-Beall  HP, Beat  BB, Needham  D, and Tran-Son-Tay  R (1993), The viscosity of passive human neutrophils undergoing small deformations, Biophys. J. 64, 1596–1601.
Yeung  A and Evans  E (1989), Cortical shell-liquid core model for passive flow of liquid-like spherical cells into micropipets, Biophys. J. 56, 139–149.
Hochmuth  RM (1990), Cell biomechanics: A brief overview, ASME J. Biomech. Eng. 112, 233–234.
Tsaı̈  MA, Frank  RS, and Waugh  RE (1993), Passive mechanical behavior of human neutrophils: Power-Law fluid, Biophys. J. 65, 2078–2088.
Sadhal SS, Ayyaswamy PS, and Chung JN (1997), Transport Phenomena with Drops and Bubbles, Springer, New York.
Stone  HA and Leal  LG (1990), Breakup of concentric double emulsion droplets in linear flows, J. Fluid Mech. 211, 123.
Eggleton  CD and Popel  AS (1998), Large deformation of red blood cell ghosts in a simple shear flow, Phys. Fluids 10, 1834–1845.
Fauci  LJ (1996), A computational model of the fluid dynamics of undulatory and flagellar swimming, Am. Zool. 36(6), 599–607.
Bottino  DC and Fauci  LJ (1998), A computational model of ameboid deformation and locomotion, Eur. Biophys. J. 27, 532–539.
Fauci  LJ and McDonald  A (1995), Sperm motility in the presence of boundaries, Bull. Math. Biol. 57, 679–699.
Stone  HA, Bentley  BJ, and Leal  LG (1986), Experimental study of transient effects in the breakup of viscous drops, J. Fluid Mech. 173, 131–158.
Stone  HA and Leal  LG (1989a), Relaxation and breakup of an initially extended drop in an otherwise quiescent fluid, J. Fluid Mech. 198, 399.
Stone  HA and Leal  LG (1998b), The influence of initial deformation on drop breakup in subcritical time-dependent flows at low Reynolds numbers, J. Fluid Mech. 206, 223–263.
Dong  C and Skalak  R (1992), Leukocyte deformability: Finite element modeling of large viscoelastic deformation, J. Theor. Biol. 158, 173–193.
Waugh R and Tsai MA (1994), Shear-rate dependence of leukocyte cytoplasmic viscosity, in Cell Mechanics and Cellular Engineering, VC Mow, F Guilak, R Tran-Son-Tay, and RM Hochmuth (eds), Springer-Verlag, New York.
Rallison  JM (1984), Deformation of small viscous drops and bubbles in shear flows, Annu. Rev. Fluid Mech. 16, 45–66.
Rallison  JM and Acrivos  A (1978), A numerical study of the deformation and burst of a liquid drop in an extensional flow, Annu. Rev. Fluid Mech. 89, 191.
Tran-Son-Tay  R, Kirk,  T F, Zhelev  DV, and Hochmuth  RM (1994a), Numerical simulation of the flow of highly viscous drops down a tapered tube, ASME J. Biomech. Eng. 116, 172–177.
Skalak  R, Dong  C, and Zhu  C (1990), Passive deformation and active motions of leukocytes, ASME J. Biomech. Eng. 112, 295–302.
Long MW (1995), Tissue microenvironments, in The Biomedical Engineering Handbook, JD Bronzino (ed), CRC Press, Boca Raton FL, Ch 114, 1692–1709.
Lauffenburger DA and Linderman JJ (1993), Receptors: Models for Binding, Trafficking, and Signaling, Oxford Univ Press, New York.
Hammer  DA and Tirrell  M (1996), Biological adhesion at interfaces, Annu. Rev. Mater. Sci. 26, 651–691.
Springer  TA (1990), Adhesion receptors of the immune system, Nature 346, 425–434.
Kitano  T, Yutani  Y, Shimazu  A, Yano  I, Ohashi  H, and Yamano  Y (1996), The role of physicochemical properies of biomaterials and bacterial cell adhesion in vitro, Int. J. Artif. Organs 19, 353–358.
Bell  G, Dembo  M, and Bongrand  P (1984), Cell adhesion: Competition between nonspecific repulsion and specific bonding, Biophys. J. 45, 1051–1064.
Evans  EA (1985a), Detailed mechanics of membrane-membrane adhesion and separation I Continuum of molecular cross-bridges, Biophys. J. 48, 175–183.
Evans  EA (1985b), Detailed mechanics of membrane-membrane adhesion and separation II Discrete kinetically trapped molecular bridges, Biophys. J. 48, 185–192.
Hammer  DA and Lauffenburger  DA (1987), A dynamical model for receptor-mediated cell adhesion to surfaces, Biophys. J. 52, 475–487.
Dembo  M, Torney  DC, Saxaman  K, and Hammer  D (1988), The reaction-limited kinetics of membrane-to-surface adhesion and detachment, Proc. R. Soc. London 234, 55–83.
Dong  C, Cao  J, Struble  EJ, and Lipowsky  HH (1999), Mechanics of leukocyte deformation and adhesion to endothelium in shear flow, Ann. Biomed. Eng. 23, 322–331.
Hill TL (1960), An Introduction to Statistical Thermodynamics, Addison-Wesley Publ, Reading MA.
Capo  C, Garrouste  F, Benoliel  AM, Bongrang  P, Ryter  A, and Bell  G (1982), Concanavalin-A-mediated thymocyte agglutination: a model for a quantitative study of cell adhesion, J. Cell. Sci. 56, 21–48.
Cozens-Roberts  C, Lauffenburger  DA, and Quinn  JA (1990), A receptor-mediated cell attachment and detachment kinetics; I Probabilistic model and analysis, Biophys. J. 58, 841–856.
Hammer  DA and Apte  SM (1992), Simulation of cell rolling and adhesion on surfaces in shear flow: General results and analysis of selectin-mediated neutrophil adhesion, Biophys. J. 63, 35–57.
Goldman  AJ, Cox  RG, and Brenner  H (1967a), Slow motion of a sphere parallel to a plane wall-I: Motion through a quiescent fluid, Chem. Eng. Sci. 22, 637–651.
Goldman  AJ, Cox  RG, and Brenner  H (1967b), Slow motion of a sphere parallel to a plane wall-II: Couette flow, Chem. Eng. Sci. 22, 653–660.
Lawrence  MB and Springer  TA (1991), Leukocytes roll on a selectin at physiologic flow rates: Distinction from and prerequisite for adhesion through integrins, Cell 65, 859–873.
Kuo  SC, Hammer  DA, and Lauffenburger  DA (1997), Simulation of detachment of specifically bound particles from surfaces by shear flow, Biophys. J. 73, 517–531.
Ward  MD, Dembo  M, and Hammer  DA (1995), Kinetics of cell detachment: effect of ligand density, Ann. Biomed. Eng. 23, 322–331.
Weiss  L (1990), Metastic inefficiency, Adv. Cancer Res. 54, 159–211.
N’dri N, Shyy W, Tran-Son-Tay R, and Udaykumar HS (2000), A multi-scale model for cell adhesion and deformation, Proc of ASME IMECE Conf., FED Vol 253, 205–213.
Oron  A, Davis  SH, and Bankoff  SG (1997), Long-scale evolution of thin liquid films, Rev. Mod. Phys. 69, 931–980.
Shyy W and Narayanan R (1999), Fluid Dynamics at Interfaces, Cambridge Univ Press, New York.
Effros RM and Chang HK (1994), Fluid and Solute Transport in the Airspace of the Lungs, Marcel Dekker, New York.
Secomb TW (1993), The mechanics of blood flow in capillaries, in AY Cheer, CP van Dam (eds), Fluid Dynamics in Biology, Am Math Soc, Providence RI, 519–542.
Hayashi TT (1977), Mechanics of Contact Lens Motion, PhD thesis, Univ of California, Berkeley.
Allaire  PE and Flack  RD (1980), Squeeze forces in contact lenses with steep base curve radius, Am. J. Optom. Physiol. Opt. 57(4), 219–227.
Conway  HD (1982), The motion of a contact lens over the eye during blinking, Am. J. Optom. Physiol. Opt. 59(10), 770–773.
Conway  HD and Knoll  HA (1986), Further studies of contact lens motion during blinking, Am. J. Optom. Physiol. Opt. 63(10), 824–829.
Raad  PE and Sabau  AS (1996), Dynamics of a gas permeable contact lens during blinking, ASME J. Appl. Mech. 63, 441–418.
Jenkins  JT and Shimbo  M (1984), The distribution of pressure behind a soft contact lens, ASME J. Appl. Mech. 106, 62–65.
Fukenbusch  GT and Benson  RC (1996), The conformity of a soft contact lens on the eye, ASME J. Biomech. Eng. 118, 341–348.
Martin  DK and Holden  BA (1986), Forces developed beneath hydrogel contact lenses due to squeeze pressure, Phys. Med. Biol. 6, 635–649.
Shyy W and Smith R (1997), A study of flexible airfoil aerodynamics with application to micro aerial vehicles, AIAA-97-1933.
Francois M, Shyy W, and Udaykumar HS (1999), Computational mechanics of soft contact lenses, APS Fluid Dynamics Conf, New Orleans LA.
Smith  R and Shyy  W (1995), Computation of unsteady laminar flow over a flexible two-dimensional membrane wing, Phys. Fluids 7(9), 2175–2184.
Smith  R W and Shyy  W (1996), Computation of aerodynamic coefficients for a flexible membrane airfoil in turbulent flow: A comparison with classical theory, Phys. Fluids 8, 3346–3353.
Shyy  W, Jenkins  DA, and Smith  RW (1997), Study of adaptive shape airfoils at low Reynolds number in oscillatory flows, AIAA J. 35, 1545–1548.
Lillberg E, Kamakoti R, and Shyy W (2000), Computation of unsteady interaction between viscous flows and flexible structure with finite inertia, AIAA 38th Aerospace Sciences Meeting and Exhibit, Paper No 2000-0142.
Knutton  S, Sumner  MCB, and Pasternak  CA (1975), Role of microvilli in surface changes of synchronized P815Y mastocytoma cells, J. Cell Biol. 66, 568–576.
Loor  F and Hagg  LB (1975), The modulation of microprojections on the lymphocyte membrane and the redistribution of membrane bound ligands, a correlation, Eur. J. Immunol. 6, 854–865.
Bell  GI (1981), Estimate of the sticking probability for cells in uniform shear flow with adhesion caused by specific bonds, Cell Biophys. 3, 289–304.
Evans  E, Berk  D, and Leung  L (1991), Detachment of agglutinin-bonded red blood cells I Forces to rupture molecular-point attachments, Biophys. J. 59, 838–848.
Schmid-Schönbein  GW, Fung  Y, and Zweifach  BW (1975), Vascular endothelium-leukocyte interactions: Sticking shear force in venules, Circ. Res. 36, 173–184.
Bell  GI (1978), Models for the specific adhesion of cells to cells, Science 200, 618–627.
Evans  EA (1983), Bending elastic modulus of red blood cell membrane derived from buckling instability in micropipet aspiration tests, Biophys. J. 43, 27–30.
Conway  HD (1982), Effects of base curvature on squeeze pressures in contact lenses, Am. J. Optom. Physiol. Opt. 59(2), 152–154.
Conway  HD and Richman  M (1982), Effects of contact lens deformation on tear film pressures induced during blinking, Am. J. Optom. Physiol. Opt. 59(1), 13–20.
Conway  HD and Richman  MW (1983), The effects of contact lens deformation on tear film pressure and thickness during motion of the lens towards the eye, ASME J. Biomech. Eng. 105, 47–50.
Halpern  D and Grotberg  JB, (1992), Fluid-elastic instabilities of liquid-lined flexible tubes, J. Fluid Mech. 244, 615–632.
Harten  A, Engquist  B, Osher  S, and Chakravarthy  SR (1997), Uniformly high-order accurate essentially non-oscillatory schemes, III, J. Comput. Phys. 131, 3–47.
Melton JE, Enomoto FY, and Berger MJ (1993), 3D automatic grid generation for Euler flows, AIAA 93-3386-CP.
Shyy W, Thakur SS, Ouyang H, Liu J, and Blosch E (1997), Computational Techniques for Complex Transport Phenomena, Cambridge Univ Press, New York.
Udaykumar HS, Tran L, Shyy W, Vanden K, and Belk DM (2000), A combined immersed interface and ENO shock capturing method for multimaterial impact dynamics, AIAA Fluids 2000 and Exhibit, Paper No AIAA-2000-2664.
Vigneron P (1998), Effect of the nucleus on leukocyte deformation, Master of Science Thesis, Univ of Florida.
Ward  MD and Hammer  DA, (1993), A theoretical analysis for the effect of focal contact formation on cell-substrate attachment strength, Biophys. J. 64, 936–959.
Wilson  G, Schwallie  JD, and Bauman  RE (1998), Comparison by contact lens cytology and clinical tests of three contact lens types, Optom. Vision Sci. 75(5), 323–329.


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Comparison of Lagrangian and Eulerian methods for interface tracking
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Illustration of the effect of the geometric conservation law on computational accuracy.
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Illustration of geometric conservation law in a moving boundary computation: a) Schematic of a moving boundary test problem with prescribed boundary velocity, b) Mass conservation residual plot for implicit and trapezoid schemes
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Illustration of a computational domain having an immersed boundary.
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Marker points considered for the estimation of the force at point P.
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Fluid points considered for the evaluation of the velocity at marker point X.
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Illustration of one level local grid refinement.
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Interfacial cell and bulk cell classification on a grid with interface passing through it. Also shown are interfacial cell properties.
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Schematic of computational domain with immersed boundaries: a) boundary cells with immersed boundary located south of cell center, b) boundary cells with immersed boundary located west of cell center, c) typical reshaped trapezoidal boundary cells corresponding to case a, d) typical boundary cells corresponding to case b.
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Schematic of interpolation for cell face values and derivative at boundary cells; a) various fluxes required for trapezoidal boundary cell, b) trapezoidal region and stencil used in computing fsw.
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Trapezoidal region and stencil used in computing fe.
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Stencil for calculation of interface flux: a) stencil for calculating, b) stencil for calculating ∂ϕ/∂x.
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Illustration of the parameters in the analysis: a) The definition of model parameters, b) computational set-up and boundary conditions
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The steady-state behavior of the simple and compound drops when subjected to uniaxial extensional flow: a) DvsCa for simple (λ2=1,γ2=1) and compound drops (λ2=1,λ3=1,γ2=1,γ3=1,R3=0.5), •: simple drop of Stone and Leal 113114, ---: simple drop (present results), o: compound drop of Stone and Leal 107, —: compound drop of Kan etal61. Shapes corresponding to the capillary numbers I to IV are shown; b) Velocity vectors at steady state for Ca=0.1.
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Effect of the capillary number or imposed flow strength on the deformation (L2=3) and subsequent recovery of the compound drop (γ2=1,γ3=1,λ2=1,λ3=100): a) Recovery shapes for the compound drop deformed at low strain rate (Ca=0.14),b) Recovery shapes for the drop deformed at higher strain rate (Ca=0.35). The sequences of figures in a and b correspond to identical extension lengths.
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The recovery behavior of the compound drop compared to several averaged simple drops: a) Lvs unscaled recovery time, b) Lvs scaled recovery time, c) Scaled rate of deformation vs scaled recovery time, d) Lvs scaled recovery time. All viscosities and scaling factors are indicated in the figures.
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Velocity vectors during recovery for the core and shell with disparate time scales (γ2=1,γ3=1,λ2=40,λ3=4000) for different initial core deformations but the same overall drop deformation. Scaled times at which the vector are shown are indicated alongside each case: a) For L3=0.618,L2=2.1, the scaling factor λapp for time is 285, b) for L3=1 and L2=2.1, the scaling factor λapp for time is 220.
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Recovery paths for compound drops with different initial core deformation and a highly viscous core (γ2=1,γ3=1,λ2=40,λ3=4000)
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Velocity vectors during recovery for the core with a time scale comparable with that of the shell (γ2=1,γ3=1,λ2=40,λ3=400) for different initial shapes. Scaled times ts during recovery are indicated in each case: a) for L3=0.618, the scaling factor λapp for times is 165; b) for L3=1, the scaling factor λapp for time is 70.
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Recovery curves for the case (γ2=1,γ3=1,λ2=40,λ3=400) when core deformation time scale is comparable with the outer layer time scale: a) Lvs scaled time ts, scaling factors obtained to match the long-time recovery asymptote of the simple drop curve are shown in legend; b) Lvsts scaled to match the initial recovery stages obtained with scaling factors shown in the legend.
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Comparison of recovery shapes from simulation results and experimental observations: a) Sequent fluorescent-illuminated pictures of a lymphocyte recovery, b) Numerical simulations.
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Recovery curves for cell and nucleus vs recovery time for the lymphocyte simulations. Solid and dash lines represent computed recovery lengths for the cell and nucleus, respectively. Open circles and asterisks correspond to the experimental data for the cell and nucleus, respectively.
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Schematic illustration of the adherent (bridged) and free (unabridged) regions adjacent to the edge of the contact zone 122. The intensive forces supported by the membrane include a principal tension, Tm, that acts tangent to the plane of the membrane surface and a transverse shear Qm, that acts normal to the membrane plus the attractive stress, σn, which represents the adhesive forces. The curvilinear coordinates (s,θ) are also shown.
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Quantities expected to influence the receptor-mediated cell adhesion to a surface include receptor number, the density of complementary surface ligands, the force and torque transmitted to the cell by the passing fluid, the mobility of receptor in the plane of the membrane, and the contract area in which cell to surface bonds may form (adopted from Hammer and Lauffenburger, 129)
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The geometry of membrane-to-surface adhesion is illustrated 130. The surface to which the membrane binds is taken as coincident with the x-axis. Position along the contour of the membrane is tracked by the arc-length coordinate, s, at the free extremity (s→∞), tension (Tfx) is applied to the membrane at a particular angle (θfx) with respect to the surface. At the clamped extremity (s→+∞) the membrane is firmly attached to the surface so as to prevent lateral slippage.
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Spatial variation of Y⁁,T⁁, and A⁁b at steady state in the case of slip-bonds. Tfx=2 (adopted from Dembo et al. 130)
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Macro-Micro model. The cellular model is shown on the left, whereas the enlarged area on the right shows the micro domain for hte receptor model.
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Flow chart showing the interaction between the micro-model (receptor scale) and the macro-model (cellular scale)
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Instantaneous droplet shapes for Ca=1.0a) and Ca=0.1b), both with Re=100
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Instantaneous droplet shapes for two different Reynolds numbers Re=100 a) and Re=1.0 b) both with Ca=1.0
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Maximum length of a bond before breaking as a function of the reverse reaction rate, for different values of forward reaction rate: (▪) for kfo=10−7cm2/sec, (▴) for kfo=10−10cm2/sec, (♦) for kfo=10−12cm2/sec, (•) for kfo=10−14cm2/sec
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Effect of the ligand density (×1010 cm−2) on the peeling or debonding time (s);fσ=0.1,σts=4.5 dyne/cm, and σ=5 dyne/cm
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Effect of the slippage constant fσ on teh debonding time (s) for σ (circle) and σts (square) held constant respectively. The circle dots correspond to σ=5 dyne/cm, and σts is allowed to vary with fσ. The square dots correspond to σts=4.5 dyne/cm, and σ is allowed to vary with fσ.Nr=Nl=5×1010cm−2.
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Illustration of the instantaneous membrane shape resulting from the pressure field, based on the macroscopic model, and the bond force, based on the receptor-ligand model. The vertical axis is normalized by the bond length, and the horizontal axis by the cell radius.
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Effect of spring constant on membrane deformation
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Forward reaction rate as a function of time for two different locations of the bonds; X is the abscise location of the bond
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Reverse reaction rate as a function of time for two different locations of the bonds; X is the abscise location of the bond
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Schematic of an elastic membrane and the key variables
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Schematic of contact lens and computational model
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Schematic of the contact lens model and thickness profile
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Time history of the applied external pressure Pa=Paequil−A sin(π/40t)
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Maximum deflection versus time for L10, L100, L1000 with variable thickness
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Maximum pressure difference inside the tear film vs time
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Variation of tear fluid volume going in/out of domain with time
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Velocity vectors and pressure contours at t=5, 20, and 30 (case L10 with variable thickness); for L100 and L1000, the qualitative features are similar
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Averaged Reynolds number vs aspect ratio




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