References
- Al-Taweel, A.M., S. Madhavan, K. Podila, M. Koksal, A. Troshko and Y.P. Gupta, 2006, CFD Simulation of Multiphase Flow: Closure Recommendations for Fluid-Fluid Systems, 12th European Conference on Mixing, Bologna, Italy, June 27-30
- Augier, F., O. Masbernat and P. Guiraud, 2003, Slip velocity and drag law in a liquid-liquid homogeneous dispersed flow, AIChE J. 49, 2300-2441 https://doi.org/10.1002/aic.690490907
- Auton, T.R., 1987, The lift force on a spherical body in a rotational flow, J. Fluid Mech. 183, 199-218 https://doi.org/10.1017/S002211208700260X
- Auton, T.R., 1984, The dynamics of bubbles, drops and particles in motion in liquids, PhD Dissertation, University of Cambridge
- Asmolov, E.S. and J.B. McLaughlin, 1999, The inertial lift on an oscillating sphere in a Iinear shear flow, Int. J. Multiphase Flow 25, 739-751 https://doi.org/10.1016/S0301-9322(98)00063-9
- Bagchi, P. and S. Balachandar, 2002a, Effects of free rotation on the motion of a solid sphere in linear shear flow at moderate Re, Phys. Fluids 14, 2719-2737 https://doi.org/10.1063/1.1487378
- Bagchi, P., and S. Balachandar, 2002b, Shear versus vortex-induced lift force on a rigid sphere at moderate Re, J. Fluid Mech. 473, 379-388
- Barnca, E. and J. Mizrahi, 1975, A generalized approach to the fluid dynamics of particulate systems. Part 2: sedimentation and fluidization of clouds of spherical liquid drops, Can. J. Chem. Eng. 53, 461-468 https://doi.org/10.1002/cjce.5450530501
- Baskurt, O.K. and H.J. Meiselman, 2007, Hemodynamic effects of red blood cell aggregation, Indian J. Exp. Biol. 45, 25-3
- Baumler, H., B. Neu, E. Donath and H. Kiesewetter, 1999, Basic phenomena of red blood cell rouleaux formation biorheologgy, Biorheology 36, 439-442
- Behzadi, A., R.I. Issa and H. Rusche, 2004, Modelling of dispersed bubble and droplet flow at high phase fractions, Chem. Eng. Sci. 59, 759-770 https://doi.org/10.1016/j.ces.2003.11.018
- Bothe, D., Schmidtke, M. and Warnecke, H.-J., 2006. VOF-simulation of the lift force for single bubbles in a simple shear flow, Chem. Eng. and Techn. 29, 1048-1053 https://doi.org/10.1002/ceat.200600168
- Buchanan, J.R., C. Kleinstreuer and J.K. Comer, 2000, Rheological effects on pulsatile hemodynamics in a stenosed tube, Comput. Fluid. 29, 695-724 https://doi.org/10.1016/S0045-7930(99)00019-5
- Buchanan, J.R., C. Kleinstreuer, S. Hyun and G.A. Truskey, 2003, Hemodynamics simulation and identification of susceptible sites of atherosclerotÎc lesion formation in a model abdominal aorta, J. Biomech. 36, 1185-1196 https://doi.org/10.1016/S0021-9290(03)00088-5
- Candelier, F., and J.R. Angilella, 2006, Analytical investigation of the combined affect of fluid inertia and unsteadiness on low-Re particle centrifugation, Phys. Rev. E 73, 047301 https://doi.org/10.1103/PhysRevE.73.047301
- Candelier, F. and M. Souhar, 2007, Time-dependent lift force acting on a particle moving arbitrarily in a pure shear flow at small reynolds numbers, Phys. Rev. E 76, 067301 https://doi.org/10.1103/PhysRevE.76.067301
- Carpinlioglu, M.O. and M.Y. Gundogdu, 2001, A critical review on pulsatile pipe flow studies directing towards future research topics, Flow. Meas. and Instrum. 12, 163-174 https://doi.org/10.1016/S0955-5986(01)00020-6
- Chakravarty, S. and S. Sen, 2005, Dynamic response of heat and mass transfer in blood flow through stenosed bifurcated arteries, Korea Aust. Rheol. J. 17, 47-62
- Cousins, R.R., 1970, A note on the shear Flow past a sphere, J. Fluid Mech. 40, 543-547
- Dandy, D.S. and Dwyer, H.A., 1990, A sphere in shear flow at finite Reynolds number effect of shear on particle lift, drag, and heat transfer, J. Fluid Mech. 216, 381-410 https://doi.org/10.1017/S0022112090000477
- Darwin, C. 1953, Note on hydrodynamics, Cambiridge Phil. Trans. 49, 342-354
- De Gruttola, S., K. Boomsma and D. Poulikakos, 2005, Computational simulation of a non-Newtonian model of the blood separation process, Artif Organs 29, 949-959 https://doi.org/10.1111/j.1525-1594.2005.00164.x
- De Vrics, A.W.G, A. Biesheuvel and L. van Wijngaarden, 2002, Notes on the path and wake of a gas bubble rising in pure water Intl. J. of Multiphase Flow 28, 1823-1835 https://doi.org/10.1016/S0301-9322(02)00036-8
- Drew, D. and R.T. Lahey, 1979, Applications of general constitutive principles to the derivation of multidimensional twophase flow equations, Intl J. Multiphase Flow 5, 243-264 https://doi.org/10.1016/0301-9322(79)90024-7
- Drew, D. and R.T. Lahey, 1987, The virtual mass and lift force on a sphere in rotating and straining inviscid flow, Intl J. Multiphase Flow 13, 113-121 https://doi.org/10.1016/0301-9322(87)90011-5
- Drew, D. and R.T. Lahey, 1990, Some supplemental analysis concerning the virtual mass and lift force on a sphere in a rotating and straining flow, Intl J. Multiphase Flow 16, 1127-1130 https://doi.org/10.1016/0301-9322(90)90110-5
- Drew, D. and R. T. Lahey, 1993, Analytical modeling of multiphase flow, Particulate Two-Phase Flow, Butterworth-Heinemann, Boston, 509-566
- Ervin, E.A. and G. Tryggvason, 1994, The rise of bubbles in an vertical shear flow, In: Proceedings of the ASME Winter Meeting, Fluids Engineering Div., Chicago
-
Fischer, T.M., M. St
$\ddot{o}$ hr-Liesen and H. Schmid-Sch$\ddot{o}$ nbein, 1978, The red cell as a fluid droplet: tank tread-like motion of the human erythrocyte membrane in shear flow, Science 202, 894-896 https://doi.org/10.1126/science.715448 - Fluent User's Guide, ver. 6.3.26, Fluent Inc., 2006
- Fung, Y.C., 1993, Biomechanics: Mechanical Properties of Living Tissues, Second Edition, Springer-Verlag, New York
- Goldsmith, H.L., D.N. Bell, S. Spain and F.A. McIntosh, 1999, Effect of red blood cells and their aggregates on platelets and white cells in flowing blood, Biorheology 36, 461-468
- Gundogdu, M.Y. and M.O. Carpinlioglu, 1999a, Present state of art on pulsatile flow theory, part 1. laminar and transitional flow regimes, JSME Int. J. 42, 384-397 https://doi.org/10.1299/jsmeb.42.384
- Gundogdu, M.Y., and M. O. Carpinlioglu, 1999b, Present state of art on pulsatile flow theory, part 2. turbulent flow regime, JSME Int. J. 42, 398-410
- Guyton, A.C. and J.E. Hall, 2006, Textbook of Medical Physiology, Eleventh Edition, EIsevier Saunders
- Hall, I.M., 1956, The displacement effect of a sphere in a two-dimensional flow. J. Fluid Mech. 1, 142-161 https://doi.org/10.1017/S002211205600010X
- Hibiki, T., and M. Ishii, 1999, Experimental study on interfacial area transport in bubbly two-phase flows, Intl J. of Heat and Mass Transfer 42, 3019-3035 https://doi.org/10.1016/S0017-9310(99)00014-9
- Hibiki, T., M. Ishii and Z. Xiao, 2001, Axial interfacial area transport of vertical bubbly flows, Intl J. of Heat and Mass Transfer 44, 1869-1888 https://doi.org/10.1016/S0017-9310(00)00232-5
- Hibiki, T., R. Situ, Y. Mi and M. Ishii, 2003, Local flow measurements of vertical upward bubbly flow in an annulus, Intl J. of Heat and Mass Tranfer 46, 1479-1496 https://doi.org/10.1016/S0017-9310(02)00421-0
- Hibiki, T., and M. Ishii, 2007, Lift force in bubbly flow systems, Chem. Eng. Sci. 62, 6457-6474 https://doi.org/10.1016/j.ces.2007.07.034
- Hyun, S., C. Kleinstreuer and Jr. J.P. Archie, 2000a, Hemodynamics analyses of arterial expansions with implications to thrombosis and restenosis, Med. Eng. Phys. 22, 13-27 https://doi.org/10.1016/S1350-4533(00)00006-0
- Hyun, S., C. Kleinstreuer and J.P. Archie, 2000b, Computer simulation and geometric design of endarterectomized carotid artery bifurcations, Crit. Rev. Biomed. Eng. 28, 53-59
- Hyun, S., C. Kleinstreuer and Jr. J.P. Archie, 2001, Computational particle hemodynamics analysis and geometric reconstruction after carotid endarterectomy, Comput. Biol. Med. 31, 365-384 https://doi.org/10.1016/S0010-4825(01)00007-5
- Ishii, M. and T.C. Chawla, 1979, Local drag laws in dispersed two-phase flow, Argonne National Laboratory Report, ANL- 79-105 (NUREG/CR-1230)
- Ishii, M., and N. Zuber, 1979, Drag coefficient and relative velocity in bubbly, droplet or particulate flows, AIChE J. 25, 843-855 https://doi.org/10.1002/aic.690250513
- Ishii, M. and T. Hibiki, 2006, Thermo-fluid Dynamics of Two-phase Flow, Springer, New York
- Jung, J. and A. Hassanein, 2008, Three-phase CFD analytical modeling of blood flow, Med. Eng. Phys. 30, 91-103 https://doi.org/10.1016/j.medengphy.2006.12.004
- Jung, J., R.W. Lyczkowski, C.B. Panchal and A. Hassanein, 2006a, Multiphase hemodynamic simulation with pulsatile flow in a coronary artery, J. of Biomech. 39, 2064-2073 https://doi.org/10.1016/j.jbiomech.2005.06.023
- Jung, J., A. Hassanein and R.W. Lyczkowski, 2006b, hemodynamic computaion using multiphase flowdynamics in a right coronary artery, Ann. Biomed. Eng. 34, 393-407 https://doi.org/10.1007/s10439-005-9017-0
- Kariyasaki, A., 1987, Behavior of a single gas bubble in a liquid flow with a linear velocity profile. Preceedings of the 1987 ASME/JSME Thermal Engineering Conference, 261-267
- Klaseboer, E., J.P. Chavaillier, A. Mate, O. Masbernat, and C. Gourdon, 2001, Model on experiments of drop impinging on an lmmersεd wall, Phys. Fluids 13, 45-57 https://doi.org/10.1063/1.1331313
- Kleinstreuer, C., 2006, Biofluid Dynamics: Principles and Selected Applications, CRC Pres
- Komori, S. and R. Kurose, 1996, The effects of shear and spin on particle lift and drag in shear flow at high Reynolds numbers, Advances in Turbulence VI, (ed. S. Gavrilakis, L. Machiels and P. Monkewitz), Kluwer, 551-554
- Kulkarni, A.A., 2008, Lift force on bubbles in a bubble column reactor: Experimental analysis, Chem. Eng. Sci. 63, 1710-1723 https://doi.org/10.1016/j.ces.2007.10.029
- Kumar, A., and S. Hartland, 1985, Gravity settling in liquid-liquid dispersions, Can. J. Chem. Eng. 63, 368-376 https://doi.org/10.1002/cjce.5450630303
- Kurose, R., and S. Komori, 1999, Drag and lift forces on a rotating sphere in a linear shear flow, J. Fluid Mech. 384, 183-206 https://doi.org/10.1017/S0022112099004164
- Legendre, D. and J. Magnaudet, 1997, A note on the lift force on a spherical bubble or drop in a low-Reynolds-number shear flow, Physics of Fluids 9, 3572-3574 https://doi.org/10.1063/1.869466
- Legendre, D. and J. Magnaudet, 1998, The lift force on a spherical bubble in a viscous linear shear flow, J. Fluid Mech. 368, 81-126 https://doi.org/10.1017/S0022112098001621
- Levich, V.G., 1962, Physicochemical Hydrodynamics, Prentice-Hall, New York
- Lighthill, M.J., 1956, Drift, J. Fluid Mech. 1, 31-53 https://doi.org/10.1017/S0022112056000032
- Liu, T.J., 1993, Bubble size and entrance length effiects on void development in a vertical channel, Intl J. of Heat and Mass Transfer 19, 99-113
- Longest, P.W. and C. Kleinstreuer, 2003, Comparison of blood particle deposition models for non-parallel flow domains, J. Biomech. 36, 421-430 https://doi.org/10.1016/S0021-9290(02)00434-7
- Longest, P.W., C. Kleinstreuer and J.R. Buchanan, 2004, Efficient computation of micro-particle dynamics including wall effects, Comput. Fluid. 33, 577-601 https://doi.org/10.1016/j.compfluid.2003.06.002
- Longest, P.W., C. Kleinstreuer and A. Deanda, 2005, Numerical simulation of wall shear stress and particle-based hemodynamic parameters in pre-cuffed and streamlined end-to-side anastomoses, Ann. Biomed. Eng. 33, 1752-1766 https://doi.org/10.1007/s10439-005-7784-2
- McLaughlin, J.B., 1991, Inertial migration of a small sphere in linear shear flows, J. Fluid Mech. 224, 261-274 https://doi.org/10.1017/S0022112091001751
- McLaughlin, J.B., 1993, The lift on a small sphere in wallbounded linear shear flows, J. Fluid Mech. 246, 249-265 https://doi.org/10.1017/S0022112093000114
- Mei, R., C.J. Lawrence and R.J. Adrian, 1991, Unsteady drag on a sphere at finite Reynolds number with small-amplitude fluctuations in the free-stream velocity, J. Fluid Mech. 233, 613-631 https://doi.org/10.1017/S0022112091000629
- Meiselman, H.J., B. Neu, M.W. Rampling and O.K. Baskurt, 2007, RBC aggregation: Laboratory data and models, Indian J. Exp. Biol. 45, 9-17
- Miyazaki, K., D. Bedeaux and J. Bonet Avalos, 1995, Drag on a Sphere in a Slow Shear Flow, J. Fluid Mech. 296, 373-390 https://doi.org/10.1017/S0022112095002163
- Morsi, S. A. and A. J. Alexander, 1972, An investigation of particle trajectories in two-phase flow systems, J. Fluid Mech. 55, 193-208 https://doi.org/10.1017/S0022112072001806
- Mying, W., S. Hosokawa and A. Tomiyama, 2006, Terminal velocity of single drops in stagnant liquids, Journal of Fluid Science and Technology 1, 72-81 https://doi.org/10.1299/jfst.1.72
-
Naciri, M.A., 1992, Contribution
$\acute{a}$ l'$\acute{e}$ tude des forces exerc$\acute{e}$ es par un liquide sur une bulle de gaz: portance, masse ajout$\acute{e}$ e et interactions hydrodynamiques, Ph.D. Thesis, L'ecole Centrale de Lyon, France - Ookawara, S., D. Street and K. Ogawa, 2004, Practical application to micro-separator/classifier of the Euler-granular model, In: International Conference on Multiphase Flow 2004, Yokohama, Japan
- Ookawara, S., D. Street and K. Ogawa, 2005, Quantitative prediction of separation efficiency of a micro-separator/classifier by Euler-granular model, In: A.I.Ch.E. 2005 Spring National Meeting, Atlanta
- Ookawara, S., D. Street and K. Ogawa, 2006, Numerical study on development of particle concentration profiles in a curved microchannel, Chemical Engineering Science 61, 3714-3724 https://doi.org/10.1016/j.ces.2006.01.016
- Oakwara, S., M. Agrawal, D. Street and K. Ogawa, 2007, Quasidirect numerical simulation of lift force-induced particle separation in a curved microchannel by use of a macroscopic particle model, Chemical Engineering Science 62, 2454-2465 https://doi.org/10.1016/j.ces.2007.01.031
- Rampling, M.W., H.J. Meiselman, B. Neu and O.K. Baskurt, 2004, Influence of cell-specific factors on red blood cell aggregation, Biorheology 41, 91-112
- Rusche, H. and R.l. Issa, 2000, The effect of voidage on the drag force on particles in dispersed two-phase flow, Japanese European Two-Phase Flow Meeting, Tsukuba, Japan
- Saffman, P.G, 1965, The lift force on a small sphere in a slow shear flow, J. Fluid Mech. 22, 385-400 https://doi.org/10.1017/S0022112065000824
- Saffman, P.G., 1968, Corrigendum to 'The lift on a small sphere in a slow shear flow', J. Fluid Mech. 31, 624 https://doi.org/10.1017/S0022112068999990
- Segre, G and A. Silberberg, 1962a, Behaviour of macroscopic rigid spheres in Poiseuille flow. Part 1. Determination of local concentration by statistical analysis of particle passages through crossed light beams, J. Fluid Mech. 14, 115-135 https://doi.org/10.1017/S002211206200110X
- Segre, G. and A. Silberberg, 1962b, Behaviour of macroscopic rigid spheres in Poiseuille flow. Part 2. Experimental results and interpretation, J. Fluid Mech. 14, 136-157 https://doi.org/10.1017/S0022112062001111
- Schiller, L. and Z. Naumann, 1935, A Drag Coefficient Correlation, Z. Ver. Deutsch. Ing. 77, 318-320
-
Schmid-Sch
$\ddot{o}$ nbein, H. and R. Wells, 1969, Fluid drop-like transition of erythrocytεs under shear, Science 165, 288-291 https://doi.org/10.1126/science.165.3890.288 - Shew, W.L., S. Poncet and J.F. Pinton, 2006, Force measurements on rising bubbles, J. Fluid Mech. 569, 51-60 https://doi.org/10.1017/S0022112006002928
- Shin, S., Y. Yang and J.S. Suh, 2009, Measurement of erythrocyte aggregation in a microchip stirring system by light transmission, Clini.l Hemorheo. and Microcirc. 41, 197-207
- Soulis, J.V., G.D. Giannoglou, V. Papaioannou, G.E. Parcharidis and G.E. Louridas, 2008, Low-density lipoprotein concentration in the normal left coronary artery tree, Biomedical Engineering On line 7, 26 https://doi.org/10.1186/1475-925X-7-26
- Srivastava, V.P. and R. Srivastava, 2009, Particulate suspension blood flow through a narrow catheterized artery, Computers and Mathematics with Applications 58, 227-238 https://doi.org/10.1016/j.camwa.2009.01.041
- Steinman, D.A., 2002, Image-based computational fluid dynamics modeling in realistic arterial geometries, Ann. Biomed. Eng. 30, 483-497 https://doi.org/10.1114/1.1467679
- Steinman, D.A. and C.A. Taylor, 2005, Flow imaging and computing: Large artery hemodynamics, Ann. Biomed. Eng. 33, 1704-1709 https://doi.org/10.1007/s10439-005-8772-2
- Stijnen, J.M.A., J. de Hart, P.H.M. Bovendeerd and F.N. van de Vosse, 2004, Evaluation of a fictitious domain method for predicting dynamic response of mechanical heart valves, J. Fluid. Struct. 19, 835-850 https://doi.org/10.1016/j.jfluidstructs.2004.04.007
- Sankaranarayanan, K. and S. Sundaresan, 2002, Lift force in bubbly suspensions, Chemical Engineering Science 57, 3521-3542 https://doi.org/10.1016/S0009-2509(02)00269-5
- Takagi, S. and Y.Matsumoto, 1995, Three dimensional calculation of a rising bubble. In: Proceedings of the Second International Conference on Multiphase Flow, Kyoto
- Tees, D.F.J., O. Coenen and H.L. Goldsmith, 1993, Interaction forces between red-cells agglutinated by antibody. 4. Time and force dependence of break-up, Biophys. J. 65, 1318-1334 https://doi.org/10.1016/S0006-3495(93)81180-9
- Tha, S.P. and H.L. Goldsmith, 1986, Interaction forces between red-cells agglutinated by antibody. 1. Theoretical, Biophys. J. 50, 1109-1116 https://doi.org/10.1016/S0006-3495(86)83555-X
- Tha, S.P. and H.L. Goldsmith, 1988, Interaction forcesbetween red-cells agglutinated by antibody. 3. Micromanipulation, Biophys. J. 53, 677-687 https://doi.org/10.1016/S0006-3495(88)83149-7
- Tomiyama, A., H. Tamai, I. Zun and S. Hosokawa, 2002, Transverse migration of single bubbles in simple shear flows, Chemical Engineering Science 57, 1849-1858 https://doi.org/10.1016/S0009-2509(02)00085-4
- Tomiyama, A., 2004, Drag, lift and virtual mass forces acting on a single bubble, Proceedings of the Third lnternational Symposium on Two-phase Flow Modeling and Expenmentation, Pisa, Italy, 22-24
- Wakaba, L. and S. Balachandar, 2005, History force on a sphere in a weak linear shear flow, Int. J. Multiphase Flow 31, 996-1014 https://doi.org/10.1016/j.ijmultiphaseflow.2005.05.009
- Wallis, G.B., 1974, The terminal speed of single drops or bubbles in an infinite medium, Int. J. Multiphase Flow 1, 491-511 https://doi.org/10.1016/0301-9322(74)90003-2
- Wen, C. and Y. Yu, 1966, Mechanics of Fluidization, Chem. Eng. Prog. Symp. Ser. 62, 100-110
- Yilmaz, F. and M.Y. Gundogdu, 2008, A critical review on blood flow in large arteries; relevance to blood rheology, viscosity models, and physiologic conditions, Korea Aust. Rheol. J. 20, 197-21
- Zeng, L., F. Najjar, S. Blachandar and P. Fischer, 2009, Force on a finite-sized particle located close to a wall in a linear shear flow, Phys. Fluids 21, 033302 https://doi.org/10.1063/1.3082232
- Zhu, C., 2000, Kinetics and mechanics of cell adhesion, J. of Biomech. 33, 23-33 https://doi.org/10.1016/S0021-9290(99)00163-3
- Zhang, D. Z. and Prosperetti, A., 1994, Averaged equations for inviscid disperse two-phase flow. J.Fluid Mech. 267, 185-219 https://doi.org/10.1017/S0022112094001151
- Zun, I., 1988, Transition from wall void peaking to core void peaking in turbulent bubbly flow, Transient Phenomena in Multiphase Flow, Hemisphere, Washington, 225-245