- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Effects of artery size on the hydrodynamic diffusivity of red cells and other contained particles

Lydia I. Kolitsi and Stergios G. Yiantsios*

  • Department of Chemical Engineering, Aristotle University of Thessaloniki, University Box 453, GR 541 24, Thessaloniki, Greece

  • *yiantsio@auth.gr
PDF

Phys. Rev. Fluids 4, 113103 – Published 26 November, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.113103

Abstract

Direct numerical simulations are presented for pressure-driven and simple shear channel flow of cell suspensions. The presence, motion, and deformation of cells are accounted for on the basis of the immersed interface method. Deformable microparticles are also included to model blood contained or pharmaceutical particles. The study focuses on the effects of channel height on the hydrodynamic diffusion characteristics of the contained particles. Although such effects are rather expected to be significant, they have not been systematically considered in the literature. The proximity with the bounding walls affects the mobility of the particles, even more so due to the low-Reynolds-number prevailing conditions. For pressure-driven flow the diffusivities increase with distance from the wall due to the increasing mobility and reach a channel-size-dependent maximum due to the diminishing local shear rate. Near the channel center, where the mean shear rates vanish, diffusivities remain finite owing to convection from cross-flow sweeps generated from the interaction of eddies formed in the opposing walls. It is suggested that the hydrodynamic mobility and its dependence on distance from the walls should be added to factors affecting the diffusivities, such as the local shear rate and the cell volume fraction and elasticity.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (59)

  1. C. Pozrikidis, Computational Hydrodynamics of Capsules and Biological Cells (CRC Press, Boca Raton, FL, 2010).
  2. S. Ramanujan and C. Pozrikidis, Deformation of liquid capsules enclosed by elastic membranes in simple shear flow: Large deformations and the effect of fluid viscosities, J. Fluid Mech. 361, 117 (1998).
  3. C. K. Aidun and J. R. Clausen, Lattice-Boltzmann method for complex flows, Annu. Rev. Fluid Mech. 42, 439 (2010).
  4. D. A. Reasor, Jr., J. R. Clausen, and C. K. Aidun, Coupling the lattice-Boltzmann and spectrin-link methods for the direct numerical simulation of cellular blood flow, Int. J. Numer. Meth. Fluids. 68, 767 (2011).
  5. H. Zhao, E. S. G. Shaqfeh, and V. Narsimhan, Shear-induced particle migration and margination in a cellular suspension, Phys. Fluids 24, 011902 (2012).
  6. H. Lei, D. A. Fedosov, B. Caswell, and G. E. Karniadakis, Blood flow in small tubes: Quantifying the transition to the non-continuum regime, J. Fluid Mech. 722, 214 (2013).
  7. X. Li, Z. Peng, H. Lei, M. Dao, and G. E. Karniadakis, Probing red blood cell mechanics, rheology and dynamics with a two-component multi-scale model, Philos. Trans. R. Soc. London, Ser. A 372, 20130389 (2014).
  8. T. Krüger, Computer Simulation Study of Collective Phenomena in Dense Suspensions of Red Blood Cells under Shear (Springer, New York, 2012).
  9. P. Balogh and P. Bagchi, A computational approach to modeling cellular-scale blood flow in complex geometry, J. Comput. Phys. 334, 280 (2017).
  10. W. Pan, D. A. Fedosov, B. Caswell, and G. E. Karniadakis, Predicting dynamics and rheology of blood flow: A comparative study of multiscale and low-dimensional models of red blood cells, Microvasc. Res. 82, 163 (2011).
  11. D. A. Fedosov, W. Pan, B. Caswell, G. Gompper, and G. E. Karniadakis, Predicting human blood viscosity in silico, Proc. Natl. Acad. Sci. USA 108, 11772 (2011).
  12. D. A. Fedosov, H. Noguchi, and G. Gompper, Multiscale modeling of blood flow: From single cells to blood rheology, Biomech. Model. Mechanobiol. 13, 239 (2014).
  13. M. Gross, T. Kruger, and F. Varnik, Rheology of dense suspensions of elastic capsules: Normal stresses, yield stress, jamming and confinement effects, Soft Matter 10, 4360 (2014).
  14. A. Yazdani, X. Li, and G. E. Karniadakis, Dynamic and rheological properties of soft biological cell suspensions, Rheol. Acta. 55, 433 (2016).
  15. C. Bacher, L. Schrack, and S. Gekle, Clustering of microscopic particles in constricted blood flow, Phys. Fluids 2, 013102 (2017).
  16. P. Balogh and P. Bagchi, Analysis of red blood cell partitioning at bifurcations in simulated microvascular networks, Phys. Fluids 30, 051902 (2018).
  17. T. Ye and L. Peng, Motion, deformation, and aggregation of multiple red blood cells in three-dimensional microvessel bifurcations, Phys. Fluids 31, 021903 (2019).
  18. A. Kumar and M. D. Graham, Segregation by membrane rigidity in flowing binary suspensions of elastic capsules, Phys. Rev. E 84, 066316 (2011).
  19. K. Muller, D. A. Fedosov, and G. Gompper, Margination of micro- and nano-particles in blood flow and its effect on drug delivery, Sci. Rep. 4, 4871 (2014).
  20. K. Vahidkhah, S. L. Diamond, and P. Bagchi, Platelet dynamics in three-dimensional simulation of whole blood, Biophys. J. 106, 2529 (2014).
  21. T. Kruger, Effect of tube diameter and capillary number on platelet margination and near-wall dynamics, Rheol. Acta. 55, 511 (2016).
  22. R. G. H. Rivera, X. Zhang, and M. D. Graham, Mechanistic theory of margination and flow-induced segregation in confined multicomponent suspensions: Simple shear and Poiseuille flows, Phys. Rev. Fluids 1, 060501 (2016).
  23. Q. M. Qi and E. S. G. Shaqfeh, Theory to predict particle migration and margination in the pressure-driven channel flow of blood, Phys. Rev. Fluids 2, 093102 (2017).
  24. Q. M. Qi and E. S. G. Shaqfeh, Time-dependent particle migration and margination in the pressure-driven channel flow of blood, Phys. Rev. Fluids 3, 034302 (2018).
  25. C. Bacher, A. Kihm, L. Schrack, L. Kaestner, M. W. Laschke, C. Wagner, and S. Gekle, Antimargination of microparticles and platelets in the vicinity of branching vessels, Biophys. J. 115, 411 (2018).
  26. P. Perdikaris, L. Grinberg, and G. E. Karniadakis, Multiscale modeling and simulation of brain blood flow, Phys. Fluids 28, 021304 (2016).
  27. D. A. Fedosov, M. Dao, G. E. Karniadakis, and S. Suresh, Computational biorheology of human blood flow in health and disease, Ann. Biomed. Engng. 42, 368 (2014).
  28. A. Nacev, C. Beni, O. Bruno, and B. Shapiro, The behaviors of ferromagnetic nano-particles in and around blood vessels under applied magnetic fields, J. Magn. Magn. Mater. 323, 651 (2011).
  29. J. B. Freund and B. Shapiro, Transport of particles by magnetic forces and cellular blood flow in a model microvessel, Phys. Fluids 24, 051904 (2012).
  30. E. M. Cherry and J. K. Eaton, A comprehensive model of magnetic particle motion during magnetic drug targeting, Int. J. Multiphase Flow 59, 173 (2014).
  31. Z. Li, Y. Zhu, R. R. Rao, J. R. Clausen, and C. K. Aidun, Nanoparticle transport in cellular blood flow, Comput. Fluids 172, 609 (2018).
  32. H. Ye, Z. Shen, L. Yu, M. Wei, and Y. Li, Manipulating nanoparticle transport within blood flow through external forces: An exemplar of mechanics in nanomedicine, Proc. R. Soc. London, Ser. A 474, 20170845 (2018).
  33. A. S. Popel and P. C. Johnson, Microcirculation and hemorheology, Annu. Rev. Fluid Mech. 37, 43 (2005).
  34. T. W. Secomb, Blood flow in the microcirculation, Annu. Rev. Fluid Mech. 49, 443 (2017).
  35. E. C. Eckstein and F. Belgacem, Model of platelet transport in flowing blood with drift and diffusion terms, Biophys. J. 60, 53 (1991).
  36. D. Leighton and A. Acrivos, The shear-induced migration of particles in concentrated suspensions, J. Fluid Mech. 181, 415 (1987).
  37. L. Crowl and A. L. Fogelson, Analysis of mechanisms for platelet near-wall excess under arterial blood flow conditions, J. Fluid Mech. 676, 348 (2011).
  38. J. Li, M. Dao, C. T. Lim, and S. Suresh, Spectrin-level modeling of the cytoskeleton and optical tweezers stretching of the erythrocyte, Biophys. J. 88, 3707 (2005).
  39. I. V. Pivkin and G. E. Karniadakis, Accurate Coarse-Grained Modeling of Red Blood Cells, Phys. Rev. Lett. 101, 118105 (2008).
  40. K. I. Tsubota, C. Wada, and T. Yamaguchi, Simulation study on effects on hematocrit on blood flow properties using particle method, J. Biomech. Sci. Eng. 1, 159 (2006).
  41. T. Wang, T.-W. Pan, Z. W. Xing, and R. Glowinski, Numerical simulation of rheology of red blood cell rouleaux in microchannels, Phys. Rev. E 79, 041916 (2009).
  42. Y. Liu, L. Zhang, X. Wang, and W. K. Liu, Coupling of Navier-Stokes equations with protein molecular dynamics and its application to hemodynamics, Int. J. Numer. Methods Fluids 46, 1237 (2004).
  43. R. Glowinski, T. W. Pan, T. I. Hesla, and D. D. Joseph, A distributed Lagrange multiplier/fictitious domain method for particulate flows, Int. J. Multiphase Flow 25, 755 (1999).
  44. R. Glowinski, T. W. Pan, T. I. Hesla, D. D. Joseph, and J. Periaux, Distributed Lagrange multiplier/fictitious domain methods for flows around moving rigid bodies: Application to particulate flow, Int. J. Numer. Method Fluids 30, 1043 (1999).
  45. R. Glowinski, T. W. Pan, T. I. Hesla, D. D. Joseph, and J. Periaux, A fictitious domain of incompressible viscous flow past moving rigid bodies: Application to particulate flow, J. Comput. Phys. 169, 363 (2001).
  46. S. G. Yiantsios, On the distributed Lagrange multiplier/fictitious domain method for rigid-particle-laden flows: A proposition for an alternative formulation of the Lagrange multipliers, Int. J. Numer. Method Fluids 70, 1027 (2012).
  47. P. Saliakellis and S. G. Yiantsios, Macroscopic characteristics of heavy particle resuspension obtained from direct numerical simulations of pressure driven channel flow, Int. J. Multiphase Flow 84, 188 (2016).
  48. A. R. Pries, D. Neuhaus, and P. Gaehtgens, Blood viscosity in tube flow: Dependence on diameter and hematocrit, Am. J. Physiol. 263, H1770 (1992).
  49. D. J. Jeffrey and Y. Onishi, The slow motion of a cylinder next to a plane wall, Quart. J. Appl. Math. Mech. 34, 129 (1981).
  50. J. Happel and Η. Brenner, Low Reynolds Number Hydrodynamics, 2nd ed. (Martinus Nijhoff Publishers, Dordrecht, 1986).
  51. A. S. Dvinsky and A. S. Popel, Motion of a rigid cylinder between parallel plates in Stokes flow: Part 1: Motion in a quiescent fluid and sedimentation, Comput. Fluids 15, 391 (1987).
  52. P. R. Nott and J. F. Brady, Pressure-driven flow of suspensions: Simulation and theory, J. Fluid Mech. 275, 157 (1994).
  53. R. M. Miller and J. F. Morris, Normal stress-driven migration and axial development in pressure-driven flow of concentrated suspensions, J. Non-Newtonian Fluid Mech. 135, 149 (2006).
  54. P. Olla, The lift on a tank-treading ellipsoidal cell in a shear flow, J. Phys. II France 7, 1533 (1997).
  55. I. Cantat and C. Misbah, Lift Force and Dynamical Unbinding of Adhering Vesicles under Shear Flow, Phys. Rev. Lett. 83, 880 (1999).
  56. S. Sukumaran and U. Seifert, Influence of shear flow on vesicles near a wall: A numerical study, Phys. Rev. E 64, 011916 (2001).
  57. M. Abkarian, C. Lartigue, and A. Viallat, Tank Treading and Unbinding of Deformable Vesicles in Shear Flow: Determination of the Lift Force, Phys Rev. Lett. 88, 068103 (2002).
  58. N. Callens, C. Minetti, G. Coupier, M.-A. Mader, F. Dubois, C. Misbah, and T. Podgorski, Hydrodynamic lift of vesicles under shear flow in microgravity, Europhys. Lett. 83, 24002 (2008).
  59. G. Coupier, B. Kaoui, T. Podgorski, and C. Misbah, Noninertial lateral migration of vesicles in bounded Poiseuille flow, Phys. Fluids, 20, 111702 (2008).

Outline

Information

Phys. Rev. Fluids 4, 113103– Published 26 November, 2019
  • Received 2 July 2019
Crossmark - Check for updates button

©2019 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation