تغییر شکل هندسی گلبول‌های قرمز در حضور میدان مغناطیسی

نویسندگان

1 صنعتی شیراز

2 دانشگاه خلیج فارس بوشهر

چکیده

در این مقاله تاثیر میدان مغناطیسی بر شکل هندسی گلبولهای قرمز خون به روش عددی و تحلیلی مورد مطالعه قرار می گیرد. گلبولهای قرمز به صورت قطراتی تغییر شکل پذیر (ذرات نرم) که در پلاسمای خون در حال شارش هستند در نظر گرفته می شوند. با استفاده از روش المان مرزی، معادلات شارش گلبول قرمز در کانال میکروسیال تخت ، با به کارگیری مولفه‌ی عمودی تنش به عنوان شرایط مرزی درسطح ذرات به روش عددی حل می شوند. نتایج عددی نشان می دهد که گلبول قرمز در جهت میدان مغناطیسی کشیده می شود، شکل نهایی گلبول قرمز نتیجه ای از تعادل بین انرژی سطحی و انرژی مغناطیسی در سطح گلبول قرمز است.

کلیدواژه‌ها


عنوان مقاله [English]

Geometric Deformation of Red Cells in the Presence of a Magnetic Field

نویسندگان [English]

  • erfan kadivar 1
  • atefe alizade 2
1 shiraz
2 khalije fars boushehr
چکیده [English]

In this study, we numerically and theoretically  investigated the effect of magnetic field on shape of red cells. The two phase model was used for the dynamics of red cells.  We considered red cells as deformable drops flowing through a flat microfluidic channel. We employed boundary element method (BEM) to numerically solve the two-dimensional Darcy equation by applying magnetic normal stress as a boundary condition at the interface of red cells and blood plasma. Our numerical and theoretical  results indicate that red cells elongate in direction of magnetic fields. The final stable shape is a result of the  balance between the surface energy and the magnetic energy of the drop. Our numerical and theoretical results are in good agreements with the experimental results.

کلیدواژه‌ها [English]

  • Red Cells
  • Microfluidic
  • Boundary Element Method Words
  1. Davis J.A., Inglis, D.W., Morton, K.J., Lawrence, D.A, Huang, L.R., Chou, S.Y., Sturm, J.C., and Austin, R.H. “Eterministic Hydrodynamics: Taking Blood Apart”, Proc. Natl. Acad. Sci., Vol. 103,  No. 40, pp. 14779-14784, 2006.
  2. Yang S., Ündar A., and Zahn J.D.  “A Microfluidic Device for Continuous, Real Timeblood Plasma Separation”, Lab Chip, Vol. 6,  No. 871, pp. 871-880, 2006.
  3. Jäggi R.D., Sandoz, R., and Effenhauser, C.S. “Microfluidic Depletion of Red Blood Cells from Whole Blood in High-Aspect-Ratio Microchannels”, Microfluid. Nanofluid.,Vol. 3, No. 47, pp. 47-53, 2007.
  4. Pamme, N. “Continuous Flow Separations in Microfluidic Devices”, Lab Chip, Vol. 7, No. 1, pp. 1644-1659, 2007.
  5. Kersaudy-Kerhoas, M., Dhariwal, R.,  Desmulliez, M.P.Y., and Jouvet, L. “Hydrodynamic Blood Plasma Separation in Microfluidic Channels”, Microfluid. Nanofluid,  Vol. 8, No. 1, pp. 105-114, 2010.
  6. Kadivar, E. “Droplet Trajectories in a Flat Microfluidic Networks”, Eur. J. Mech. B. Fluids, Vol. 57, No.1, pp. 75-81, 2016.
  7. Chien, S.   “Determinants of Blood Viscosity and Red Cell Deformability”, Scand. J. Clin. Lab. Inv, Vol. 461, No. 156, pp.7-12, 1981.
  8. Pries A.R. and Secomb, T.W, “Microvascular blood Viscosity in Vivo and the Endothelial Surface Layer”, Am. J. Physiol Heart Circ Physiol,  Vol. 289, No. 6, pp. 2657-2664, 2005.
  9. Barber J.O., Alberding, J.P., Restrepo J. and Secomb T.W. “Simulated Two-dimensional Red Blood Cell Motion, Deformation, And Partitioning in Microvessel Bifurcations”, Ann  Biomed Eng., Vol. 36, No. 10, pp. 1690-1698, 2008.

10. Brando, M.M., Fontes, A., Barjas-Castro, M.L., Barbosa, L.C., Costa, F.F., Cesar, C.L., and Saad, S.T.O. “Optical Tweezers for Measuring Red Blood Cell Elasticity: Application to the Study of Drug Response in Sickle Cell Disease”, Eur. J. Haematol. Vol. 70, No. 4, pp. 207-211, 2003.

11. Tao, R. and Huang, K. “Reducing Blood Viscosity with Magnetic fields”, Phys. Rev. E., Vol. 84, No. 1, pp. 011905, 2011.

12. Wang, C.H. and Popel, A.S. “Effect of Red Blood Cell Shape on Oxygen Transport in Capillaries”, Mathematical Biosciences, Vol. 116, No. 1, pp. 89-110, 1993.

13. Swede, H., Andemariam, B., Gregorio, D.I., Jones, B.A, Braithwaite, D., Rohan, T.E., and Stevens, R.G. “Adverse Events in Cancer Patients with Sickle Cell Trait or Disease: Case Reports”, Genetics in medicine. Vol. 17, No. 1, pp. 237-241, 2015.

14. Wu, Y., Fu, T., Ma, Y., and Li, H.Z. “Active Control of Ferrofluid Droplet Breakup Dynamics in a Microfluidic T-Junction”, Microfluid. Nanofluid, Vol. 18, No. 1, pp. 19-27, 2010.

15. Kadivar, E. “Magnetocoalescence of Ferrofluid Droplets in a Flat Microfluidic Channel”, EPL (Europhysics Letters), Vol. 106, No. 2, pp. 24003, 2014.

16. Martin, J.D., Marhefka, J.N., Migler, K., and Hudson, S. “Interface Rheology Through Microfluidics”, Adv. Mater. Vol. 23, No. 3, pp. 426-432, 2011.

17. Seric, I., Afkhami, S., and Kondic, L.  “Interfacial Instability of Thin Ferrofluid Films Under a Magnetic Field”, Vol. 755, No. 1, pp. 1-12, 2014.

18. Brosseau, Q., Vrignon, J., Baret, J.C. “Microfluidic Dynamics Interface Tensiometry”,  Soft Matter, Vol. 10, No. 1, pp. 3066-3076, 2014.

19. Amiri-Hezaveh, A., Salimi, M.A., and Taeibi Rahni, M. “Numerical Analysis of ِSame Scales Droplet-Particle Interaction Inside a Porous Medium, Using Lattice Boltzmann Method”, Mech. Aerospace Eng. J., Vol. 5, No. 2, pp. 1-14, 2017 (In Persian).      

  1. 20.  Rosensweig, R.E. “Ferrohydrodynamics”, Cambridge University Press, London, UK 1985.

21. Kadivar, E., Herminghaus S., and Brinkmann, M. “Droplet Sorting in a Loop of Flat Microfluidic Channels”, J. Phys. Condens Matter, Vol. 25, No. 28, pp. 285102, 2013.

22. Pozrikidis, C. “A Practical Guide to Boundary Element Methods”, CRC Press, Fla., USA, 2002.

23. Bacri J.C. and Salin, D. “Instability of Ferrofluid Magnetic Drops Under Magnetic Field”, J. Phys. Lett., Vol. 43, No. 17, pp. 649-654, 1982.