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Deformation dynamics of biconcave red blood cells in viscous fluid driven by ultrasound

Published online by Cambridge University Press:  20 November 2025

Feilong Xu ,
Yifan Liu  and
Fengxian Xin Open the ORCID record for Fengxian Xin [Opens in a new window]
Feilong Xu
Affiliation:
State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University , Xi’an 710049, PR China MOE Key Laboratory for Multifunctional Materials and Structures, Xi’an Jiaotong University, Xi’an 710049, PR China
Yifan Liu
Affiliation:
State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University , Xi’an 710049, PR China MOE Key Laboratory for Multifunctional Materials and Structures, Xi’an Jiaotong University, Xi’an 710049, PR China
Fengxian Xin*
Affiliation:
State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University , Xi’an 710049, PR China MOE Key Laboratory for Multifunctional Materials and Structures, Xi’an Jiaotong University, Xi’an 710049, PR China
*
Corresponding author: Fengxian Xin, fxxin@mail.xjtu.edu.cn
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Abstract

A theoretical model is developed to study the deformation dynamics of a biconcave red blood cell (RBC) in a viscous fluid driven by an ultrasonic standing wave. The model considers the true physiological shape of RBCs with biconcave geometry, overcoming the challenges of modelling the nonlinear acoustomechanical coupling of complex biconcave curved shells. The hyperelastic shell theory is used to describe the cell membrane deformation. The acoustic perturbation method is employed to divide the Navier–Stokes equations for viscous flows into the acoustic wave propagation equation and the mean time-averaged dynamic equation. The time-average flow–membrane interaction is considered to capture the cell deformation in acoustic waves. Numerical simulations are performed using the finite element method by formulating the final governing equation in weak form. And a curvature-adaptive mesh refinement algorithm is specifically developed to solve the error problem caused by the nonlinear response of biconcave boundaries (such as curvature transitions) in fluid–structure coupling calculations. The results show that when the acoustic input is large enough, the shape of the cell at the acoustic pressure node changes from a biconcave shape to an oblate disk shape, thereby predicting and discovering for the first time the snap-through instability phenomenon in bioncave RBCs driven by ultrasound. The effects of fluid viscosity, surface shear modulus and membrane bending stiffness on the deformation of the cell are analysed. This numerical model has the ability to accurately predict the acoustic streaming fields and associated time-averaged fluid stress, thus providing insights into the acoustic deformation of complex-shaped particles. Given the important role of the mechanical properties of RBCs in disease diagnosis and biological research, this work will contribute to the development of acoustofluidic technology for the detection of RBC-related diseases.

JFM classification

Biological Fluid Dynamics: Capsule/cell dynamics Acoustics: Acoustics

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Type
JFM Papers
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Journal of Fluid Mechanics , Volume 1023 , 25 November 2025 , A22
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© The Author(s), 2025. Published by Cambridge University Press

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References

Aubert, V., Wunenburger, R., Valier-Brasier, T., Rabaud, D., Kleman, J.-P. & Poulain, C. 2016 A simple acoustofluidic chip for microscale manipulation using evanescent scholte waves. Lab Chip 16 (13), 2532–2539.10.1039/C6LC00534ACrossRefGoogle ScholarPubMed
Barthès-Biesel, D. 2016 Motion and deformation of elastic capsules and vesicles in flow. In Annual Review Of Fluid Mechanics, (ed. S. H. Davis & P. Moin), vol. 48, 25–52.Google Scholar
Barthès-Biesel, D., Diaz, A. & Dhenin, E. 2002 Effect of constitutive laws for two-dimensional membranes on flow-induced capsule deformation. J. Fluid Mech. 460, 211–222.10.1017/S0022112002008352CrossRefGoogle Scholar
Bera, K. 2022 Extracellular fluid viscosity enhances cell migration and cancer dissemination. Nature 611 (7935), 365–373.10.1038/s41586-022-05394-6CrossRefGoogle ScholarPubMed
Bow, H., Pivkin, I.V., Diez-Silva, M., Goldfless, S.J., Dao, M., Niles, J.C., Suresh, S. & Han, J. 2011 A microfabricated deformability-based flow cytometer with application to malaria. Lab Chip 11 (6), 1065–1073.10.1039/c0lc00472cCrossRefGoogle ScholarPubMed
Bruus, H. 2012 Acoustofluidics 2: perturbation theory and ultrasound resonance modes. Lab Chip 12 (1), 20–28.10.1039/C1LC20770ACrossRefGoogle Scholar
Chini, G.P., Malecha, Z. & Dreeben, T.D. 2014 Large-amplitude acoustic streaming. J. Fluid Mech. 744, 329–351.10.1017/jfm.2014.61CrossRefGoogle Scholar
Cordasco, D., Yazdani, A. & Bagchi, P. 2014 Comparison of erythrocyte dynamics in shear flow under different stress-free configurations. Phys. Fluids 26 (4), 041902.10.1063/1.4871300CrossRefGoogle Scholar
Costa, K.D. 2003 Single-cell elastography: probing for disease with the atomic force microscope. Dis. Markers 19 (2–3), 139–154.10.1155/2004/482680CrossRefGoogle ScholarPubMed
Cui, S.Y., Bhosale, Y. & Gazzola, M. 2024 Three-dimensional soft streaming. J. Fluid Mech. 979 (A7), 1–13.10.1017/jfm.2023.1050CrossRefGoogle Scholar
Dao, M., Lim, C.T. & Suresh, S. 2003 Mechanics of the human red blood cell deformed by optical tweezers. J. Mech. Phys. Solids 51 (11–12), 2259–2280.10.1016/j.jmps.2003.09.019CrossRefGoogle Scholar
Das, S., Deshmukh, S.D. & Thaokar, R.M. 2019 Deformation of a biconcave-discoid capsule in extensional flow and electric field. J. Fluid Mech. 860, 115–144.10.1017/jfm.2018.879CrossRefGoogle Scholar
Dondorp, A.M., Angus, B.J., Chotivanich, K., Silamut, K., Ruangveerayuth, R., Hardeman, M.R., Kager, P.A., Vreeken, J. & White, N.J. 1999 Red blood cell deformability as a predictor of anemia in severe falciparum malaria. Am. J. Trop. Med. Hyg. 60 (5), 733–737.10.4269/ajtmh.1999.60.733CrossRefGoogle ScholarPubMed
Dubrovski, O., Friend, J. & Manor, O. 2023 Theory of acoustic streaming for arbitrary Reynolds number flow. J. Fluid Mech. 975 (A4), 1–22.10.1017/jfm.2023.790CrossRefGoogle Scholar
Duong, T.X., Roohbakhshan, F. & Sauer, R.A. 2017 A new rotation-free isogeometric thin shell formulation and a corresponding continuity constraint for patch boundaries. Comput. Method. Appl. M. 316, 43–83.10.1016/j.cma.2016.04.008CrossRefGoogle Scholar
Gossett, D.R., Tse, H.T.K., Lee, S.A., Ying, Y., Lindgren, A.G., Yang, O.O., Rao, J., Clark,  A.T. & Di Carlo, D. 2012 Hydrodynamic stretching of single cells for large population mechanical phenotyping. Proc. Natl. Acad. Sci. USA 109 (20), 7630–7635.10.1073/pnas.1200107109CrossRefGoogle ScholarPubMed
Guglietta, F., Behr, M., Biferale, L., Falcucci, G. & Sbragaglia, M. 2020 On the effects of membrane viscosity on transient red blood cell dynamics. Soft Matter 16 (26), 6191–6205.10.1039/D0SM00587HCrossRefGoogle ScholarPubMed
Haase, K. & Pelling, A.E. 2015 Investigating cell mechanics with atomic force microscopy. J. R. Soc. Interface 12 (104), 1–16.10.1098/rsif.2014.0970CrossRefGoogle ScholarPubMed
Hahn, P., Lamprecht, A. & Dual, J. 2016 Numerical simulation of micro-particle rotation by the acoustic viscous torque. Lab Chip 16 (23), 4581–4594.10.1039/C6LC00865HCrossRefGoogle ScholarPubMed
Helfrich, W. 1973 Elastic properties of lipid bilayers - theory and possible experiments. Z. Naturforsch. C 28 (11–1), 693–703.10.1515/znc-1973-11-1209CrossRefGoogle ScholarPubMed
Jakobsson, O., Antfolk, M. & Laurell, T. 2014 Continuous flow two-dimensional acoustic orientation of nonspherical cells. Anal. Chem. 86 (12), 6111–6114.10.1021/ac5012602CrossRefGoogle ScholarPubMed
Karlsen, J.T., Augustsson, P. & Bruus, H. 2016 Acoustic force density acting on inhomogeneous fluids in acoustic fields. Phys. Rev. Lett. 117 (11), 114504.10.1103/PhysRevLett.117.114504CrossRefGoogle ScholarPubMed
Khani, M.-M., Tafazzoli-Shadpour, M., Rostami, M., Peirovi, H. & Janmaleki, M. 2014 Evaluation of mechanical properties of human mesenchymal stem cells during differentiation to smooth muscle cells. Ann. Biomed. Eng. 42 (7), 1373–1380.10.1007/s10439-013-0889-0CrossRefGoogle ScholarPubMed
Li, P.J., Nunn, A.R., Brumley, D.R., Sader, J.E. & Collis, J.F. 2024 The propulsion direction of nanoparticles trapped in an acoustic field. J. Fluid Mech. 984 (R1), 1–11.10.1017/jfm.2024.217CrossRefGoogle Scholar
Link, A. & Franke, T. 2020 Acoustic erythrocytometer for mechanically probing cell viscoelasticity. Lab Chip 20 (11), 1991–1998.10.1039/C9LC00999JCrossRefGoogle ScholarPubMed
Liu, Y.F. & Xin, F.X. 2022 Nonlinear large deformation of a spherical red blood cell induced by ultrasonic standing wave. Biomech. Model. Mechan. 21 (2), 589–604.10.1007/s10237-021-01550-5CrossRefGoogle ScholarPubMed
Liu, Y.F. & Xin, F.X. 2023 a Deformation dynamics of spherical red blood cells in viscous fluid driven by ultrasound. Phys. Fluids 35 (1), 012011.10.1063/5.0122017CrossRefGoogle Scholar
Liu, Y.F. & Xin, F.X. 2023 b Shape dynamics of capsules in two phase-shifted orthogonal ultrasonic standing waves: a numerical investigation. J. Fluid Mech. 964 (A18), 1–29.10.1017/jfm.2023.277CrossRefGoogle Scholar
Liu, Y.F. & Xin, F.X. 2024 Controlled mean dynamics of red blood cells by two orthogonal ultrasonic standing waves. J. Fluid Mech. 979 (A11), 1–33.10.1017/jfm.2024.419CrossRefGoogle Scholar
Mishra, P., Hill, M. & Glynne-Jones, P. 2014 Deformation of red blood cells using acoustic radiation forces. Biomicrofluidics 8 (3), 034109.10.1063/1.4882777CrossRefGoogle ScholarPubMed
Nama, N., Huang, T.J. & Costanzo, F. 2017 Acoustic streaming: an arbitrary lagrangian-eulerian perspective. J. Fluid Mech. 825, 600–630.10.1017/jfm.2017.338CrossRefGoogle ScholarPubMed
Pierrat, S., Brochard-Wyart, F. & Nassoy, P. 2004 Enforced detachment of red blood cells adhering to surfaces: statics and dynamics. Biophys. J. 87 (4), 2855–2869.10.1529/biophysj.104.043695CrossRefGoogle ScholarPubMed
Quinto-Su, P.A., Kuss, C., Preiser, P.R. & Ohl, C.-D. 2011 Red blood cell rheology using single controlled laser-induced cavitation bubbles. Lab Chip 11 (4), 672–678.10.1039/C0LC00182ACrossRefGoogle ScholarPubMed
Rajendran, V.K., Jayakumar, S., Azharudeen, M. & Subramani, K. 2022 Theory of nonlinear acoustic forces acting on inhomogeneous fluids. J. Fluid Mech. 940 (A 32), 1–20.10.1017/jfm.2022.257CrossRefGoogle Scholar
Rocha, U., Silva, G.C., Sales, M.V.S., D’amato, F.O.S., Leite, A.C.R. & Silva, G.T. 2023 Advancing raman spectroscopy of erythrocytes with 3D-printed acoustofluidic devices. Appl. Phys. Lett. 123 (3), 034105.10.1063/5.0145565CrossRefGoogle Scholar
Salari, A., Appak-Baskoy, S., Ezzo, M., Hinz, B., Kolios, M.C. & Tsai, S.S.H. 2020 Dancing with the cells: acoustic microflows generated by oscillating cells. Small 16 (9), 1903788.10.1002/smll.201903788CrossRefGoogle ScholarPubMed
Silva, G.T., Tian, L., Franklin, A., Wang, X., Han, X., Mann, S. & Drinkwater, B.W. 2019 Acoustic deformation for the extraction of mechanical properties of lipid vesicle populations. Phys. Rev. E 99 (6), 063002.10.1103/PhysRevE.99.063002CrossRefGoogle ScholarPubMed
Skalak, R., Tozeren, A., Zarda, R.P. & Chien, S. 1973 Strain enegry function of red blood cell membranes. Biophys. J. 13 (3), 245–280.10.1016/S0006-3495(73)85983-1CrossRefGoogle Scholar
Starodubtseva, M.N. 2011 Mechanical properties of cells and ageing. Ageing Res. Rev. 10 (1), 16–25.10.1016/j.arr.2009.10.005CrossRefGoogle ScholarPubMed
Sujith, T., Malik, L. & Sen, A.K. 2024 Fluid viscoelasticity affects ultrasound force field-induced particle transport. J. Fluid Mechan. A 75, 1–30, 1000.Google Scholar
Suresh, S., Spatz, J., Mills, J.P., Micoulet, A., Dao, M., Lim, C.T., Beil, M. & Seufferlein, T. 2005 Connections between single-cell biomechanics and human disease states: gastrointestinal cancer and malaria. Acta Biomater. 1 (1), 15–30.10.1016/j.actbio.2004.09.001CrossRefGoogle ScholarPubMed
Tandiono, T., Klaseboer, E., Ohl, S.-W., Ow, D.S.-W., Choo, A.B.-H., Li, F. & Ohl, C.-D. 2013 Resonant stretching of cells and other elastic objects from transient cavitation. Soft Matter 9 (36), 8687–8696.10.1039/c3sm51399hCrossRefGoogle Scholar
Wijaya, F.B., Mohapatra, A.R., Sepehrirahnama, S. & Lim, K.-M. 2016 Coupled acoustic-shell model for experimental study of cell stiffness under acoustophoresis. Microfluid. Nanofluid. 20 (5), 1–15.10.1007/s10404-016-1734-1CrossRefGoogle Scholar
Xie, Y., Bachman, H. & Huang, T.J. 2019 Acoustofluidic methods in cell analysis. Trac-Trends Anal. Chem. 117, 280–290.10.1016/j.trac.2019.06.034CrossRefGoogle ScholarPubMed
Xie, Y.L., Nama, N., Li, P., Mao, Z.M., Huang, P.H., Zhao, C.L., Costanzo, F. & Huang, T.J. 2016 Probing cell deformability via acoustically actuated bubbles. Small 12 (7), 902–910.10.1002/smll.201502220CrossRefGoogle ScholarPubMed
Zhang, H., Shen, Z., Hogan, B., Barakat, A.I. & Misbah, C. 2018 Atp release by red blood cells under flow: model and simulations. Biophys. J. 115 (11), 2218–2229.10.1016/j.bpj.2018.09.033CrossRefGoogle ScholarPubMed
Zheng, Y., Nguyen, J., Wang, C. & Sun, Y. 2013 Electrical measurement of red blood cell deformability on a microfluidic device. Lab Chip 13 (16), 3275–3283.10.1039/c3lc50427aCrossRefGoogle ScholarPubMed
Supplementary material: File

Xu et al. supplementary movie 1

Complete transient deformation process of red blood cells (RBCs) under extensional flow with the capillary number $C{a_f} = 0.038$ within 0.5s. (Snap-through instability has not yet occurred.)
Download Xu et al. supplementary movie 1(File)
File 493 KB
Supplementary material: File

Xu et al. supplementary movie 2

Complete transient deformation process of red blood cells (RBCs) under extensional flow with the capillary number $C{a_f} = 0.040$ within 2.0s. (Snap-through instability has occurred.)
Download Xu et al. supplementary movie 2(File)
File 1.2 MB
Supplementary material: File

Xu et al. supplementary movie 3

Complete transient deformation process of red blood cells (RBCs) under extensional flow with the capillary number $C{a_f} = 0.042$ within 0.6s. (Snap-through instability has occurred.)
Download Xu et al. supplementary movie 3(File)
File 373.5 KB
Supplementary material: File

Xu et al. supplementary material 4

Xu et al. supplementary material
Download Xu et al. supplementary material 4(File)
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