Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-24T18:28:17.198Z Has data issue: false hasContentIssue false
  • English
  • Français

Elastic solid dynamics in a coupled oscillatory Couette flow system

Published online by Cambridge University Press:  03 August 2022

Tejaswin Parthasarathy ,
Yashraj Bhosale  and
Mattia Gazzola Open the ORCID record for Mattia Gazzola [Opens in a new window]
Tejaswin Parthasarathy
Affiliation:
Mechanical Sciences and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
Yashraj Bhosale
Affiliation:
Mechanical Sciences and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
Mattia Gazzola*
Affiliation:
Mechanical Sciences and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
*
†Email address for correspondence: mgazzola@illinois.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We report analytical solutions of a problem involving a visco-elastic solid material layer sandwiched between two fluid layers, in turn confined by two long planar walls that undergo oscillatory motion. The resulting system dynamics is rationalized, based on fluid viscosity and solid elasticity, via wave and boundary layer theory. This allows for physical interpretation of elasto-hydrodynamic coupling, potentially connecting to a broad set of biophysical phenomena and applications, from synovial joint mechanics to elastometry. Further, obtained solutions are demonstrated to be rigorous benchmarks for testing coupled incompressible fluid–hyperelastic solid and multi-phase numerical solvers, towards which we highlight challenging parameter sets. Finally, we provide an interactive online sandbox to build physical intuition, and open-source our code-base.

JFM classification

Aerodynamics: Flow-structure interactions Waves/Free-surface Flows: Elastic waves Mathematical Foundations: General fluid mechanics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 946 , 10 September 2022 , A15
Check for updates
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alben, S., Shelley, M. & Zhang, J. 2002 Drag reduction through self-similar bending of a flexible body. Nature 420 (6915), 479–481.10.1038/nature01232CrossRefGoogle ScholarPubMed
Alben, S., Shelley, M. & Zhang, J. 2004 How flexibility induces streamlining in a two-dimensional flow. Phys. Fluids 16 (5), 1694–1713.10.1063/1.1668671CrossRefGoogle Scholar
Argentina, M. & Mahadevan, L. 2005 Fluid-flow-induced flutter of a flag. Proc. Natl Acad. Sci. 102 (6), 1829–1834.10.1073/pnas.0408383102CrossRefGoogle ScholarPubMed
Argentina, M., Skotheim, J. & Mahadevan, L. 2007 Settling and swimming of flexible fluid-lubricated foils. Phys. Rev. Lett. 99 (22), 224503.10.1103/PhysRevLett.99.224503CrossRefGoogle ScholarPubMed
Bakker, D.P., Huijs, F.M., de Vries, J., Klijnstra, J.W., Busscher, H.J. & van der Mei, H.C. 2003 Bacterial deposition to fluoridated and non-fluoridated polyurethane coatings with different elastic modulus and surface tension in a parallel plate and a stagnation point flow chamber. Colloids Surf. B: Biointerfaces 32 (3), 179–190.10.1016/S0927-7765(03)00159-0CrossRefGoogle Scholar
Barthes-Biesel, D. 2016 Motion and deformation of elastic capsules and vesicles in flow. Annu. Rev. Fluid Mech. 48, 25–52.10.1146/annurev-fluid-122414-034345CrossRefGoogle Scholar
Bhosale, Y., Esmaili, E., Bhar, K. & Jung, S. 2020 Bending, twisting and flapping leaf upon raindrop impact. Bioinspir. Biomim. 15 (3), 036007.10.1088/1748-3190/ab68a8CrossRefGoogle ScholarPubMed
Bhosale, Y., Parthasarathy, T. & Gazzola, M. 2021 A remeshed vortex method for mixed rigid/soft body fluid–structure interaction. J. Comput. Phys. 444, 110577.10.1016/j.jcp.2021.110577CrossRefGoogle Scholar
Bodnár, T., Galdi, G.P. & Nečasová, Š. 2014 Fluid–Structure Interaction and Biomedical Applications. Springer.10.1007/978-3-0348-0822-4CrossRefGoogle Scholar
Bower, A.F. 2009 Applied Mechanics of Solids. CRC Press.10.1201/9781439802489CrossRefGoogle Scholar
Carr, M.E., Shen, L.L. & Hermans, J. 1976 A physical standard of fibrinogen: measurement of the elastic modulus of dilute fibrin gels with a new elastometer. Analyt. Biochem. 72 (1-2), 202–211.10.1016/0003-2697(76)90522-4CrossRefGoogle ScholarPubMed
Christov, I.C. 2021 Soft hydraulics: from Newtonian to complex fluid flows through compliant conduits. Preprint. arXiv:2106.07164.10.1088/1361-648X/ac327dCrossRefGoogle Scholar
Di Carlo, D. 2009 Inertial microfluidics. Lab on a Chip 9 (21), 3038–3046.10.1039/b912547gCrossRefGoogle ScholarPubMed
Dowell, E.H. & Hall, K.C. 2001 Modeling of fluid–structure interaction. Annu. Rev. Fluid Mech. 33 (1), 445–490.10.1146/annurev.fluid.33.1.445CrossRefGoogle Scholar
Dowson, D. & Jin, Z.-M. 1986 Micro-elastohydrodynamic lubrication of synovial joints. Engng Med. 15 (2), 63–65.10.1243/EMED_JOUR_1986_015_019_02CrossRefGoogle ScholarPubMed
Duncombe, T.A., Tentori, A.M. & Herr, A.E. 2015 Microfluidics: reframing biological enquiry. Nat. Rev. Mol. Cell Biol. 16 (9), 554–567.10.1038/nrm4041CrossRefGoogle ScholarPubMed
Gad-el Hak, M. 2002 Compliant coatings for drag reduction. Prog. Aerosp. Sci. 38 (1), 77–99.10.1016/S0376-0421(01)00020-3CrossRefGoogle Scholar
Gazzola, M., Argentina, M. & Mahadevan, L. 2015 Gait and speed selection in slender inertial swimmers. Proc. Natl Acad. Sci. 112 (13), 3874–3879.10.1073/pnas.1419335112CrossRefGoogle ScholarPubMed
Grotberg, J.B. & Jensen, O.E. 2004 Biofluid mechanics in flexible tubes. Annu. Rev. Fluid Mech. 36, 121–147.10.1146/annurev.fluid.36.050802.121918CrossRefGoogle Scholar
Guimarães, C.F., Gasperini, L., Marques, A.P. & Reis, R.L. 2020 The stiffness of living tissues and its implications for tissue engineering. Nat. Rev. Mater. 5 (5), 351–370.10.1038/s41578-019-0169-1CrossRefGoogle Scholar
Hairer, E., Nørsett, S.P. & Wanner, G. 1991 Solving Ordinary Differential Equations I, Nonstiff Problems. Springer.10.1007/978-3-662-09947-6CrossRefGoogle Scholar
Heil, M. & Hazel, A.L. 2011 Fluid–structure interaction in internal physiological flows. Annu. Rev. Fluid Mech. 43, 141–162.10.1146/annurev-fluid-122109-160703CrossRefGoogle Scholar
Heil, M., Hazel, A.L. & Smith, J.A. 2008 The mechanics of airway closure. Respir. Physiol. Neurobiol. 163 (1-3), 214–221.10.1016/j.resp.2008.05.013CrossRefGoogle ScholarPubMed
Kou, W., Pandolfino, J.E., Kahrilas, P.J. & Patankar, N.A. 2017 Simulation studies of the role of esophageal mucosa in bolus transport. Biomech. Model. Mechanobiol. 16 (3), 1001–1009.10.1007/s10237-016-0867-1CrossRefGoogle ScholarPubMed
Landau, L.D. & Lifshitz, E.M. 1987 Fluid Mechanics. In Theoretical Physics, vol. 6, pp. 336–343. Pergamon.Google Scholar
Leclaire, S., Pellerin, N., Reggio, M. & Trépanier, J.Y. 2014 Unsteady immiscible multiphase flow validation of a multiple-relaxation-time lattice Boltzmann method. J. Phys. A: Math. Theor. 47 (10), 105501.10.1088/1751-8113/47/10/105501CrossRefGoogle Scholar
Li, X., Vlahovska, P.M. & Karniadakis, G.E. 2013 Continuum- and particle-based modeling of shapes and dynamics of red blood cells in health and disease. Soft Matt. 9 (1), 28–37.10.1039/C2SM26891DCrossRefGoogle ScholarPubMed
Nalim, R., Pekkan, K., Sun, H.B. & Yokota, H. 2004 Oscillating Couette flow for in vitro cell loading. J. Biomech. 37 (6), 939–942.10.1016/j.jbiomech.2003.11.004CrossRefGoogle ScholarPubMed
Pozrikidis, C. 2003 Modeling and Simulation of Capsules and Biological Cells. CRC Press.10.1201/9780203503959CrossRefGoogle Scholar
Raghavan, M.L. & Vorp, D.A. 2000 Toward a biomechanical tool to evaluate rupture potential of abdominal aortic aneurysm: identification of a finite strain constitutive model and evaluation of its applicability. J. Biomech. 33 (4), 475–482.10.1016/S0021-9290(99)00201-8CrossRefGoogle Scholar
Sengul, Y. 2021 a Nonlinear viscoelasticity of strain rate type: an overview. Proc. R. Soc. A 477 (2245), 20200715.10.1098/rspa.2020.0715CrossRefGoogle ScholarPubMed
Sengul, Y. 2021 b Viscoelasticity with limiting strain. Discr. Contin. Dyn. Syst.-Ser. S 14 (1), 57–70.Google Scholar
Sim, W.-G. 2006 Stratified steady and unsteady two-phase flows between two parallel plates. J. Mech. Sci. Technol. 20 (1), 125.10.1007/BF02916206CrossRefGoogle Scholar
Song, F., Koo, H. & Ren, D. 2015 Effects of material properties on bacterial adhesion and biofilm formation. J. Dental Res. 94 (8), 1027–1034.10.1177/0022034515587690CrossRefGoogle ScholarPubMed
Sugiyama, K., Ii, S., Takeuchi, S., Takagi, S. & Matsumoto, Y. 2010 Full Eulerian simulations of biconcave neo-Hookean particles in a Poiseuille flow. Comput. Mech. 46 (1), 147–157.10.1007/s00466-010-0484-2CrossRefGoogle Scholar
Sugiyama, K., Ii, S., Takeuchi, S., Takagi, S. & Matsumoto, Y. 2011 A full Eulerian finite difference approach for solving fluid–structure coupling problems. J. Comput. Phys. 230 (3), 596–627.10.1016/j.jcp.2010.09.032CrossRefGoogle Scholar
Sun, H.B. 2010 Mechanical loading, cartilage degradation, and arthritis. Ann. N.Y. Acad. Sci. 1211 (1), 37–50.10.1111/j.1749-6632.2010.05808.xCrossRefGoogle Scholar
Sun, H.B., Nalim, R. & Yokota, H. 2003 Expression and activities of matrix metalloproteinases under oscillatory shear in IL-1-stimulated synovial cells. Connect. Tissue Res. 44 (1), 42–49.10.1080/03008200390151954CrossRefGoogle ScholarPubMed
Tytell, E.D., Leftwich, M.C., Hsu, C.-Y., Griffith, B.E., Cohen, A.H., Smits, A.J., Hamlet, C. & Fauci, L.J. 2016 Role of body stiffness in undulatory swimming: insights from robotic and computational models. Phys. Rev. Fluids 1 (7), 073202.10.1103/PhysRevFluids.1.073202CrossRefGoogle Scholar
Velve-Casquillas, G., Le Berre, M., Piel, M. & Tran, P.T. 2010 Microfluidic tools for cell biological research. Nano Today 5 (1), 28–47.10.1016/j.nantod.2009.12.001CrossRefGoogle ScholarPubMed
Vlahovska, P.M. & Gracia, R.S. 2007 Dynamics of a viscous vesicle in linear flows. Phys. Rev. E 75 (1), 016313.10.1103/PhysRevE.75.016313CrossRefGoogle ScholarPubMed
Wang, X. & Christov, I.C. 2019 Theory of the flow-induced deformation of shallow compliant microchannels with thick walls. Proc. R. Soc. A 475 (2231), 20190513.10.1098/rspa.2019.0513CrossRefGoogle ScholarPubMed
Wu, P.-H., et al. 2018 A comparison of methods to assess cell mechanical properties. Nat. Meth. 15, 491–498.10.1038/s41592-018-0015-1CrossRefGoogle ScholarPubMed
Zhu, D. & Jane Wang, Q. 2011 Elastohydrodynamic lubrication: a gateway to interfacial mechanics – review and prospect. J. Tribol. 133 (4), 041001.10.1115/1.4004457CrossRefGoogle Scholar
Supplementary material: File

Parthasarathy et al. supplementary material

Parthasarathy et al. supplementary material

Download Parthasarathy et al. supplementary material(File)
File 2.7 MB