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Purely elastic instabilities in the airways and oral area

Published online by Cambridge University Press:  06 October 2021

Ramkarn Patne Open the ORCID record for Ramkarn Patne [Opens in a new window]
Ramkarn Patne*
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology (Indian School of Mines), Dhanbad826004, India
*
†Email address for correspondence: [email protected]
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Abstract

The present study considers a shear-thinning viscoelastic liquid layer sheared by the air and flowing past a deformable-solid layer in the presence of a surfactant at the air–liquid interface to model the airflow in the oral area and airways. The stability analysis reveals the existence of purely elastic and unconditionally unstable ‘liquid elastic’ and ‘solid elastic’ modes. The mechanism responsible for the destabilisation of the solid elastic mode is the shear stresses exerted by the air on the liquid and by the liquid on the deformable solid while for the liquid elastic mode, the mechanism is the first normal stress difference across the air–liquid interface. The liquid and solid elastic modes undergo resonance, resulting in the ‘resonance mode’ of instability. The resonance mode exhibits a much higher growth rate than the liquid and solid elastic modes. The shear-thinning characteristic of the liquid and presence of the surfactant leads to enhancement in the growth rate of the resonance mode. An estimate shows a good correlation between the exhaled fluid particle (i.e. droplets and aerosols) diameters and the wavelength of the perturbations with maximum growth rate. In essence, the present analysis predicts that the airflow in the airways and oral area could lead to an elastic instability arising due to the elastic nature of the saliva, mucus and underlying muscle layers.

JFM classification

Biological Fluid Dynamics: Pulmonary fluid mechanics Instability: Absolute/convective instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 928 , 10 December 2021 , A22
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Bassom, A.P., Blyth, M.G. & Papageorgiou, G.T. 2012 Using surfactants to stabilize two-phase pipe flows of core-annular type. J. Fluid Mech. 704, 333–359.CrossRefGoogle Scholar
Bird, R.B., Armstrong, R.C. & Hassager, O. 1977 Dynamics of Polymeric Liquids, Vol 1: Fluid Mechanics. John Wiley.Google Scholar
Bistagnino, A., Boffetta, G., Celani, A., Mazzino, A., Puliafito, A. & Vergassola, M. 2007 Nonlinear dynamics of the viscoelastic Kolmogorov flow. J. Fluid Mech. 590, 61–80.CrossRefGoogle Scholar
Blyth, M.G. & Pozrikidis, C. 2004 Effect of surfactant on the stability of flow down an inclined plane. J. Fluid Mech. 521, 241–250.CrossRefGoogle Scholar
Blyth, M.G. & Pozrikidis, C. 2006 Stability of axisymmetric core–annular flow in the presence of an insoluble surfactant. J. Fluid Mech. 548, 207–235.CrossRefGoogle Scholar
Bodiguel, H., Beaumont, H., Machado, A., Martinie, L., Kellay, H. & Colin, A. 2015 Flow enhancement due to elastic turbulence in channel flows of shear thinning fluids. Phys. Rev. Lett. 114, 028302.CrossRefGoogle ScholarPubMed
Bustamante-Marin, X.M. & Ostrowski, L.E. 2017 Cilia and mucociliary clearance. Cold Spring Harb. Perspect. Biol. 9, a028241.CrossRefGoogle ScholarPubMed
Castillo, H.A. & Wilson, H.J. 2017 Towards a mechanism for instability in channel flow of highly shear-thinning viscoelastic fluids. J. Non-Newtonian Fluid Mech. 247, 15–21.CrossRefGoogle Scholar
Chandra, B., Shankar, V. & Das, D. 2018 Onset of transition in the flow of polymer solutions through microtubes. J. Fluid Mech. 844, 1052–1083.CrossRefGoogle Scholar
Chen, Z., Zhong, M., Luo, Y., Deng, L., Hu, Z. & Song, Y. 2019 Determination of rheology and surface tension of airway surface liquid: a review of clinical relevance and measurement techniques. Respir. Res. 20, 274.CrossRefGoogle ScholarPubMed
Cheng, S., Gandevia, S.C., Green, M., Sinkus, R. & Bilston, L.E. 2011 Viscoelastic properties of the tongue and soft palate using MR elastography. J. Biomech. 44 (3), 450–454.CrossRefGoogle ScholarPubMed
Chokshi, P. & Kumaran, V. 2007 Stability of the flow of a viscoelastic fluid past a deformable surface in the low Reynolds number limit. Phys. Fluids 19, 104103.CrossRefGoogle Scholar
Chokshi, P. & Kumaran, V. 2008 a Weakly nonlinear analysis of viscous instability in flow past a neo-Hookean surface. Phys. Rev. E 77, 056303.CrossRefGoogle Scholar
Chokshi, P. & Kumaran, V. 2008 b Weakly nonlinear stability analysis of a flow past a neo-Hookean solid at arbitrary Reynolds numbers. Phys. Fluids 20, 094109.CrossRefGoogle Scholar
Choueiri, G.H., Lopez, J.M. & Hof, B. 2018 Exceeding the asymptotic limit of polymer drag reduction. Phys. Rev. Lett. 120, 124501.CrossRefGoogle ScholarPubMed
Collins, L.M.C. & Dawes, C. 1987 The surface area of the adult human mouth and thickness of the salivary film covering the teeth and oral mucosa. J. Dent. Res. 66, 1300–1302.CrossRefGoogle ScholarPubMed
Davies, C. & Carpenter, P.W. 1997 Instabilities in a plane channel flow between compliant walls. J. Fluid Mech. 352, 205–243.CrossRefGoogle Scholar
Gajjar, J.S.B. & Sibanda, P. 1996 The hydrodynamic stability of channel flow with compliant boundaries. Theor. Comput. Fluid Dyn. 8, 105–129.CrossRefGoogle Scholar
Gaurav, , & Shankar, V. 2010 Stability of pressure-driven flow in a deformable neo-Hookean channel. J. Fluid Mech. 659, 318–350.CrossRefGoogle Scholar
Geoghegan, P.H., Laffra, A.M., Hoogendorp, N.K., Taylor, M.C. & Jermy, M.C. 2017 Experimental measurement of breath exit velocity and expirated bloodstain patterns produced under different exhalation mechanisms. Intl J. Legal Med. 131, 1193–1201.CrossRefGoogle ScholarPubMed
Giribabu, D. & Shankar, V. 2017 Stability of plane Couette flow of a power-law fluid past a neo-Hookean solid at arbitrary Reynolds number. Phys. Fluids 29, 074106.CrossRefGoogle Scholar
Gkanis, V. & Kumar, S. 2003 Instability of creeping couette flow past a neo-Hookean solid. Phys. Fluids 15, 2864–2471.CrossRefGoogle Scholar
Gkanis, V. & Kumar, S. 2005 Stabilty of pressure-driven creeping flows in channels lined with a nonlinear elastic solid. J. Fluid Mech. 524, 357–375.CrossRefGoogle Scholar
Gorodtsov, V.A. & Leonov, A.I. 1967 On a linear instability of plane parallel Couette flow of viscoelastic fluid. Z. Angew. Math. Mech. 31, 289–299.Google Scholar
Grotberg, J.B. 2001 Respiratory fluid mechanics and transport processes. Annu. Rev. Biomed. Engng 3, 421–457.CrossRefGoogle ScholarPubMed
Grotberg, J.B. & Jensen, O.E. 2004 Biofluid mechanics in flexible tubes. Annu. Rev. Fluid Mech. 36, 121–147.CrossRefGoogle Scholar
Hains, F.D. & Price, J.F. 1962 Effect of a flexible wall on the stability of Poiseuille flow. Phys. Fluids 5, 365.CrossRefGoogle Scholar
Halpern, D & Frenkel, A.L. 2003 Destabilization of a creeping flow by interfacial surfactant: linear theory extended to all wavenumbers. J. Fluid Mech. 485, 191–220.CrossRefGoogle Scholar
Halpern, D., Fujioka, H. & Grotberg, J.B. 2010 The effect of viscoelasticity on the stability of a pulmonary airway liquid layer. Phys. Fluids 22, 011901.CrossRefGoogle ScholarPubMed
Halpern, D & Grotberg, J.B. 1992 Fluid-elastic instabilities of liquid-lined flexible tubes. J. Fluid Mech. 244, 615–632.CrossRefGoogle Scholar
Halpern, D & Grotberg, J.B. 1993 Surfactant effects on fluid-elastic instabilitiies of liquid-lined flexible tubes: A model of airway closure. Trans. ASME J. Biomech. Engng 115, 271–277.CrossRefGoogle Scholar
Hamed, R. & Fiegel, J. 2014 Synthetic tracheal mucus with native rheological and surface tension properties. J. Biomed. Mater. Res. A 102 (6), 1788–1798.CrossRefGoogle ScholarPubMed
Heil, M. & White, J.P. 2002 Airway closure: surface-tension-driven nonaxisymmetric instabilities of liquid-lined elastic rings. J. Fluid Mech. 462, 79–109.CrossRefGoogle Scholar
Holzapfel, G.A. 2000 Nonlinear Solid Mechanics. John Wiley.Google Scholar
Hwang, S.H., Litt, M. & Forsman, W.C. 1969 Rheological properties of mucus. Rheol. Acta 8, 438–448.CrossRefGoogle Scholar
Joshi, P. & Shankar, V. 2019 Flow-induced resonant shear-wave instability between a viscoelastic fluid and an elastic solid. Phys. Fluids 31, 084107.CrossRefGoogle Scholar
Kistler, S.F. & Schweizer, P.M. 1997 Liquid Film Coating: Scientific Principles and Their Technological Implications. Springer.CrossRefGoogle Scholar
Kumaran, V. 1995 Stability of the viscous flow of a fluid through a flexible tube. J. Fluid Mech. 294, 259–281.CrossRefGoogle Scholar
Kumaran, V., Fredrickson, G.H. & Pincus, P. 1994 Flow induced instability of the interface between a fluid and a gel at low Reynolds number. J. Phys. II France 4, 893–904.CrossRefGoogle Scholar
Kumaran, V. & Muralikrishnan, R. 2000 Spontaneous growth of fluctuations in the viscous flow of a fluid past a soft interface. Phys. Rev. Lett. 84, 3310–3313.CrossRefGoogle Scholar
Lafforgue, O., Seyssiecq-Guarante, I., Poncet, S. & Favier, J. 2017 Rheological properties of synthetic mucus for airway clearance. J. Biomed. Mater. Res. A 106, 386.CrossRefGoogle ScholarPubMed
Lai, S.K., Wang, Y.Y., Wirtz, D. & Hanes, J. 2009 Micro- and macrorheology of mucus: implications for drug and gene delivery to mucosal tissues. Adv. Drug Deliv. Rev. 61, 86–100.CrossRefGoogle Scholar
Lawrence, D.A., Branson, B., Oliva, I. & Rubinowitz, A. 2014 MDCT of the central airways: anatomy and pathology. Appl. Radiol. 43, 8–21.Google Scholar
Macosko, C.W. 1994 Rheology: Principles, Measurements, and Applications. VCH.Google Scholar
Malvern, L.E. 1969 Introduction to the Mechanics of a Continuous Medium. Prentice-Hall.Google Scholar
Miles, J.W. 1960 The hydrodynamic stability of a thin film of liquid in uniform shearing motion. J. Fluid Mech. 8, 593–610.CrossRefGoogle Scholar
Mittal, R., Ni, R. & Seo, J.-H. 2020 The flow physics of COVID-19. J. Fluid Mech. 894, F2.CrossRefGoogle Scholar
Moriarty, J.A. & Grotberg, J.B. 1999 Flow-induced instabilities of a mucus-serous bilayer. J. Fluid Mech. 397, 1–22.CrossRefGoogle Scholar
Nakamori, M., et al. 2020 Tongue thickness measured by ultrasonography is associated with tongue pressure in the Japanese elderly. PLoS ONE 15 (8), e0230224.CrossRefGoogle ScholarPubMed
Neelamegam, R., Giribabu, D. & Shankar, V. 2014 Instability of viscous flow over a deformable two-layered gel: experiment and theory. Phys. Rev. E 90, 043004.CrossRefGoogle Scholar
Nouar, C. & Frigaard, I. 2009 Stability of plane Couette-Poiseuille flow of shear-thinning fluid. Phys. Fluids 21, 064104.CrossRefGoogle Scholar
Papineni, R.S. & Rosenthal, F.S. 1997 The size distribution of droplets in the exhaled breath of healthy human subjects. J. Aerosol. Med. 10 (2), 105–116.CrossRefGoogle ScholarPubMed
Patne, R., Giribabu, D. & Shankar, V. 2017 Consistent formulations for stability of fluid flow through deformable channels and tubes. J. Fluid Mech. 827, 31–66.CrossRefGoogle Scholar
Patne, R. & Shankar, V. 2017 Absolute and convective instability in combined Couette-Poiseuille flow past a neo-Hookean solid. Phys. Fluids 29, 124104.CrossRefGoogle Scholar
Patne, R. & Shankar, V. 2019 Stability of flow through deformable channels and tubes: implications of consistent formulation. J. Fluid Mech. 860, 837–885.CrossRefGoogle Scholar
Patne, R. & Shankar, V. 2020 Instability induced by wall deformability in sliding Couette flow. Phys. Fluids 32, 114102.CrossRefGoogle Scholar
Picaut, L., Ronsin, O., Caroli, C. & Baumberger, T. 2017 Experimental evidence of a helical, supercritical instability in pipe flow of shear thinning fluids. Phys. Rev. Fluids 2, 083303.CrossRefGoogle Scholar
Poole, R.J. 2016 Elastic instabilities in parallel shear flows of a viscoelastic shear-thinning liquid. Phys. Rev. Fluids 1, 041301.CrossRefGoogle Scholar
Renardy, M. & Renardy, Y. 1986 Linear stability of plane Couette flow of an upper convected Maxwell fluid. J. Non-Newtonian Fluid Mech. 22, 23–33.CrossRefGoogle Scholar
Roberts, S.A. & Kumar, S. 2006 Stability of creeping Couette flow of a power-law fluid past a deformable solid. J. Non-Newtonian Fluid Mech. 139, 93–102.CrossRefGoogle Scholar
Samanta, D., Dubief, Y., Holzner, M., Schäfer, C., Morozov, A.N., Wagner, C. & Hof, B. 2013 Elasto-inertial turbulence. Proc. Natl Acad. Sci. USA 110, 10557–10562.CrossRefGoogle ScholarPubMed
Schmid, P.J. & Henningson, D.S. 2001 Stability and Transition in Shear Flows. Springer.CrossRefGoogle Scholar
Shah, P.L., Scott, S.F., Knight, R.A., Marriott, C., Ranasinha, C. & Hodson, M.E. 1996 In vivo effects of recombinant human DNase I on sputum in patients with cystic fibrosis. Thorax 51, 119–125.CrossRefGoogle ScholarPubMed
Shankar, V. & Kumar, S. 2004 Instability of viscoelastic plane Couette flow past a deformable wall. J. Non-Newtonian Fluid Mech. 116, 371–393.CrossRefGoogle Scholar
Shields, P.A. & Jeffery, P.K. 1987 The combined effects of vitamin A-deficiency and cigarette smoke on rat tracheal epithelium. Br. J. Expl Pathol. 68 (5), 705–717.Google ScholarPubMed
Sims, D.E. & Horne, M.M. 1997 Heterogeneity of the composition and thickness of tracheal mucus in rats. Am. J. Physiol. 273 (5), L1036–L1041.Google ScholarPubMed
Smith, M.K. & Davis, S.H. 1982 The instability of sheared liquid layers. J. Fluid Mech. 121, 187–206.CrossRefGoogle Scholar
Stokes, J.R. & Davies, G.A. 2007 Viscoelasticity of human whole saliva collected after acid and mechanical stimulation. Biorheology 44 (3), 141–160.Google ScholarPubMed
Tang, J.W., Nicolle, A., Pantelic, J., Koh, G.C., Wang, L.D. & Amin, M. 2012 Airflow dynamics of coughing in healthy human volunteers by shadowgraph imaging: an aid to aerosol infection control. PLoS ONE 7, e34818.CrossRefGoogle ScholarPubMed
Tang, J.W., Nicolle, A., Pantelic, J., Koh, G.C., Wang, L.D. & Amin, M. 2013 Airflow dynamics of coughing in healthy human volunteers by shadowgraph imaging: an aid to aerosol infection control. PLoS ONE 8 (4), e59970.CrossRefGoogle Scholar
Tanmay, V.S., Patne, R. & Shankar, V. 2018 Stability of plane Couette flow of Carreau fluids past a deformable solid at arbitrary Reynolds numbers. Phys. Fluids 30, 074103.CrossRefGoogle Scholar
Thaokar, R.M. & Kumaran, V. 2002 Stability of fluid flow past a membrane. J. Fluid Mech. 472, 29–50.CrossRefGoogle Scholar
Theriault, M.M., Eddy, K., Borgaonkar, J.N., Babar, J.L. & Manos, D. 2018 Diseases involving the central bronchi: multidetector CT for detection, characterization, and differential diagnosis. Radiographics 38, 58.CrossRefGoogle ScholarPubMed
Trefethen, L.N. 2000 Spectral Methods in MATLAB. SIAM.CrossRefGoogle Scholar
Verma, M.K.S. & Kumaran, V. 2013 A multifold reduction in the transition Reynolds number, and ultra-fast mixing, in a micro-channel due to a dynamical instability induced by a soft wall. J. Fluid Mech. 727, 407–455.CrossRefGoogle Scholar
Wang, J.Y., Mesquida, P. & Lee, T. 2011 Young's modulus measurement on pig trachea and bronchial airways. Conf. Proc. IEEE Engng Med. Biol. Soc. 8, 2089–2092.Google Scholar
Weinstein, S.J. & Ruschak, K.J. 2004 Coating flows. Annu. Rev. Fluid Mech. 36, 29–53.CrossRefGoogle Scholar
Wen, C., Poole, R.J., Willis, A.P. & Dennis, D.J.C. 2017 Experimental evidence of symmetry-breaking supercritical transition in pipe flow of shear-thinning fluids. Phys. Rev. Fluids 2, 031901.CrossRefGoogle Scholar
White, J. & Heil, M. 2005 Three-dimensional instabilities of liquid-lined elastic tubes: a thin-film fluid-structure interaction model. Phys. Fluids 17, 031506.CrossRefGoogle Scholar
White, J.L. & Metzner, A.B. 1963 Development of constitutive equations for polymeric melts and solutions. J. Appl. Polym. Sci. 7, 1867–1889.CrossRefGoogle Scholar
Widdicombe, J. 1997 Airway and alveolar permeability and surface liquid thickness: theory. J. Appl. Physiol. 82 (1), 3–12.CrossRefGoogle ScholarPubMed
Widdicombe, J.H. & Widdicombe, J.G. 1995 Regulation of human airway surface liquid. Respir. Physiol. 99 (1), 3–12.CrossRefGoogle ScholarPubMed
Wilson, H.J. & Loridan, V. 2015 Linear instability of a highly shear-thinning fluid in channel flow. J. Non-Newtonian Fluid Mech. 223, 200–208.CrossRefGoogle Scholar
Wilson, H.J. & Rallison, J.M. 1999 Instability of channel flow of a shear-thinning White-Metzner fluid. J. Non-Newtonian Fluid Mech. 87, 75–96.CrossRefGoogle Scholar
Wu, R. & Carlson, D.M. 1991 Structure and synthesis of mucins. In The Lung: Scientific Foundations, vol. 1, pp. 183–188. Raven Press, Ltd.Google Scholar
Zhou, Z.-Q., Peng, J., Zhang, Y.-J. & Zhuge, W.-L. 2014 Instabilities of viscoelastic liquid film coating tube in the presence of surfactant. J. Non-Newtonian Fluid Mech. 204, 94–103.CrossRefGoogle Scholar
Zussman, E., Yarin, A.L. & Nagler, R.M. 2007 Age- and flow-dependency of salivary viscoelasticity. J. Dent. Res. 86 (3), 281–285.CrossRefGoogle ScholarPubMed