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On the role of viscoelasticity in mucociliary clearance: a hydrodynamic continuum approach

Published online by Cambridge University Press:  21 September 2023

Anjishnu Choudhury Open the ORCID record for Anjishnu Choudhury [Opens in a new window] ,
Marcel Filoche Open the ORCID record for Marcel Filoche [Opens in a new window] ,
Neil M. Ribe Open the ORCID record for Neil M. Ribe [Opens in a new window] ,
Nicolas Grenier Open the ORCID record for Nicolas Grenier [Opens in a new window]  and
Georg F. Dietze Open the ORCID record for Georg F. Dietze [Opens in a new window]
Anjishnu Choudhury*
Affiliation:
Université Paris-Saclay, CNRS, FAST, 91405 Orsay, France
Marcel Filoche
Affiliation:
INSERM U955, CNRS, ERM7000, Université Paris-Est Créteil Val de Marne, 94000 Créteil, France Institut Langevin, ESPCI Paris, Université PSL, CNRS, 75005 Paris, France
Neil M. Ribe
Affiliation:
Université Paris-Saclay, CNRS, FAST, 91405 Orsay, France
Nicolas Grenier
Affiliation:
Université Paris-Saclay, CNRS, LISN, 91405 Orsay, France
Georg F. Dietze
Affiliation:
Université Paris-Saclay, CNRS, FAST, 91405 Orsay, France
*
†Email address for correspondence: anjishnu.choudhury@espci.fr
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Abstract

We present numerical and analytical predictions of mucociliary clearance based on the continuum description of a viscoelastic mucus film, where momentum transfer from the beating cilia is represented via a Navier-slip boundary condition introduced by Bottier et al. (PLoS Comput. Biol., vol. 13, issue 7, 2017a, e1005552). Mucus viscoelasticity is represented via the Oldroyd-B model, where the relaxation time and the viscosity ratio have been fitted to experimental data for the storage and loss moduli of different types of real mucus, ranging from healthy to diseased conditions. We solve numerically the fully nonlinear governing equations for inertialess flow, and develop analytical solutions via asymptotic expansion in two limits: (i) weak viscoelasticity, i.e. low Deborah number; (ii) low cilia beat amplitude (CBA). All our approaches predict a drop in the mucus flow rate in relation to the Newtonian reference value, as the cilia beat frequency is increased. This relative drop increases with decreasing CBA and slip length. In diseased conditions, e.g. mucus properties characteristic of cystic fibrosis, the drop reaches 30 % in the physiological frequency range. In the case of healthy mucus, no significant drop is observed, even at very high frequency. This contrasts with the deterioration of microorganism propulsion predicted by the low-amplitude theory of Lauga (Phys. Fluids, vol. 19, issue 8, 2007, 083104), and is due to the larger beat amplitude and slip length associated with mucociliary clearance. In the physiological range of the cilia beat frequency, the low-amplitude prediction is accurate for both healthy and diseased conditions. Finally, we find that shear-thinning, modelled via a multi-mode Giesekus model, does not significantly alter our weakly viscoelastic and low-amplitude predictions based on the Oldroyd-B model.

JFM classification

Biological Fluid Dynamics: Pulmonary fluid mechanics Non-Newtonian Flows: Viscoelasticity Nonlinear Dynamical Systems: Low-dimensional models
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 971 , 25 September 2023 , A33
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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