The role of viscoelasticity in mucociliary clearance - a continuum approach
Abstract
We present numerical simulations and analytical predictions of mucociliary clearance based on a continuum description for a viscoelastic mucus film, where momentum transfer from the beating cilia is represented via a moving-envelope boundary condition introduced by Bottier et al. (PLoS Comp. Biol., 2017). Mucus viscoelasticity is represented via the Oldroyd-B model, where we have fitted the relaxation time and the total viscosity to the dynamic moduli of real mucus, ranging from `healthy' to `diseased' conditions. We solve the nonlinear governing equations using the code Basilisk and also obtain an analytical solution in the weakly-viscoelastic limit. Both approaches predict a drop in the mucus flow rate q versus its Newtonian limit qN as the cilia beat frequency, f, is increased. In the case of diseased mucus, q/qN drops by 40% in the physiological range of f. Further, we find that this drop increases with decreasing cilia beat amplitude and film thickness. For healthy mucus, q/qN remains close to unity, even at large f. This contrasts with the drop in swimming speed observed for microorganisms (Lauga, CUP, 2021) and suggests that, while elasticity of mucus hinders the propulsion of pathogens, it does not deteriorate mucociliary clearance.