The respiratory tract is protected by mucus, a complex fluid transported along the epithelial surface by the coordinated beating of millions of microscopic cilia, hence the name of mucociliary clearance. Its impairment is associated with all severe chronic respiratory diseases. Yet, the relationship between ciliary density and the spatial scale of mucus transport, as well as the mechanisms that drive ciliary-beat orientations are much debated. Here, we show on polarized human bronchial epithelia that mucus swirls and circular orientational order of the underlying ciliary beats emerge and grow during ciliogenesis, until a macroscopic mucus transport is achieved for physiological ciliary densities. By establishing that the macroscopic ciliary-beat order is lost and recovered by removing and adding mucus respectively, we demonstrate that cilia/mucus hydrodynamic interactions govern the collective dynamics of ciliary-beat directions. We propose a two-dimensional model that predicts a phase diagram of mucus transport in accordance with the experiments. It paves the way to a predictive in-silico modeling of bronchial mucus transport in health and disease.

International audienceThe vortex-induced vibrations of an elastically mounted circular cylinder are investigated on the basis of direct numerical simulations. The body is free to move in the in-line and cross-flow directions. The natural frequencies of the oscillator are the same in both directions. The Reynolds number, based on the free stream velocity and cylinder diameter, is set to 3900 and kept constant in all simulations. The behavior of the coupled flow-structure system is analyzed over a wide range of the reduced velocity (inverse of the natural frequency) encompassing the lock-in range, i.e. where body motion and flow unsteadiness are synchronized. The statistics of the structural responses and forces are in agreement with prior experimental results. Large-amplitude vibrations develop in both directions. The in-line and cross-flow oscillations are close to harmonic; they exhibit a frequency ratio of 2 and a variable phase difference across the lock-in range. Distinct trends are noted in the force-displacement phasing mechanisms in the two directions: a phase difference jump associated with a sign change of the effective added mass and a vibration frequency crossing the natural frequency is observed in the cross-flow direction, while no phase difference jump occurs in the in-line direction. Higher harmonic components arise in the force spectra; their contributions become predominant when the cylinder oscillates close to the natural frequency. The force higher harmonics are found to impact the transfer of energy between the flow and the moving body, in particular, by causing the emergence of new harmonics in the energy transfer spectrum

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In the lung, the airway surface is protected by mucus, whose transport and evacuation is ensured through active ciliary beating. the mechanisms governing the long-range directional organization of ciliary beats, required for effective mucus transport, are much debated. Here, we experimentally show on human bronchial epithelium reconstituted in-vitro that the dynamics of ciliary-beat orientation is closely connected to hydrodynamic effects. To examine the fundamental mechanisms of this selforganization process, we build a two-dimensional model in which the hydrodynamic coupling between cilia is provided by a streamwise-alignment rule governing the local orientation of the ciliary forcing. The model reproduces the emergence of the mucus swirls observed in the experiments. The predicted swirl sizes, which scale with the ciliary density and mucus viscosity, are in agreement with in-vitro measurements. A transition from the swirly regime to a long-range unidirectional mucus flow allowing effective clearance occurs at high ciliary density and high mucus viscosity. In the latter case, the mucus flow tends to spontaneously align with the bronchus axis due to hydrodynamic effects. Billions of microscopic active cilia on the surface of the bronchial epithelium propel a viscous fluid, called mucus. Its function is to capture and eliminate inhaled pathogens, allergens and pollutants 1. This process, referred to as mucociliary clearance, is impaired in respiratory diseases such as primary dyskinesia, severe asthma 2 , COPD 3 and cystic fibrosis 4,5 , which affect hundreds of millions of people worldwide. The transport of mucus requires a long-range coordination of ciliary beat directions along the airways. In in-vitro cell cultures, observations of large-scale circular mucus flows spanning the culture chamber was reported by Matsui et al. 6. Recently, Khelloufi et al. 7 showed that this swirly transport is associated with a circular order of the ciliary beating directions underneath the mucus. Furthermore, mucus swirls of various sizes were observed, whose size was shown to scale with the ciliary density. Due to the invasive nature of in-vivo experiments, the mechanisms underlying mucus transport and collective dynamics of the ciliary activity remain poorly understood. In particular, the mechanisms involved in the directional self-organization of the ciliary beats over distances spanning the bronchi and trachea are yet to be elucidated. At the tissue scale, the planar polarization of the epithelial ciliated cells, established during development, is expected to determine the rotational polarity of the basal body at the base of the cilia, which sets the direction of beating 8,9. However, daily variations of ciliary-driven cerebrospinal fluid flow patterns have recently been observed in in-vivo mouse brain ventricles 10. In addition, Guirao et al. 11 showed that ciliary-beat directions on cell cultures issued from the subventrical zone of newborn mice could be drastically changed by applying an external flow. Finally, the direct...

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in: http://oatao. The three-dimensional structure of the flow downstream of a circular cylinder, either fixed or subjected to vortex-induced vibrations, is investigated by means of numerical simulation, at Reynolds number 3900, based on the cylinder diameter and current velocity. The flow exhibits pronounced fluctuations distributed along the span in all studied cases. Qualitatively, it is characterized by spanwise undulations of the shear layers separating from the body and the development of vortices elongated in the plane normal to its axis (planar vortices). A quantitative analysis of crossflow vorticity fluctuations in the spanwise direction reveals a peak of fluctuation amplitude in the near region (i.e., area of formation of the spanwise wake vortices) and opposite trends of the spanwise wavelength in the shear layer and wake regions; the wavelength tends to decrease as a function of the streamwise distance in the shear layers down to a minimum value close to 0.5 body diameters and then slowly increases further in the wake. The spanwise structure of the flow is differently altered in these two regions, once the cylinder vibrates. In the shear layer region, body motion is associated with an enhancement of planar vortex formation. The amplification of vorticity spanwise fluctuations in this region is accompanied by a reduction of the spanwise wavelength; it is found to decrease as a function of the instantaneous Reynolds number based on the instantaneous flow velocity seen by the moving body, following the global trend of the wavelength versus Reynolds number previously reported for fixed cylinders. In the wake region, the flow spanwise structure is essentially unaltered compared to the fixed body case, in spite of the major distortions of the streamwise and crossflow length scales.

The one-versus two-degree-of-freedom vortex-induced vibrations of a circular cylinder are investigated on the basis of direct numerical simulation results. The Reynolds number, based on the oncoming flow velocity and cylinder diameter, is set to 3900. Three cases are examined: the elastically mounted body is free to oscillate either in the direction aligned with the current (in-line direction; IL case), in the direction normal to the current (crossflow direction; CF case), or in both directions (IL+CF case). In each case, the behavior of the flow-structure system is studied over a range of values of the reduced velocity (inverse of the oscillator natural frequency). The in-line and cross-flow responses observed in the IL+CF case substantially differ from their one-degree-of-freedom counterparts, especially in the intermediate reduced velocity region. In this region, no vibrations develop in the IL case and in-line oscillations only occur if cross-flow motion is allowed. These in-line oscillations are accompanied by a major increase of the cross-flow responses, compared to the CF case. The two-degree-of-freedom vibrations are associated with the emergence of large-amplitude higher harmonics in the fluid force spectra. These aspects and more specifically the impact of the existence of a degree-of-freedom and oscillations in a given direction, on the fluid force and structural response in the perpendicular direction, do not seem to be systematically connected to changes in wake topology. Here, they are discussed in light of the orientation and magnitude of the instantaneous flow velocity seen by the moving body.

The accuracy of the lattice-Boltzmann (LB) method is related to the relaxation time controlling the flow viscosity. In particular, it is often recommended to avoid large fluid viscosities in order to satisfy the low-Knudsen-number assumption that is essential to recover hydrodynamic behavior at the macroscopic scale, which may in principle limit the possibility of simulating creeping flows and non-Newtonian flows involving important viscosity variations. Here it is shown, based on the continuous Boltzmann equations, that a two-relaxation-time (TRT) model can however recover the steady Navier-Stokes equations without any restriction on the fluid viscosity, provided that the Knudsen number is redefined as a function of both relaxation times. This effective Knudsen number is closely related to the previously-described parameter controlling numerical errors of the TRT model, providing a consistent theory at both the discrete and continuous levels. To simulate incompressible flows, the viscous incompressibility condition M a 2 /Re 1 also needs to be satisfied, where M a and Re are the Mach and Reynolds numbers. This concept is extended by defining a local incompressibility factor, allowing one to locally control the accuracy of the simulation for flows involving varying viscosities. These theoretical arguments are illustrated based on numerical simulations of the two-dimensional flow past a square cylinder. In the case of a Newtonian flow, the viscosity independence is confirmed for relaxation times up to 10 4 , and the ratio M a 2 /Re = 0.1 is small enough to ensure reliable incompressible simulations. The Herschel-Bulkley model is employed to introduce shear-dependent viscosities in the flow. The proposed numerical strategy allows to achieve major viscosity variations, avoiding the implementation of artificial viscosity cut-off in high-viscosity regions. Highly non-linear flows are simulated over ranges of the Bingham number Bn ∈ [1, 1000] and flow index n ∈ [0.2, 1.8], and successfully compared to prior numerical works based on Navier-Stokes solvers. This work provides a general framework to simulate complex creeping flows, as encountered in many biological and industrial systems, using the lattice-Boltzmann method.

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 18137 The system composed of a circular cylinder, either fixed or elastically mounted, and immersed in a current linearly sheared in the cross-flow direction, is investigated via numerical simulations. The impact of the shear and associated symmetry breaking are explored over wide ranges of values of the shear parameter (non-dimensional inflow velocity gradient, β ∈ [0, 0.4]) and reduced velocity (inverse of the non-dimensional natural frequency of the oscillator, U * ∈ [2, 14]), at Reynolds number Re = 100; β, U * and Re are based on the inflow velocity at the centre of the body and on its diameter. In the absence of large-amplitude vibrations and in the fixed body case, three successive regimes are identified. Two unsteady flow regimes develop for β ∈ [0, 0.2] (regime L) and β ∈ [0.2, 0.3] (regime H). They differ by the relative influence of the shear, which is found to be limited in regime L. In contrast, the shear leads to a major reconfiguration of the wake (e.g. asymmetric pattern, lower vortex shedding frequency, synchronized oscillation of the saddle point) and a substantial alteration of the fluid forcing in regime H. A steady flow regime (S), characterized by a triangular wake pattern, is uncovered for β > 0.3. Free vibrations of large amplitudes arise in a region of the parameter space that encompasses the entire range of β and a range of U * that widens as β increases; therefore vibrations appear beyond the limit of steady flow in the fixed body case (β = 0.3). Three distinct regimes of the flow-structure system are encountered in this region. In all regimes, body motion and flow unsteadiness are synchronized (lock-in condition). For β ∈ [0, 0.2], in regime VL, the system behaviour remains close to that observed in uniform current. The main impact of the shear concerns the amplification of the in-line response and the transition from figure-eight to ellipsoidal orbits. For β ∈ [0.2, 0.4], the system exhibits two well-defined regimes: VH1 and VH2 in the lower and higher ranges of U * , respectively. Even if the wake patterns, close to the asymmetric pattern observed in regime H, are comparable in both regimes, the properties of the vibrations and fluid forces clearly depart. The responses differ by their spectral contents, i.e. sinusoidal versus multi-harmonic, and their amplitudes are much larger in regime VH1, where the in-line responses reach 2 diameters (0.03 diameters in uniform flow) and the cross-flow responses 1.3 diameters. Aperiodic, intermittent oscillations are found to occur in the transition region between regimes VH1 and VH2; it appears that wake-body synchronization persists in this case.