Longitudinal to Transverse Metachronal Wave Transitions in an In Vitro Model of Ciliated Bronchial Epithelium.

Myriads of cilia beat on ciliated epithelia, which are ubiquitous in life. When ciliary beats are synchronized, metachronal waves emerge, whose direction of propagation depends on the living system in an unexplained way. We show on a reconstructed human bronchial epithelium in vitro that the direction of propagation is determined by the ability of mucus to be transported at the epithelial surface. Numerical simulations show that longitudinal waves maximize the transport of mucus while transverse waves, observed when the mucus is rigid and still, minimize the energy dissipated by the cilia.

Phase separation dynamics in deformable droplets.

Phase separation can drive spatial organization of multicomponent mixtures. For instance in developing animal embryos, effective phase separation descriptions have been used to account for the spatial organization of different tissue types. Similarly, separation of different tissue types is also observed in stem cell aggregates, where the emergence of a polar organization can mimic early embryonic axis formation. Here, we describe such aggregates as deformable two-phase fluid droplets, which are suspended in a fluid environment (third phase). Using hybrid finite-volume Lattice-Boltzmann simulations, we numerically explore the out-of-equilibrium routes that can lead to the polar equilibrium state of such a droplet. We focus on the interplay between spinodal decomposition and advection with hydrodynamic flows driven by interface tensions, which we characterize by a Peclet number Pe. Consistent with previous work, for large Pe the coarsening process is generally accelerated. However, for intermediate Pe we observe long-lived, strongly elongated droplets, where both phases form an alternating stripe pattern. We show that these "croissant" states are close to mechanical equilibrium and coarsen only slowly through diffusive fluxes in an Ostwald-ripening-like process. Finally, we show that a surface tension asymmetry between both droplet phases leads to transient, rotationally symmetric states whose resolution leads to flows reminiscent of Marangoni flows. Our work highlights the importance of advection for the phase separation process in finite, deformable systems.

Multigrid dual-time-stepping lattice Boltzmann method.

The lattice Boltzmann method often involves small numerical time steps due to the acoustic scaling (i.e., scaling between time step and grid size) inherent to the method. In this work, a second-order dual-time-stepping lattice Boltzmann method is proposed in order to avoid any time-step restriction. The implementation of the dual time stepping is based on an external source in the lattice Boltzmann equation, related to the time derivatives of the macroscopic flow quantities. Each time step is treated as a pseudosteady problem. The convergence rate of the steady lattice Boltzmann solver is improved by implementing a multigrid method. The developed solver is based on a two-relaxation time model coupled to an immersed-boundary method. The reliability of the method is demonstrated for steady and unsteady laminar flows past a circular cylinder, either fixed or towed in the computational domain. In the steady-flow case, the multigrid method drastically increases the convergence rate of the lattice Boltzmann method. The dual-time-stepping method is able to accurately reproduce the unsteady flows. The physical time step can be freely adjusted; its effect on the simulation cost is linear, while its impact on the accuracy follows a second-order trend. Two major advantages arise from this feature. (i) Simulation speed-up can be achieved by increasing the time step while conserving a reasonable accuracy. A speed-up of 4 is achieved for the unsteady flow past a fixed cylinder, and higher speed-ups are expected for configurations involving slower flow variations. Significant additional speed-up can also be achieved by accelerating transients. (ii) The choice of the time step allows us to alter the range of simulated timescales. In particular, increasing the time step results in the filtering of undesired pressure waves induced by sharp geometries or rapid temporal variations, without altering the main flow dynamics. These features may be critical to improve the efficiency and range of applicability of the lattice Boltzmann method.

Hydrodynamic model of directional ciliary-beat organization in human airways.

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 self-organization 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.

Explicit and viscosity-independent immersed-boundary scheme for the lattice Boltzmann method.

Viscosity independence of lattice-Boltzmann methods is a crucial issue to ensure the physical relevancy of the predicted macroscopic flows over large ranges of physical parameters. The immersed-boundary (IB) method, a powerful tool that allows one to immerse arbitrary-shaped, moving, and deformable bodies in the flow, suffers from a boundary-slip error that increases as a function of the fluid viscosity, substantially limiting its range of application. In addition, low fluid viscosities may result in spurious oscillations of the macroscopic quantities in the vicinity of the immersed boundary. In this work, it is shown mathematically that the standard IB method is indeed not able to reproduce the scaling properties of the macroscopic solution, leading to a viscosity-related error on the computed IB force. The analysis allows us to propose a simple correction of the IB scheme that is local, straightforward and does not involve additional computational time. The derived method is implemented in a two-relaxation-time D2Q9 lattice-Boltzmann solver, applied to several physical configurations, namely, the Poiseuille flow, the flow around a cylinder towed in still fluid, and the flow around a cylinder oscillating in still fluid, and compared to a noncorrected immersed-boundary method. The proposed correction leads to a major improvement of the viscosity independence of the solver over a wide range of relaxation times (from 0.5001 to 50), including the correction of the boundary-slip error and the suppression of the spurious oscillations. This improvement may considerably extend the range of application of the IB lattice-Boltzmann method, in particular providing a robust tool for the numerical analysis of physical problems involving fluids of varying viscosity interacting with solid geometries.