We simulate numerically the full dynamics of Faraday waves in three dimensions for two incompressible and immiscible viscous fluids. The Navier–Stokes equations are solved using a finite-difference projection method coupled with a front-tracking method for the interface between the two fluids. The critical accelerations and wavenumbers, as well as the temporal behaviour at onset are compared with the results of the linear Floquet analysis of Kumar & Tuckerman (J. Fluid Mech., vol. 279, 1994, p. 49). The finite-amplitude results are compared with the experiments of Kityk et al (Phys. Rev. E, vol. 72, 2005, p. 036209). In particular, we reproduce the detailed spatio-temporal spectrum of both square and hexagonal patterns within experimental uncertainty. We present the first calculations of a three-dimensional velocity field arising from the Faraday instability for a hexagonal pattern as it varies over its oscillation period.

Numerical simulation of Faraday waves

Novel approaches, combining technology, biomaterial design, and cutting-edge cell culture, have been increasingly considered to advance the field of tissue engineering and regenerative medicine. Within this context, acoustic manipulation to remotely control spatial cellular organization within a carrier matrix has arisen as a particularly promising method during the last decade. Acoustic or sound-induced manipulation takes advantage of hydrodynamic forces exerted on systems of particles within a liquid medium by standing waves. Inorganic or organic particles, cells, or organoids assemble within the nodes of the standing wave, creating distinct patterns in response to the applied frequency and amplitude. Acoustic manipulation has advanced from micro- or nanoparticle arrangement in 2D to the assembly of multiple cell types or organoids into highly complex in vitro tissues. In this review, we discuss the past research achievements in the field of acoustic manipulation with particular emphasis on biomedical application. We survey microfluidic, open chamber, and high throughput devices for their applicability to arrange non-living and living units in buffer or hydrogels. We also investigate the challenges arising from different methods, and their prospects to gain a deeper understanding of in vitro tissue formation and application in the field of biomedical engineering.

The waves that make the pattern: a review on acoustic manipulation in biomedical research.

Recent Advances in Physics of Fluid Parametric Sloshing and Related Problems

We present the results of a theoretical investigation of the dynamics of a droplet walking on a vibrating fluid bath under the influence of a harmonic potential. The walking droplet's horizontal motion is described by an integro-differential trajectory equation, which is found to admit steady orbital solutions. Predictions for the dependence of the orbital radius and frequency on the strength of the radial harmonic force field agree favorably with experimental data. The orbital quantization is rationalized through an analysis of the orbital solutions. The predicted dependence of the orbital stability on system parameters is compared with experimental data and the limitations of the model are discussed.

Pilot-wave dynamics in a harmonic potential: Quantization and stability of circular orbits

Rapports d’activité 2010

Motives par la variete des motifs offerts
 par l'instabilite de Faraday (quasi-cristaux, oscillons, super-reseaux), nous en
 realisons la premiere simulation 3D non lineaire par un code joignant les methodes de
 differences finies et de 'front-tracking'. Les seuils d'instabilite et les modes propres
 s'accordent avec la theorie. Les motifs carres et hexagonaux observes experimentalement
 ont ete retrouves. Cependant, le regime hexagonal serait transitoire et appartiendrait a
 une orbite heterocline.

We simulate numerically the full dynamics of Faraday waves in three dimensions for two incompressible and immiscible viscous fluids. The Navier-Stokes equations are solved using a finite-difference projection method coupled with a front-tracking method for the interface between the two fluids. The domain of calculation is periodic in the horizontal directions and bounded in the vertical direction by two rigid horizontal plates. The critical accelerations and wavenumbers, as well as the temporal behaviour at onset are compared with the results of the linear Floquet analysis of Kumar and Tuckerman [J. Fluid Mech. 279, 49-68 (1994)]. The finite amplitude results are compared with the experiments of Kityk et al. [Phys. Rev. E 72, 036209 (2005)]. In particular we reproduce the detailed spatiotemporal spectrum of both square and hexagonal patterns within experimental uncertainty.

We present simulation results for several two-phase flow problems using a high performance, parallel code for the simulation of such incompressible flows in three dimensions. The code which we call BLUE is based on a high fidelity hybrid Front-Tracking/Level Set algorithm for Lagrangian tracking of arbitrarily deformable phase interfaces including breakup and coalescence and a precise treatment of surface tension forces, interface advection and mass conservation. BLUE couples an implicit, incompressible Navier-Stokes solver with multigrid pressure solution to the Lagrangian tracking method for implementation on large-scale parallel computing architectures. The modular program structure allows for the application of the code to a wide variety of physical scenarios: free surface instabilities, flow of bubbles or drops with coalescence and breakup, droplet impact or flow around immersed solid objects for microchannel flows for example. We present simulations and evaluate the parallel numerical performance of BLUE for several physical phenomena of large spatio-temporal extent where high performance is indispensable: the canonical phenomenon of a water droplet splash onto a film of water, the merging of two bubbles and the Faraday instability in the highly nonlinear regime.

Parallel Direct Numerical Simulation of Three-Dimensional Two-Phase Flows

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Numerical simulation of Faraday waves

Numerical simulation of Faraday waves

Numerical simulation of Faraday waves

Parallel Direct Numerical Simulation of Three-Dimensional Two-Phase Flows