This critical review discusses the current understanding of the formation, transport, and merging of drops in microfluidics. We focus on the physical ingredients which determine the flow of drops in microchannels and recall classical results of fluid dynamics which help explain the observed behaviour. We begin by introducing the main physical ingredients that differentiate droplet microfluidics from single-phase microfluidics, namely the modifications to the flow and pressure fields that are introduced by the presence of interfacial tension. Then three practical aspects are studied in detail: (i) The formation of drops and the dominant interactions depending on the geometry in which they are formed.(ii) The transport of drops, namely the evaluation of drop velocity, the pressure-velocity relationships, and the flow field induced by the presence of the drop. (iii) The fusion of two drops, including different methods of bridging the liquid film between them which enables their merging.

Droplets are natural candidates for use as microfluidic reactors, if active control of their formation and transport can be achieved. We show here that localized heating from a laser can block the motion of a water-oil interface, acting as a microfluidic valve for two-phase flows. A theoretical model is developed to explain the forces acting on a drop due to thermocapillary flow, predicting a scaling law which favors miniaturization. Finally, we show how the laser forcing can be applied to sorting drops, thus demonstrating how it may be integrated in complex droplet microfluidic systems.

The Bénard-von Karman vortex shedding instability in the wake of a cylinder is perhaps the best known example of a supercritical Hopf bifurcation in fluid dynamics. However, a simplified physical description that accurately accounts for the saturation amplitude of the instability is still missing. Here we present a simple self-consistent model that provides a clear description of the saturation mechanism and quantitatively predicts the saturated amplitude and flow fields. The model is formally constructed by a set of coupled equations governing the mean flow together with its most unstable eigenmode with finite size. The saturation amplitude is determined by requiring the mean flow to be neutrally stable. Without requiring any input from numerical or experimental data, the resolution of the model provides a good prediction of the amplitude and frequency of the vortex shedding, as well as the spatial structure of the mean flow and the Reynolds stress.Simple models are essential to our understanding of complex nonlinear phenomena. The van der Pol oscillator, for example, demonstrates how nonlinear oscillations can be described by the appearance of a limit cycle [1]. In large dimensional systems, however, these simple models do not entirely reveal the mechanisms that determine relevant parameters like the dominant frequency or saturation amplitude. For supercritical instabilities in fluid dynamics, the mean flow has been proposed as a key element to explain the origin of the dominant frequency [2-5] and the physical mechanism of the saturation process [5][6][7]. The physical picture thus invoked to understand the saturation is the following: perturbations feeding on an unstable flow induce mean flow modifications that increase while perturbations grow, up to the point where the mean flow becomes neutrally stable and perturbations stop growing and saturate. The present Letter aims at assessing this scenario.An early formulation of this concept of marginal stability of the mean flow was given by Malkus [8] in the context of turbulent flows. Shortly after, aiming for an equation describing the saturation of supercritical instabilities, Stuart [6] devised a simplified closed system wherein the mean flow was only affected by the Reynolds stress divergence of its leading eigenmode. By further assuming that the eigenmode was given by the unperturbed base flow, Stuart managed to obtain an equation for the saturation amplitude through the exact balance between the dissipation of the perturbation and the energy transfer from the mean flow. It wasn't until after two more years, through a more rigorous perturbative analysis close to threshold, that he mathematically derived an amplitude equation, the Stuart-Landau equation, directly from the Navier-Stokes equations [9].Despite the beauty and consistency of the multiplescale expansion method, its perturbative nature implies that the spatial structure of the growing unstable mode is in large part fixed by the unperturbed base flow. However, there are cases in which the spatial ...

The well-known Rayleigh criterion is a necessary and sufficient condition for inviscid centrifugal instability of axisymmetric perturbations. We have generalized this criterion to disturbances of any azimuthal wavenumber m by means of large-axialwavenumber WKB asymptotics. A sufficient condition for a free axisymmetric vortex with angular velocity Ω(r) to be unstable to a three-dimensional perturbation of azimuthal wavenumber m is that the real part of the growth rateis positive at the complex radius r = r 0 where ∂σ(r)/∂r =0, i.e.where φ =(1/r 3 )∂r 4 Ω 2 /∂r is the Rayleigh discriminant, provided that some ap o s t e r i o r ichecks are satisfied. The application of this new criterion to various classes of vortex profiles shows that the growth rate of non-axisymmetric disturbances decreases as m increases until a cutoff is reached. The criterion is in excellent agreement with numerical stability analyses of the Carton & McWilliams (1989) vortices and allows one to analyse the competition between the centrifugal instability and the shear instability. The generalized criterion is also valid for a vertical vortex in a stably stratified and rotating fluid, except that φ becomes φ =(1/r 3 )∂r 4 (where Ω b is the background rotation about the vertical axis. The stratification is found to have no effect. For the Taylor-Couette flow between two coaxial cylinders, the same criterion applies except that r 0 is real and equal to the inner cylinder radius. In sharp contrast, the maximum growth rate of non-axisymmetric disturbances is then independent of m.

International audienceThe spiral form of vortex breakdown observed in the numerical simulations of Ruith et al. (J. Fluid Mech., vol. 486, 2003, p. 331) is interpreted as a nonlinear global mode originating at the convective/absolute instability transition point in the lee of the vortex breakdown bubble. The local absolute frequency at the transition station is shown to yield a satisfactory prediction of the precession frequency measured in the three-dimensional direct numerical simulations. © 2006 Cambridge University Press

Temporal linear stability modes depending on two space directions are computed for a two-dimensional boundary-layer flow along a flat plate. The spatial structure of each individual temporally stable mode is shown to be reminiscent of the spatial exponential growth of perturbations along the flat plate, as predicted by local analyses. It is shown using an optimal temporal growth analysis, that an appropriate superposition of a moderate number of temporal modes gives rise to a spatially localized wave packet, starting at inflow and exhibiting transient temporal growth when evolving downstream along the plate. This wave packet is in qualitative agreement with the convectively unstable disturbance observed when solving the Navier–Stokes equations for an equivalent initial condition.

Various manufacturing techniques exist to produce double-curvature shells, including injection, rotational and blow molding, as well as dip coating. However, these industrial processes are typically geared for mass production and are not directly applicable to laboratory research settings, where adaptable, inexpensive and predictable prototyping tools are desirable. Here, we study the rapid fabrication of hemispherical elastic shells by coating a curved surface with a polymer solution that yields a nearly uniform shell, upon polymerization of the resulting thin film. We experimentally characterize how the curing of the polymer affects its drainage dynamics and eventually selects the shell thickness. The coating process is then rationalized through a theoretical analysis that predicts the final thickness, in quantitative agreement with experiments and numerical simulations of the lubrication flow field. This robust fabrication framework should be invaluable for future studies on the mechanics of thin elastic shells and their intrinsic geometric nonlinearities.

Wind tunnel measurements were performed for the wake produced by a three-bladed wind turbine immersed in uniform flow. These tests show the presence of a vorticity structure in the near-wake region mainly oriented along the streamwise direction, which is denoted as the hub vortex. The hub vortex is characterized by oscillations with frequencies lower than that connected to the rotational velocity of the rotor, which previous works have ascribed to wake meandering. This phenomenon consists of transversal oscillations of the wind turbine wake, which might be excited by the vortex shedding from the rotor disc acting as a bluff body. In this work, temporal and spatial linear stability analyses of a wind turbine wake are performed on a base flow obtained with time-averaged wind tunnel velocity measurements. This study shows that the low-frequency spectral component detected experimentally matches the most amplified frequency of the counter-winding single-helix mode downstream of the wind turbine. Then, simultaneous hot-wire measurements confirm the presence of a helicoidal unstable mode of the hub vortex with a streamwise wavenumber roughly equal to that predicted from the linear stability analysis