François Gallaire

Dynamics of microfluidic droplets

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.

Thermocapillary valve for droplet production and sorting

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 that 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.

On two-dimensional temporal modes in spatially evolving open flows: the flat-plate boundary layer

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.

Mode selection in swirling jet experiments: a linear stability analysis

The primary goal of the study is to identify the selection mechanism responsible for the appearance of a double-helix structure in the pre-breakdown stage of so-called screened swirling jets for which the circulation vanishes away from the jet. The family of basic flows under consideration combines the azimuthal velocity profiles of Carton & McWilliams (1989) and the axial velocity profiles of Monkewitz (1988). This model satisfactorily represents the nozzle exit velocity distributions measured in the swirling jet experiment of Billant et al. (1998). Temporal and absolute/convective instability properties are directly retrieved from numerical simulations of the linear impulse response for different swirl parameter settings. A large range of negative helical modes, winding with the basic flow, are destabilized as swirl is increased, and their characteristics for large azimuthal wavenumbers are shown to agree with the asymptotic analysis of Leibovich & Stewartson (1983). However, the temporal study fails to yield a clear selection principle. The absolute/convective instability regions are mapped out in the plane of the external axial flow and swirl parameters. The absolutely unstable domain is enhanced by rotation and it remains open for arbitrarily large swirl. The swirling jet with zero external axial flow is found to first become absolutely unstable to a mode of azimuthal wavenumber

Spiral vortex breakdown as a global mode

m\,{=}\,{-}2

Microchannel deformations due to solvent-induced PDMS swelling

, winding with the jet. It is suggested that this selection mechanism accounts for the experimental observation of a double-helix structure.

Two-dimensional global low-frequency oscillations in a separating boundary-layer flow

The 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.

Three-dimensional transverse instabilities in detached boundary layers

The compatibility of polydimethylsiloxane (PDMS) channels with certain solvents is a well known problem of soft lithography techniques, in particular when it leads to the swelling of the PDMS blocks. However, little is known about the modification of microchannel geometries when they are subjected to swelling solvents. Here, we experimentally measure the deformations of the roof of PDMS microchannels due to such solvents. The dynamics of impregnation of the solvents in PDMS and its relation to volume dilation are first addressed in a model experiment, allowing the precise measurement of the diffusion coefficients of oils in PDMS. When Hexadecane, a swelling solvent, fills a microchannel 1 mm in width and 50 μm in height, we measure that the channel roof bends inwards and takes a parabolic shape with a maximum deformation of 7 μm. The amplitude of the subsidence is found to increase with the channel width, reaching 28 μm for a 2 mm wide test section. On the other hand, perfluorinated oils do not swell the PDMS and the microchannel geometry is not affected by the presence of perfluorodecalin. Finally, we observe that the trajectories of droplets flowing in this microchannel are strongly affected by the deformations: drops carried by swelling oils are pushed towards the edges of the channel while those carried by non-swelling oils remain in the channel center.

Laser-Induced Force on a Microfluidic Drop : Origin and Magnitude

A separated boundary-layer flow at the rear of a bump is considered. Two-dimensional equilibrium stationary states of the Navier–Stokes equations are determined using a nonlinear continuation procedure varying the bump height as well as the Reynolds number. A global instability analysis of the steady states is performed by computing two-dimensional temporal modes. The onset of instability is shown to be characterized by a family of modes with localized structures around the reattachment point becoming almost simultaneously unstable. The optimal perturbation analysis, by projecting the initial disturbance on the set of temporal eigenmodes, reveals that the non-normal modes are able to describe localized initial perturbations associated with the large transient energy growth. At larger time a global low-frequency oscillation is found, accompanied by a periodic regeneration of the flow perturbation inside the bubble, as the consequence of non-normal cancellation of modes. The initial condition provided by the optimal perturbation analysis is applied to Navier–Stokes time integration and is shown to trigger the nonlinear ‘flapping’ typical of separation bubbles. It is possible to follow the stationary equilibrium state on increasing the Reynolds number far beyond instability, ruling out for the present flow case the hypothesis of some authors that topological flow changes are responsible for the ‘flapping’.

Instability mechanisms in swirling flows

The direct numerical simulation of the incompressible Navier-Stokes equations of the flow above a bump shows a stationary longitudinal instability at a Reynolds number of Re=400. A three-dimensional global mode linear analysis is used to interpret these results and shows that the most unstable eigenmode is steady and localized in the recirculation bubble, with spanwise wavelength of approximatively ten bump heights. An inviscid geometrical optics analysis along closed streamlines is then proposed and modified accordingly to account for viscous effects. This motivates a final discussion regarding the physical origin of the observed instability.