Charles N. Baroud

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.

Capillary Origami: Spontaneous Wrapping of a Droplet with an Elastic Sheet

The interaction between elasticity and capillarity is used to produce three-dimensional structures through the wrapping of a liquid droplet by a planar sheet. The final encapsulated 3D shape is controlled by tailoring the initial geometry of the flat membrane. Balancing interfacial energy with elastic bending energy provides a critical length scale below which encapsulation cannot occur, which is verified experimentally. This length is found to depend on the thickness as h3/2, a scaling favorable to miniaturization which suggests a new way of mass production of 3D micro- or nanoscale objects.

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.

Microchannel deformations due to solvent-induced PDMS swelling

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.

Thermocapillary manipulation of droplets using holographic beam shaping: Microfluidic pin ball

We demonstrate that holographically generated optical patterns offer greater flexibility for the thermocapillary control of water droplets than Gaussian spots; droplets can be stopped in faster flows while using less optical intensity when the surface tension variations are created by line patterns instead of single spots. Further, experiments are performed making use of variable light patterns to achieve controlled droplet routing in a four-way cross microfluidic channel. Finally, multiple droplet storage is demonstrated as well as changing drop order.

Scaling in three-dimensional and quasi-two-dimensional rotating turbulent flows

We have made velocity time series measurements (using hot film probes) and velocity field measurements (using particle image velocimetry) on turbulent flow in a rotating annulus. For low annulus rotation rates the Rossby number was of order unity and the flow was three-dimensional (3D), but at high rotation rates the Rossby number was only about 0.1, comparable to the value for oceans and the atmosphere on large length scales. The low Rossby number (quasi-geostrophic) flow was nearly two-dimensional (2D), as expected from the Taylor–Proudman theorem. For the 3D flow we found that the probability distribution function (PDF) for velocity differences along the direction of the flow, δv(d)=v(x0+d)−v(x0), was Gaussian for large separations d and non-Gaussian (with exponential tails) for small d, as has been found for nonrotating turbulent flows. However, for low Rossby number flow, the PDF was self-similar (independent of d) and non-Gaussian. The exponents characterizing the structure functions, Sp=〈(δv)p〉∼dζp...

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

The localized heating produced by a tightly focused infrared laser leads to surface tension gradients at the interface of microfluidic drops covered with surfactants, resulting in a net force on the drop whose origin and magnitude are the focus of this paper. First, by colocalization of the surfactant micelles with a fluorescent dye, we demonstrate that the heating alters their spatial distribution, driving the interface out of equilibrium. This soluto-capillary effect opposes and overcomes the purely thermal dependence of the surface tension, leading to reversed interfacial flows. As the surface of the drop is set into motion, recirculation rolls are created outside and inside the drop, which we measure using time-resolved micro-Particle Image Velocimetry. Second, the net force produced on the drop is measured using an original microfluidic design. For a drop 300 microm-long and 100 microm-wide, we obtain a force of 180 nN for a laser power of 100 mW. This micro-dynanometer further shows that the magnitude of the heating, which is determined by the laser power and its absorption in the water, sets the magnitude of the net force on the drop. On the other hand, the dynamics of the force generation is limited by the time scale for heating, which has independently been measured to be tau(Theta) = 4 ms. This time scale sets the maximum velocity that the drops can have and still be blocked, by requiring that the interface passes the laser spot in a time longer than tau(Theta). The maximum velocity is measured at U(max) = 0.7 mm/s for our geometric conditions. Finally, a scaling model is derived that describes the blocking force in a confined geometry as the result of the viscous stresses produced by the shear between the drop and the lateral walls.

Transitions between three swimming gaits in Paramecium escape

Paramecium and other protists are able to swim at velocities reaching several times their body size per second by beating their cilia in an organized fashion. The cilia beat in an asymmetric stroke, which breaks the time reversal symmetry of small scale flows. Here we show that Paramecium uses three different swimming gaits to escape from an aggression, applied in the form of a focused laser heating. For a weak aggression, normal swimming is sufficient and produces a steady swimming velocity. As the heating amplitude is increased, a higher acceleration and faster swimming are achieved through synchronized beating of the cilia, which begin by producing oscillating swimming velocities and later give way to the usual gait. Finally, escape from a life-threatening aggression is achieved by a “jumping” gait, which does not rely on the cilia but is achieved through the explosive release of a group of trichocysts in the direction of the hot spot. Measurements through high-speed video explain the role of trichocysts in defending against aggressions while showing unexpected transitions in the swimming of microorganisms. These measurements also demonstrate that Paramecium optimizes its escape pattern by taking advantage of its inertia.

Sickling of red blood cells through rapid oxygen exchange in microfluidic drops

We have developed a microfluidic approach to study the sickling of red blood cells associated with sickle cell anemia by rapidly varying the oxygen partial pressure within flowing microdroplets. By using the perfluorinated carrier oil as a sink or source of oxygen, the oxygen level within the water droplets quickly equilibrates through exchange with the surrounding oil. This provides control over the oxygen partial pressure within an aqueous drop ranging from 1 kPa to ambient partial pressure, i.e. 21 kPa. The dynamics of the oxygen exchange is characterized through fluorescence lifetime measurements of a ruthenium compound dissolved in the aqueous phase. The gas exchange is shown to occur primarily during and directly after droplet formation, in 0.1 to 0.5 s depending on the droplet diameter and speed. The controlled deoxygenation is used to trigger the polymerization of hemoglobin within sickle red blood cells, encapsulated in drops. This process is observed using polarization microscopy, which yields a robust criterion to detect polymerization based on transmitted light intensity through crossed polarizers.

Monitoring a Reaction at Submillisecond Resolution in Picoliter Volumes

Well-established rapid mixing techniques such as stopped-flow have been used to push the dead time for kinetic experiments down to a few milliseconds. However, very fast reactions are difficult to resolve below this limit. We now outline an approach that provides access to ultrafast kinetics but does not rely on active mixing at all. Here, the reagents are compartmentalized into water-in-oil emulsion microdroplets (diameter ∼50 μm) that are statically arrayed in pairs, resting side-by-side in a well feature of a poly(dimethylsiloxane) (PDMS) device. A reaction between the contents of two droplets arrayed in such a holding trap is initiated by droplet fusion that is brought about by electrocoalescence and known to occur on a time scale of about 100 μs. A reaction between the reactants (Fe(3+) and SCN(-)) is monitored by image analysis measuring the product formation in the newly merged drop in both space and time, by use of a fast camera. A comparison of the concentration field of the reaction product with the output of a reaction-diffusion system of equations yields a rate constant k ∼ 3 × 10(4) M(-3)·s(-1). Since reaction and diffusion are formally included in the mathematical model, measurements can proceed immediately after the drop fusion, removing the need to allow time for mixing. This approach is different from existing methodologies, for example, experiments in a conventional stopped-flow apparatus but also electrofusion of moving droplets where contents are mixed by chaotic advection before a reaction is monitored. Our analysis makes kinetics accessible that are several times faster than techniques that have to allow time for mixing.