Droplet-based microfluidics
Microfluidics offers unprecedented advantages for controlling droplets from their formation up to their storage on the chip.
We performed experiments in microfluidic junctions of various angles [1]. We discovered and explained the existence of a geometrical criterion (based on the channel geometry) governing the droplet break-up at small capillary numbers. In the same spirit, we revisited the description of droplet breakup in microfluidic T-junctions as proposed by Link et al., a work that is often cited and surprisingly does not use the notion we singled out in [1]. We showed that, for small capillary numbers, break-up critically depends on whether droplets do or do not fill the microchannels and again, the notion of critical droplet length is crucial for describing the various breakup regimes that take place.
We also proposed a novel approach that simplifies the description of the interaction between electric fields and oil/water interfaces in microchannels. In this approach the problem is reduced to two dimensions. The justification bears on theoretical arguments and on the analysis of oil-water interfaces distorted by electric fields in a shallow microchannel. By considering two examples, we further showed that one may predict, without much complication, the effect of electric fields on droplets in microfluidic devices on a quantitative basis. Electric fields are extremely useful for controlling droplet behavior and our contribution may facilitate the modeling of these situations.
We perfomed an experimental study of microfluidic droplets produced in T junctions and subjected to a local mechanical periodic forcing, using MSL technology [2]. This study emphasized the importance of complex dynamical behaviour in digital microfluidics. Synchronized and quasiperiodic regimes, organized into Arnold tongues and devil staircases, were reported for the first time for a system dedicated to droplet emission. The nature of the dynamical regime controls the droplet characteristics. This is why it may be important to determine in which regime forced droplet emittors operate. This work was extended by investigating the dynamics of two microfluidic droplet emitters placed in parallel [3]. Again, we observed complex dynamical behavior including synchronization, quasiperiodicity and chaos. This dynamics has a considerable impact on the properties of the resulting emulsions : chaotic and quasi periodic regimes give rise to polydisperse emulsions with poorly controllable characteristics while synchronized regimes generate well controlled monodispersed emulsions. We derived a dynamical model that reproduces the trends observed in the experiment. This study pointed to a fundamental difficulty in parallelizing droplet emittors. We suggested decoupling, as much as possible, the emittors so as to avoid the onset of complex, uncontrollable dynamical behavior.
We showed that wetting properties crucially control the patterns in two-phase flows of immiscible fluids in microchannels [4]. This paper underlined for the first time the exceeding importance of the walls, an aspect that often generates tremendous difficulties in the handling of droplets whenever unavoidable physico-chemical constraints have to be taken into account. Ordered patterns, continuously entrained by the flow, are obtained when one phase completely wets the walls, while disordered patterns, intermittently adhering to the channel walls, are unavoidably produced when wetting is partial. A lower limit for the channel sizes capable of generating well structured objects (drops, pears, pearl necklaces,..) was suggested.
Purifying droplets on a chip (for instance droplets incorporating individual cells for which we desire to isolate RNA) is an interesting task we analysed in depth here using simple (model) liquids. How long does it take to transfer species from a droplet to the external phase and what are the basic mechanisms that are involved ? No answer was available thus far for the particular context of microfluidic technology.
[1] Droplet breakup in microfluidic junctions of arbitrary angles L. Ménétrier-Deremble and P. Tabeling Phys. Rev. E 74, 035303 (2006)
[2] Arnold tongues in microfluidic systems, H. Willaime, V. Barbier, P. Tabeling, Phys. Rev. Lett., 96, 054501 (2006) 6
[3] Producing droplets in parallel microfluidic systems V. Barbier, H. Willaime, P. Tabeling, and F. Jousse Phys. Rev. E 74, 046
[4]Ordered and Disordered Patterns in Two-Phase Flows in Microchannels R. Dreyfus, H. Willaime, P. Tabeling Phys. Rev. Lett. 90 (14), 144505 (2003)
Double emulsions
Double emulsions are collections of droplets in droplets. These structures play an important role in various domains (such as drug delivery). Non-miniaturized techniques do not control their sizes and their dispersitivy. Microfluidics is expected to considerably impact this domain by achieving unprecedented levels of control and producing structures impossible to obtain with the standard technologies. These aspects provide strong incentives for producing and studying these structures.
In order to produce oil/water/oil structures on a chip, one must work with different wetting propertes on the same microsystem. Our objective here is to keep working with PDMS technology and invent a stable method for treating and patterning the surfaces of the microchannels. This topics is interesing in its own right. Being supported by a collaboration with M. Tatoulian, from ENSCP, we could apply a method based on plasma polymerization of PAA for the modification and control of the surface properties of PDMS surfaces [1]. By depositing PPAA coatings (Plasma Polymerized Acrylic Acid coatings) on PDMS we fabricate stable (several days) hydrophilic and patterned hydrophobic/hydrophilic surfaces. We used this approach to generate direct and (for the first time in this material) double emulsions oil/water/oil in PDMS microchannels.
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Depending on the interfacial energies of each pair of fluids (and the spreading parameters that one may generate) the equilibrium morphologies for a given triplet of fluids are Janus, complete encapsulation or no encapsulation at all. Which structure do we obtain ? Theory based on energy minimization provides the answer. The problem we addressed here is whether the experiment generates the expected shapes or whether additional phenomena (formation of a microscopic film, or existence a 2D gaseous layer at the interfaces) may complicate the problem and make these predictions irrelevant. We used thirty triplets of fluids to test the minimum energy theory, and as a whole succeeded to obtain an agreement between the predictions and the observations. Two key points are measuring the interfacial surface tension after mixing the three fluids together and stopping the flow to determine the equilibrium state. From this work one may interpret shapes produced under flow conditions as non equilibrium shapes. An interesting feature we showed is that microfluidic technologies allows one to control them in the sense they are reproducible and long lived. This work clarifies the potentialities of this technology.
[1] Stable modification of PDMS surface properties by plasma polymerization: application to the formation of double emulsions in microfluidic systems V. Barbier, M. Tatoulian, H. Li, F. Arefi-Khonsari, A. Ajdari, P. Tabeling Langmuir 22 (12), 5230-5232 (2006)
Micro and nanovelocimetry
Investigating flows in microsystems raises a number of instrumental issues that have been addressed by several groups over the last decade. There exists now commercial instruments dedicated to determining velocity profiles in microchannels, with a spatial resolution of a few microns and a time resolution that can reach tens of microseconds. In the MMN group, we developed a MicroPIV technique with a 700 nm resolution [1]; the incentive was to measure slip lengths above smooth and patterned surfaces. Recently, we developed a new technique, called nanoPIV, that allows to measure velocity profiles down to 25 nm from the wall with a spatial resolution of 20 nm. This work represents a progress of one order of magnitude in resolution compared to the state of the art.
We measured velocity profiles in water flowing through thin microchannels (12 micrometers high), using particle image velocimetry (PIV) combined with a nano–positionning system. From the velocity profiles we determined the slip lengths in two cases : smooth hydrophilic glass surfaces, and smooth hydrophobic glass surfaces, grafted with a monolayer of silane. The slip length was determined within 100 nm, i.e five times more accurately than the state of the art. In all cases, we found that the slip length is below 100 nm. These measurements contradicted a paper published in Meinhards group, who reported slip lenghts on the order of one micron or so on similar systems. There is a consensus now that tends to consider that slip lengths on smooth surfaces do not exceed 30nm for water, the maximum being reached for hydrophobic surfaces and water as the working fluid.
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With Lyderic Bocquets group, we measured slip lengths over surfaces patterned with carbon nanotubes. The surfaces were prepared and characterized in Lyon. In this case, air bubbles are trapped within the forest of nanocarbon tubes, favoring flow lubrication. We provided, still using MicroPIV, measurements of the slip lengths for these surfaces[2]. The range of slip lengths we determined lied in the range 0 - 2 microns. Theory which we could check in the experiment - predicts that with some optimization one can reach 100 microns slip lengths over such surfaces. After a first attempt (see [3]), the group of C.G.Kim succeeded in preparing such surfaces and announced 100 microns slip lengths. We tend to trust at the moment these impressive measurements.
We have also conducted Nano Particle Trajectory Velocimetry experiments. Fluorescent particles (20 nm diameter) were dispersed in ultrapure. A flow of this liquid was driven in microchannels as described above and movies were recorded (1000 images, acquisition rate of 25 Hz) while tracers were illuminated by an objective created evanescent wave (Figure 4). Given the small size of the tracers compared to the illumination wavelength, the detection of tracers on each image of the movie was made by a method based on cross-correlation between images and the Point Spread Function (PSF) of the optical system. This protocol allows a measurement of the position of single tracers in the horizontal plane with 30 nm accuracy and a measurement of the intensity, with an error negligible compared to the dispersion due to the tracer size variations. Given the structure of the evanescent illumination, fluorescence intensity is a decreasing exponential function of the altitude, and its measurement provides a determination of the altitude of individual tracers. This allows tracking of single particles in 3D tracking and the measurement of the speed of single tracers with constant intensity between two successive frames, remaining at the same distance from the surface. Some tracers remain stuck to the surface and their intensity is the maximal emission intensity, which consequently allows an absolute determination of the altitude of the tracers.
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The velocity of a single tracer is a struggle between Brownian diffusion and speed of drift due to the flow. By tracking thousands of tracers, the distribution of velocities at a given altitude was measured, which revealed the diffusion coefficient of the tracers and the speed of the flow in the same time. The reconstruction of speed (Figure 4) and diffusion coefficient profiles with a better resolution than 50 nm is thus possible by this method. These two quantities allow two independent determinations of the slip length with an accuracy of 10 nm in both cases. The speed profile provides a direct measurement of b and the variations of the diffusion coefficient are function of the slip length value due to hydrodynamic coupling of the particle with the surface. It appears that on hydrophilic surfaces no slippage was observed: b= 37 nm with the speed profile and b = -112 nm with the diffusion coefficient profile. On the contrary, the slip length is non zero on smooth hydrophobic surfaces produced by silanization of the glass surface. In that case, we measured a slip length b = 29+/-11 nm by speed profile analysis and b =2110 nm by analysis of the diffusion coefficient profile. These results are consistent with slip length expected from earlier results showing a reduction of water density at 1 nm of the solid surface
[1] Direct measurement of the apparent slip length P. Joseph, P.Tabeling Phys. Rev. E71, 035303(R) (2005)
[2] Slippage of water past superhydrophobic carbon nanotube forests in microchannels, P. Joseph, C. Cottin-Bizonne, J.-M. Benoît, C. Ybert, C. Journet, P.Tabeling, and L. Bocquet Phys. Rev. Lett. 97, 156104
[3] Comment on ”Large Slip of Aqueous Liquid Flow over a Nanoengineered Superhydrophobic Surface” Lydéric Bocquet, Patrick Tabeling, and Sébastien Manneville Phys. Rev. Lett. 97, 109601 (2006)
Complex fluids
Miniaturization may provide alternative approaches for determining the rheology of complex fluids for several reasons: practical (using small samples, parallelizing, integrating the measurement system on chip, portability) and physical (producing high shear rates under low Reynolds number conditions, visualizing the flow, tuning the flow geometry to enhance particular properties). Here we describe the work done on polymers (such as PEO) and surfactant solutions.
A scheme of the experimental set-up is shown on Fig.7 in ref. [1]. A stationary pressure driven flow is imposed inside a glass-PDMS microchannel. The solution is seeded with fluorescent latex particles (200 nm diameter), used as tracers at low volume fraction. An oil immersion, large numerical aperture objective is used to reach a narrow depth of field, smaller than one micron (700 nm). The position of the focal plane is controlled with a piezoelectric position controller. The velocity of tracers in this plane is measured by particle image velocimetry. The entire velocity profile v(z) is obtained by scanning the microchannel from the glass wall to the PDMS wall with 200 nm steps. Figure 5 represents velocity profiles obtained with a model shear-thinning fluid (PolyEthyleneOxide (PEO), Mw = 5 000 000 g/mol, C = 7.5 g/L) at different pressure drops in a 19 Am deep microchannel. Non-linearity shows up in the non-parabolic profiles and in the non-linear dependence of velocity on the applied pressure drops. We could obtain a remarkable collapse of the data on a stress versus shear rate curve (Figure 5 right., empty symbols). These data also agree very well with macroscopic measurements (Figure 5 right., full squares) made using classical rheometer with a Couette geometry at the same temperature.
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Here we take advantage of a novel rapid prototyping technology, resistant to high pressures (10 bars), optically transparent, to characterize by Particle Image Velocimetry the velocity profiles and the non linear rheology of solutions of wormlike micelles in the semi-dilute regime. Microchannels are made of a photopolymer that bonds strongly to glass, and are fabricated with a high resolution soft imprint technique developed in the laboratory. We build high aspect ratio channels (with a 70μm by 1mm section) that are 5 cm long and sustain a 5 bars pressure without deformation or leakage. We drive semi-dilute CTAB and sodium nitrate aqueous solutions reaching velocities up to 1mm/s. For such systems, viscosity ranges between 1 and 1000000 cp. By the addition of 500 nm fluorescent particles to the solution and PIV measurements, we reconstructed velocity profiles along the smallest dimension of the channel. The experimental set-up allows one to characterize slippage at the channel walls along with the rheology of the solution.
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As the pressure driving the flow is increased, the velocity profiles reveal first a newtonian phase, then apparition of a dramatically lower viscosity second phase at the walls; this is the so-called shear banding regime. According to a method validated on non-newtonian polymer solutions [1], we obtain the rheology of the fluid by a local calculation of the stress and shear rate from the velocity profiles, at a few hundred microns from the channel inlet. The rheology we find is in excellent agreement with global measurements made in a Couette rheometer (see Fig 6). The advantages of microfluidic technology here lies in the volume reduction, rapidity of the measurements, and full control of the flow. Instabilities known to occur in this type of systems appear far from the inlet in our case. In our contribution, we explore precisely the phenomenon by local velocity profiles measurements. In conclusion, the association of a new soft imprint technology in a UV-curable optical glue and a PIV set-up offers the opportunity to use microfluidic as a new context for highly viscous complex fluids study. We achieve local velocimetry and rheological measurements and take the full benefit of this context to observe and characterize more complex spatio-temporal behavior of shear-banding fluids.
[1] Rheology of complex fluids by particle image velocimetry in microchannels G. Degré, P. Joseph, P. Tabeling, S. Lerouge, M. Cloitre, A. Ajdari Appl. Phys. Lett. 89, 024104 (2006)
Pervaporation based screening
Determination of the phase diagram of multicomponent systems is of importance in a number of realms: industrial formulation, protein cristallization, bottom up material assembly from spontaneous ordering of surfactant, polymeric or colloidal systems [1]. Depending on the application, one may want to access only the equilibrium phase diagram or gain additional information as to the metastable phases that can appear for kinetic reasons. Methods to reach these goals often imply tedious and systematic measurements, requiring for screening purposes the use of robotic platforms. Two generic strategies consist in varying (in space or time) the temperature of samples of given concentrations on the one hand, and on the other hand isothermal concentration by either removal of the solvent (osmosis, drying), external action on the solutes (sedimentation or dielectrophoresis for colloids), or studies of spontaneous interdiffusion in contact experiments. In this work we introduce microfluidic tools for controlled isothermal concentration of a wide range of systems, covering solutions of ions, polymers, proteins, surfactants and colloidal suspensions.
Our work is inspired by recent observations that in standard microsytems built of PolyDiMethylSiloxane (PDMS), spontaneous water permeation through the PDMS matrix induces flows that can be used to concentrate colloids. Taking a step further, we have engineered specialized microgeometries that allow us to control spatially and temporally the evaporation process as well as the resulting concentration of solutes [2]. Their parallel implementation in microfluidic format has started with a thesis supported by Rhodia. We realized a system including 6 chambers, with a system of integrated valves and concentration distribution (first developed by G. Whitesides) enabling the flow control. We developed an original technique for monitoring in real time the averaged concentration in each chamber. The technique was illustrated for the case of salt crystallisation where the equivalence of recalescence curves could be obtained in each chamber. We are not aware of a similar measurement done thus far in the field of crystallisation. The parallized pervaporation approach is important to consider when highly viscous phases are to be characterized ; the strategy consists here to dilute transport and concentrate in situ. This task is achieved by our system. Whether the parallelized pervaporation approach may offer an alternative method in comparison with existing microfluidic technologies - for screening systems (for instance in view of producing protein crystals) is still an open issue.
[1] Experimental Study and Nonlinear Dynamic Analysis of Time-periodic Micro Chaotic Mixers, Y.K. Lee, C. Shih, P. Tabeling and C.M. Ho Journal of Fluid Mechanics, 575, 425-448 (2007)
[2] Microevaporators for kinetic exploration of phase diagrams, J. Leng, M.Joanicot, A.Ajdari, P. Tabeling, Phys. Rev. Lett. 96, 084503 (2006)
