Dry microfoams: Formation and flow in a confined channel

We present an experimental investigation of the agglomeration of microbubbles into a 2D microfoam and its flow in a rectangular microchannel. Using a flow-focusing method, we produce the foam in situ on a microfluidic chip for a large range of liquid fractions, down to a few percent in liquid. We can monitor the transition from separated bubbles to the desired microfoam, in which bubbles are closely packed and separated by thin films. We find that bubble formation frequency is limited by the liquid flow rate, whatever the gas pressure. The formation frequency creates a modulation of the foam flow, rapidly damped along the channel. The average foam flow rate depends non-linearly on the applied gas pressure, displaying a threshold pressure due to capillarity. Strong discontinuities in the flow rate appear when the number of bubbles in the channel width changes, reflecting the discrete nature of the foam topology. We also produce an ultra flat foam, reducing the channel height from 250 $\mu$m to 8 $\mu$m, resulting in a height to diameter ration of 0.02; we notice a marked change in bubble shape during the flow.Comment: 7 pages; 7 figures; 1 tex file+ 22 eps-file

A periodic microfluidic bubbling oscillator: insight into the stability of two-phase microflows

This letter describes a periodically oscillating microfoam flow. For constant input parameters, both the produced bubble volume and the flow rate vary over a factor two. We explicit the link between foam topology alternance and flow rate changes, and construct a retroaction model where bubbles still present downstream determine the volume of new bubbles, in agreement with experiment. This gives insight into the various parameters important to maintain monodispersity and at the same time shows a method to achieve controlled polydispersity.Comment: 4 page

Ligament-mediated spray formation

The spray formed when a fast gas stream blows over a liquid volume presents a wide distribution of fragment sizes. The process involves a succession of changes of the liquid topology, the last being the elongation and capillary breakup of ligaments torn off from the liquid surface. The coalescence of the liquid volumes constitutive of a ligament at the very moment it detaches from the liquid bulk produces larger drops. This aggregation process has its counterpart on the shape of the size distribution associated with the ligament breakup, found to be very well represented by gamma distributions. The exponential shape of the overall distribution in the spray coincides with the large excursion wing of these elementary distributions, underlying the crucial role played by the ligament dynamics in building up the broad statistics of sprays

Discrete rearranging disordered patterns, part I: Robust statistical tools in two or three dimensions

Discrete rearranging patterns include cellular patterns, for instance liquid foams, biological tissues, grains in polycrystals; assemblies of particles such as beads, granular materials, colloids, molecules, atoms; and interconnected networks. Such a pattern can be described as a list of links between neighbouring sites. Performing statistics on the links between neighbouring sites yields average quantities (hereafter "tools") as the result of direct measurements on images. These descriptive tools are flexible and suitable for various problems where quantitative measurements are required, whether in two or in three dimensions. Here, we present a coherent set of robust tools, in three steps. First, we revisit the definitions of three existing tools based on the texture matrix. Second, thanks to their more general definition, we embed these three tools in a self-consistent formalism, which includes three additional ones. Third, we show that the six tools together provide a direct correspondence between a small scale, where they quantify the discrete pattern's local distortion and rearrangements, and a large scale, where they help describe a material as a continuous medium. This enables to formulate elastic, plastic, fluid behaviours in a common, self-consistent modelling using continuous mechanics. Experiments, simulations and models can be expressed in the same language and directly compared. As an example, a companion paper (Marmottant, Raufaste and Graner, joint paper) provides an application to foam plasticity

Fast acoustic tweezers for the two-dimensional manipulation of individual particles in microfluidic channels

This paper presents a microfluidic device that implements standing surface acoustic waves in order to handle single cells, droplets, and generally particles. The particles are moved in a very controlled manner by the two-dimensional drifting of a standing wave array, using a slight frequency modulation of two ultrasound emitters around their resonance. These acoustic tweezers allow any type of motion at velocities up to few 10mm/s, while the device transparency is adapted for optical studies. The possibility of automation provides a critical step in the development of lab-on-a-chip cell sorters and it should find applications in biology, chemistry, and engineering domains

Plastic and viscous dissipations in foams: cross-over from low to high shear rates

International audienceSoft glassy materials made of deformable cells, such as liquid foams, simultaneously display elastic, plastic and viscous behaviours. Bubble deformation is elastic until the material plastically yields and bubbles swap neighbours, then bubbles relax dissipatively towards a new energy minimum. This relaxation occurs in a finite time, and shearing a foam at a fast strain rate compared to that time leads to a viscous flow. To describe such an elastic, plastic and viscous behaviour we introduce a simplified scalar model of foam deformation and flow with a periodic pinning potential. The continuum mechanics behaviour of the foam emerges as an ensemble average over disordered units without requiring that they are coupled. Our model captures surprisingly well various features of the viscous dissipation during plastic deformation. At low shear rates, the time averaged stress is smaller than the static yield stress. A critical shear rate exists: any flow at fixed stress has a shear rate above this critical value. Moreover, the model only involves measurable parameters, which enables us to compare it with existing experiments and simulations

Buckling instability causes inertial thrust for spherical swimmers at all scales

Microswimmers, and among them aspirant microrobots, generally have to cope with flows where viscous forces are dominant, characterized by a low Reynolds number ($Re$). This implies constraints on the possible sequences of body motion, which have to be nonreciprocal. Furthermore, the presence of a strong drag limits the range of resulting velocities. Here, we propose a swimming mechanism, which uses the buckling instability triggered by pressure waves to propel a spherical, hollow shell. With a macroscopic experimental model, we show that a net displacement is produced at all $Re$ regimes. An optimal displacement caused by non-trivial history effects is reached at intermediate $Re$. We show that, due to the fast activation induced by the instability, this regime is reachable by microscopic shells. The rapid dynamics would also allow high frequency excitation with standard traveling ultrasonic waves. Scale considerations predict a swimming velocity of order 1 cm/s for a remote-controlled microrobot, a suitable value for biological applications such as drug delivery.Comment: To appear in Phys. Rev. Lett See demonstration movie on https://www.youtube.com/watch?v=cEXMsFwEqs

Plastic and viscous dissipations in foams: cross-over from low to high shear rates

International audienceSoft glassy materials made of deformable cells, such as liquid foams, simultaneously display elastic, plastic and viscous behaviours. Bubble deformation is elastic until the material plastically yields and bubbles swap neighbours, then bubbles relax dissipatively towards a new energy minimum. This relaxation occurs in a finite time, and shearing a foam at a fast strain rate compared to that time leads to a viscous flow. To describe such an elastic, plastic and viscous behaviour we introduce a simplified scalar model of foam deformation and flow with a periodic pinning potential. The continuum mechanics behaviour of the foam emerges as an ensemble average over disordered units without requiring that they are coupled. Our model captures surprisingly well various features of the viscous dissipation during plastic deformation. At low shear rates, the time averaged stress is smaller than the static yield stress. A critical shear rate exists: any flow at fixed stress has a shear rate above this critical value. Moreover, the model only involves measurable parameters, which enables us to compare it with existing experiments and simulations

Role of the Channel Geometry on the Bubble Pinch-Off in Flow-Focusing Devices

The formation of bubbles by flow focusing of a gas and a liquid in a rectangular channel is shown to depend strongly on the channel aspect ratio. Bubble breakup consists in a slow linear 2D collapse of the gas thread, ending in a fast 3D pinch-off. The 2D collapse is predicted to be stable against perturbations of the gas-liquid interface, whereas the 3D pinch-off is unstable, causing bubble polydispersity. During 3D pinch-off, a scaling wm~tau1/3 between the neck width wm and the time tau before breakup indicates that breakup is driven by the inertia of both gas and liquid, not by capillarity

Discrete rearranging disordered patterns, part II: 2D plasticity, elasticity and flow of a foam

The plastic flow of a foam results from bubble rearrangements. We study their occurrence in experiments where a foam is forced to flow in 2D: around an obstacle; through a narrow hole; or sheared between rotating disks. We describe their orientation and frequency using a topological matrix defined in the companion paper (Graner et al., preprint), which links them with continuous plasticity at large scale. We then suggest a phenomenological equation to predict the plastic strain rate: its orientation is determined from the foam's local elastic strain; and its rate is determined from the foam's local elongation rate. We obtain a good agreement with statistical measurements. This enables us to describe the foam as a continuous medium with fluid, elastic and plastic properties. We derive its constitutive equation, then test several of its terms and predictions