Breaking anchored droplets in a microfluidic Hele-Shaw cell

We study microfluidic self digitization in Hele-Shaw cells using pancake droplets anchored to surface tension traps. We show that above a critical flow rate, large anchored droplets break up to form two daughter droplets, one of which remains in the anchor. Below the critical flow velocity for breakup the shape of the anchored drop is given by an elastica equation that depends on the capillary number of the outer fluid. As the velocity crosses the critical value, the equation stops admitting a solution that satisfies the boundary conditions; the drop breaks up in spite of the neck still having finite width. A similar breaking event also takes place between the holes of an array of anchors, which we use to produce a 2D array of stationary drops in situ.Comment: 5 pages, 4 figures, to appear in Phys. Rev. Applie

Valveless pumping at low Reynolds numbers

Pumping at low Reynolds number is a ubiquitously encountered feature, both in biological organisms and engineered devices. Generating net flow requires the presence of an asymmetry in the system, which traditionally comes from geometric flow rectifiers. Here, we study a valveless system of $N$ oscillating pumps in series, where the asymmetry comes not from the geometry but from time, that is the phase shifts between the pumps. Experimental and theoretical results are in very good agreement. We provide the optimal phase shifts leading to the maximal net flow in the continuous $N\rightarrow \infty$ limit, larger by 25\% than that of a traditional peristaltic sinusoidal wave. Our results pave the way for the design of more efficient microfluidic pumps.Comment: 6 pages, 5 figure

A Stochastic Description of Dictyostelium Chemotaxis

Chemotaxis, the directed motion of a cell toward a chemical source, plays a key role in many essential biological processes. Here, we derive a statistical model that quantitatively describes the chemotactic motion of eukaryotic cells in a chemical gradient. Our model is based on observations of the chemotactic motion of the social ameba Dictyostelium discoideum, a model organism for eukaryotic chemotaxis. A large number of cell trajectories in stationary, linear chemoattractant gradients is measured, using microfluidic tools in combination with automated cell tracking. We describe the directional motion as the interplay between deterministic and stochastic contributions based on a Langevin equation. The functional form of this equation is directly extracted from experimental data by angle-resolved conditional averages. It contains quadratic deterministic damping and multiplicative noise. In the presence of an external gradient, the deterministic part shows a clear angular dependence that takes the form of a force pointing in gradient direction. With increasing gradient steepness, this force passes through a maximum that coincides with maxima in both speed and directionality of the cells. The stochastic part, on the other hand, does not depend on the orientation of the directional cue and remains independent of the gradient magnitude. Numerical simulations of our probabilistic model yield quantitative agreement with the experimental distribution functions. Thus our model captures well the dynamics of chemotactic cells and can serve to quantify differences and similarities of different chemotactic eukaryotes. Finally, on the basis of our model, we can characterize the heterogeneity within a population of chemotactic cells

Monitoring the orientation of rare-earth-doped nanorods for flow shear tomography

Rare-earth phosphors exhibit unique luminescence polarization features originating from the anisotropic symmetry of the emitter ion's chemical environment. However, to take advantage of this peculiar property, it is necessary to control and measure the ensemble orientation of the host particles with a high degree of precision. Here, we show a methodology to obtain the photoluminescence polarization of Eu-doped LaPO4 nano rods assembled in an electrically modulated liquid-crystalline phase. We measure Eu3+ emission spectra for the three main optimal configurations ({\sigma}, {\pi} and {\alpha}, depending on the direction of observation and the polarization axes) and use them as a reference for the nano rod orientation analysis. Based on the fact that flowing nano rods tend to orient along the shear strain profile, we use this orientation analysis to measure the local shear rate in a flowing liquid. The potential of this approach is then demonstrated through tomographic imaging of the shear rate distribution in a microfluidic system.Comment: 8 pages, 3 figures + supplementary files for experimental and numerical method

Accessible quantification of multiparticle entanglement

Entanglement is a key ingredient for quantum technologies and a fundamental signature of quantumness in a broad range of phenomena encompassing many-body physics, thermodynamics, cosmology and life sciences. For arbitrary multiparticle systems, entanglement quantification typically involves nontrivial optimisation problems, and it may require demanding tomographical techniques. Here, we develop an experimentally feasible approach to the evaluation of geometric measures of multiparticle entanglement. Our framework provides analytical results for particular classes of mixed states of N qubits, and computable lower bounds to global, partial, or genuine multiparticle entanglement of any general state. For global and partial entanglement, useful bounds are obtained with minimum effort, requiring local measurements in just three settings for any N. For genuine entanglement, a number of measurements scaling linearly with N are required. We demonstrate the power of our approach to estimate and quantify different types of multiparticle entanglement in a variety of N-qubit states useful for uantum information processing and recently engineered in laboratories with quantum optics and trapped ion setups

Directional Sensing und Chemotaxis eukaryotischer Zellen - eine quantitative Studie

Wir untersuchen die Mechanismen eukaryotischer Chemotaxis am Beispiel des Modelorganismus Dictyostelium discoideum. Zunächst stellen wir ein theoretisches Modell für Directional Sensing vor, das auf einer Kopplung zwischen einem Aktivator-Inhibitor Mechanismus (lokale Aktivierung/globale Inhibierung) und bistabilen Reaktionskinetiken basiert. Der Übergang zwischen den beiden stabilen Zuständen wird dabei durch intrazelluläres Rauschen getrieben. Desweiteren werden verschiedene Modelle für Directional Sensing mit Experimenten verglichen. Dazu setzen wir einzelne D. discoideum Zellen Gradienten und gleichförmigen Konzentrationen des Chemoattraktants cAMP aus und verfolgen gleichzeitig die intrazelluläre Dynamik des Directional Sensing mit Hilfe des Markers PHCRAC-GFP. Gradienten von cAMP werden dabei mit einer Kombination von Photo-uncaging und Mikrofluidik erzeugt. Im letzten Teil der Arbeit korrelieren wir die chemotaktische Motilität von D. discoideum in linearen cAMP-Gradienten mit dem Signal-Rausch-Verhältnis aktivierter sekundärer Botenstoffe. Zur genaueren Charakterisierung chemotaktischer Motilität benutzen wir hier eine Langevin-Gleichung, deren Parameter aus den experimentellen Daten bestimmt werden und mit deren Hilfe chemotaktische Zellbewegung modelliert werden kann.We investigate the mechanisms behind eukaryotic chemotaxis using the model organism Dictyostelium discoideum. We propose a theoretical model of directional sensing based on a local excitation/global inhibition mechanism, coupled to bistable chemical kinetics. The transition between the two stable states is driven by intracellular noise. Models of directional sensing are then tested experimentally by exposing individual D. discoideum to gradients and uniform concentrations of the chemoattractant cAMP, while monitoring the intracellular dynamics of PHCRAC-GFP, a marker of directional sensing. The gradients of cAMP are produced using a combination of photo-uncaging and microfluidics. In the last part of this work, the chemotactic motility of D. discoideum in linear profiles of cAMP is correlated with the signal to noise ratio of activated intracellular second messengers. For a better characterization of the chemotactic motility of wild-type and mutants cells, we use a Langevin equation whose parameters are retrieved from the experimental data to model chemotactic cell motion

Flows induced by a capsule of microalgae

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Memory effects in the phototactic behaviour of Chlamydomonas reinhardtii

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Short-term memory effects in the phototactic behavior of microalgae

International audiencePhototaxis, the directed motion in response to a light stimulus, is crucial for motile microorganisms that rely on photosynthesis, such as the unicellular microalga \textit{Chlamydomonas reinhardtii}. It is well known that microalgae adapt to ambient light stimuli. On time scales of several dozen minutes, when stimulated long enough, the response of the microalga evolves as if the light intensity were decreasing~[Mayer, \textit{Nature} (1968)]. Here, we show experimentally that microalgae also have a short-term memory, on the time scale of a couple of minutes, which is the opposite of adaptation. At these short time scales, when stimulated consecutively, the response of \textit{C. reinhardtii} evolves as if the light intensity were increasing. Our experimental results are rationalized by the introduction of a simplified model of phototaxis. Memory comes from the interplay between an internal biochemical time scale and the time scale of the stimulus; as such, these memory effects are likely to be widespread in phototactic microorganisms