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The droplet size in emulsions is known to affect the rheological properties and plays a crucial role in the many applications of emulsions. Despite its importance, the underlying mechanisms governing droplet size in emulsification remain poorly understood. We investigate the average drop size and size distribution upon emulsification with a high-shear mixer for model oil-in-water emulsions stabilized by a surfactant. The size distribution is found to be a log-normal distribution, resulting from the repetitive random breakup of drops. High-shear emulsification, the usual way of making emulsions, is therefore found to be very different from turbulent emulsification given by the Kolmogorov-Hinze theory for which power-law distributions of the drop size are expected. In agreement with this, the mean droplet size does not follow a scaling with the Reynolds number of the emulsification flow, but rather a capillary number scaling based on the viscosity of the continuous phase.

We provide a complete description of the ideal that serves as the resultant ideal for n univariate polynomials of degree d. We in particular describe a set of generators of this resultant ideal arising as maximal minors of a set of cascading matrices formed from the coefficients of the polynomials, generalising the classical Sylvester resultant of two polynomials., Comment: 9 pages; v2: added some classical references and a new result on projective scheme structure, communicated by Jan Stevens

We experimentally and numerically study the structure and dynamics of a mono-disperse packing of spontaneously aligning self-propelled hard disks. The packings are such that their equilibrium counterparts form perfectly ordered hexagonal structures. Experimentally, we first form a perfect crystal in an hexagonal arena which respects the same crystalline symmetry. Frustration of the hexagonal order, obtained by removing a few particles, leads to the formation of a rapidly diffusing "droplet". Removing more particles, the whole system spontaneously forms a macroscopic sheared flow, while conserving an overall crystalline structure. This flowing crystalline structure, which we call a "rheo-crystal" is made possible by the condensation of shear along localized stacking faults. Numerical simulations very well reproduce the experimental observations and allow us to explore the parameter space. They demonstrate that the rheo-crystal is induced neither by frustration nor by noise. They further show that larger systems flow faster while still remaining ordered., Comment: 4 pages, 5 figures

We propose a conservative two-dimensional particle model in which particles carry a continuous and classical spin. The model includes standard ferromagnetic interactions between spins of two different particles, and a nonstandard coupling between spin and velocity of the same particle inspired by the coupling observed in self-propelled hard discs. Because of this coupling Galilean invariance is broken and the conserved linear momentum associated to translation invariance is not proportional to the velocity of the center of mass. Also, the dynamics is not invariant under a global rotation of the spins alone. This, in principle, leaves room for collective motion and thus raises the question whether collective motion can arise in Hamiltonian systems. We study the statistical mechanics of such a system, and show that, in the fully connected (or mean-field) case, a transition to collective motion does exist in spite of momentum conservation. Interestingly, the velocity of the center of mass, which in the absence of Galilean invariance, is a relevant variable, also feeds back on the magnetization properties, as it acts as an external magnetic field that smoothens the transition. Molecular dynamics simulations of finite size systems indeed reveal a rich phase diagram, with a transition from a disordered to a homogeneous polar phase, but also more complex inhomogeneous phases with local order interrupted by topological defects.

Colloidal systems observed in video microscopy are often analysed using the displacements correlation matrix of particle positions. In non-thermal systems, the inverse of this matrix can be interpreted as a pair-interaction potential between particles. If the system is thermally agitated, however, only an effective interaction is accessible from the correlation matrix. We show how this effective interaction differs from the non-thermal case by comparing with high-statistics numerical data from hard-sphere crystals., Comment: 12 pages, 10 figures, Soft Matter 2016

We develop a cavity-based method which allows to extract thermodynamic properties from position information in hard-sphere/disk systems. So far, there are 'available-volume' and 'free-volume' methods. We add a third one, which we call 'available-volume-after-takeout', and which is shown to be mathematically equivalent to the others. In applications, where data sets are finite, all three methods show limitations, and they do this in different parameter ranges. We illustrate the principal equivalence and the limitations on data from molecular dynamics -- In particular, we test robustness against missing data. We have in mind experimental limitations where there is a small polydispersity, say 4% in the particle radii, but individual radii cannot be determined. We observe that, depending on the used method, the errors in such a situation are easily 100% for the pressure and 10kT for the chemical potentials. Our work is meant as guideline to the experimentalist for choosing the right one of the three methods, in order to keep the outcome of experimental data analysis meaningful., Comment: 13 pages, 6 figures. The final publication is available at Springer via http://dx.doi.org/10.1140/epje/i2015-15097-0

We show that low density homogeneous phases of self propelled hard disks exhibit a transition from isotropic to polar collective motion, albeit of a qualitatively distinct class from the Vicsek one. In the absence of noise, an abrupt discontinuous transition takes place between the isotropic phase and a fully polar absorbing state. Increasing the noise, the transition becomes continuous at a tri-critical point. We explain all our numerical findings in the framework of Boltzmann theory, on the basis of the binary scattering properties. We show that the qualitative differences observed between the present and the Vicsek model at the level of their phase behavior, take their origin in the complete opposite physics taking place during scattering events. We argue that such differences will generically hold for systems of self-propelled particles with repulsive short range interactions., Comment: 6 pages, 5 figures

We study the spatially homogeneous phases of polar active particles in the low density limit, and specifically the transition from the isotropic phase to collective polar motion. We show that the fundamental quantity of interest for the stability of the isotropic phase is the forward component of the momentum change induced by binary scattering events. Building on the Boltzmann formalism, we introduce an ansatz for the one-particle distribution and derive a closed-form evolution equation for the order parameter. This approach yields a very intuitive and physically meaningful criterion for the destabilization of the isotropic phase, where the ansatz is exact. The criterion also predicts whether the transition is continuous or discontinuous, as illustrated in three different classes of models. The theoretical predictions are in excellent agreement with numerical results., Comment: 20 pages, 6 figures Publised at IOP, Journal of Statistical Mechanics, available at http://dx.doi.org/10.1088/1742-5468/2015/10/P10017

The vibrational modes of pristine and polycrystalline monolayer colloidal crystals composed of thermosensitive microgel particles are measured using video microscopy and covariance matrix analysis. At low frequencies, the Debye relation for two dimensional harmonic crystals is observed in both crystal types; at higher frequencies, evidence for van Hove singularities in the phonon density of states is significantly smeared out by experimental noise and measurement statistics. The effects of these errors are analyzed using numerical simulations. We introduce methods to correct for these limitations, which can be applied to disordered systems as well as crystalline ones, and we show that application of the error correction procedure to the experimental data leads to more pronounced van Hove singularities in the pristine crystal. Finally, quasi-localized low-frequency modes in polycrystalline two-dimensional colloidal crystals are identified and demonstrated to correlate with structural defects such as dislocations, suggesting that quasi-localized low-frequency phonon modes may be used to identify local regions vulnerable to rearrangements in crystalline as well as amorphous solids., Comment: 8 pages, 6 figures 09/11/2013 major revisions

Studies by video microscopy on fluctuating colloids measure the real-space cross-correlations in particle motion. This set of correlations is then treated as a matrix, in order to study the spectrum and mode structure. We show that in general the modes are modified by the truncation of the full real-space correlations. We perform a theoretical analysis of the truncation, find the boundary conditions imposed by the truncation, and propose practical windowing strategies to eliminate artefacts. We study the problem from various perspectives, to compile a survey for experimentalists., Comment: 11 pages, 9 figures

Recent confocal experiments on colloidal solids motivate a fuller study of the projection of three-dimensional fluctuations onto a two-dimensional confocal slice. We show that the effective theory of a projected crystal displays several exceptional features, such as non-standard exponents in the dispersion relations. We provide analytic expressions for the effective two-dimensional elastic properties which allow one to work back from sliced experimental observations to three-dimensional elastic constants., Comment: 5 pages, 2 figures

The correlations of the fluctuating stress tensor are calculated in an equilibrium molecular-dynamics simulation of a Lennard--Jones liquid. We define a coarse-grained local stress tensor which can be calculated numerically and which allows for the first time to determine the stress correlation function both in time and in space. Our findings corroborate the assumptions made in fluctuating hydrodynamics as long as the liquid is isotropic, that is in bulk. In the vicinity of a rigid plate, however, the isotropy is restricted, and major modifications must be done with respect to the usual theory. Among these are the appearance of five different viscosities instead of two and a non-trivial dependence of the distance from the wall. We determine these viscosities from the simulation data and find that their values are very different from the bulk values. We further find much longer relaxation times of the stress correlations than in bulk., Comment: 12 pages, 10 figures. To be published in the special issue "Stochastic Processes in Physics and Chemistry" of Chemical Physics, on occasion of Peter Hanggi's 60th birthday

The overall traffic of droplets in a network of microfluidic channels is strongly influenced by the liquid properties of the moving droplets. In particular, the effective hydrodynamic resistance of individual droplets plays a key role in their global behavior. We here propose two simple and low-cost experimental methods for measuring this parameter by analyzing the dynamics of a regular sequence of droplets injected into an "asymmetric loop" network. The choice of a droplet taking either route through the loop is influenced by the presence of previous droplets which modulate the hydrodynamic resistance of the branches they are sitting in. We propose to extract the effective resistance of a droplet from easily observable time series, namely from the choices the droplets make at junctions and from the inter-droplet distances. This becomes possible when utilizing a recently proposed theoretical model, based on a number of simplifying assumptions. We here present several sets of measurements of the hydrodynamic resistance of droplets, expressed in terms of a "resistance length". The aim is twofold, (1) to reveal its dependence on a number of parameters, such as the viscosity, the volume of droplets, their velocity as well as the spacing between them. At the same time (2), by using a standard measurement technique, we compare the limitations of the proposed methods. As an important result of this comparison we obtain the range of validity of the simplifying assumptions made in the theoretical model., Comment: 11 pages, 11 figures