arXiv subjects

Jens Eggers

Publications and source records attributed to Jens Eggers.

At least 37 records · Page 2Linked to original sources

arXiv2016

Oil-in-water microfluidics on the colloidal scale: new routes to self-assembly and glassy packings

We have developed Norland Optical Adhesive (NOA) flow focusing devices, making use of the excellent solvent compatibility and surface properties of NOA to generate micron scale oil-in-water emulsions with polydispersities as low as 5%. While current work on microfluidic oil-in-water emulsification largely concerns the production of droplets with sizes on the order of 10s of micrometres, large enough that Brownian motion is negligible, our NOA devices can produce droplets with radii ranging from 2 μm to 12 μm. To demonstrate the utility of these emulsions as colloidal model systems we produce fluorescently labelled polydimethylsiloxane droplets suitable for particle resolved studies with confocal microscopy. We analyse the structure of the resulting emulsion in 3D using coordinate tracking and the topological cluster classification and reveal a new mono-disperse thermal system.

cond-mat.soft↗

arXiv2015

Probing colloidal gels at multiple lengthscales: the role of hydrodynamics

Colloidal gels are out-of-equilibrium structures, made up of a rarefied network of colloidal particles. Comparing experiments to numerical simulations, with hydrodynamic interactions switched off, we demonstrate the crucial role of the solvent for gelation. Hydrodynamic interactions suppress the formation of larger local equilibrium structures of closed geometry, and instead lead to the formation of highly anisotropic threads, which promote an open gel network. We confirm these results with simulations which include hydrodynamics. Based on three-point correlations, we propose a scale-resolved quantitative measure for the anisotropy of the gel structure. We find a strong discrepancy for interparticle distances just under twice the particle diameter between systems with and without hydrodynamics, quantifying the role of hydrodynamics from a structural point of view.

cond-mat.soft↗

arXiv2013

Identification of structure in condensed matter with the topological cluster classification

We describe the topological cluster classification (TCC) algorithm. The TCC detects local structures with bond topologies similar to isolated clusters which minimise the potential energy for a number of monatomic and binary simple liquids with $m\leq13$ particles. We detail a modified Voronoi bond detection method that optimizes the cluster detection. The method to identify each cluster is outlined, and a test example of Lennard-Jones liquid and crystal phases is considered and critically examined.

cond-mat.soft↗

arXiv2013

Investigating isomorphs with the topological cluster classification

Isomorphs are lines in the density-temperature plane of certain "strongly-correlating" or "Roskilde simple" liquids where two-point structure and dynamics have been shown to be close to identical up to a scale transformation. Here we consider such a liquid, a Lennard-Jones glassformer, and investigate the behavior along isomorphs of higher-order structural and dynamical correlations. We then consider an inverse power law reference system mapped to the Lennard-Jones system [Pedersen et al., Phys. Rev. Lett. 105, 157801 (2010)]. Using the topological cluster classification to identify higher-order structures, in both systems we find bicapped square anti-prisms, which are known to be a locally favored structure in the Lennard-Jones glassformer. The population of these locally favored structures is up to 80% higher in the Lennard-Jones system than the equivalent inverse power law system. The structural relaxation time of the two systems, on the other hand, is almost identical, and the four-point dynamical susceptibility is marginally higher in the inverse power law system. Upon cooling the lifetime of the locally favored structures in the Lennard-Jones system are up to 40% higher relative to the reference system.

cond-mat.soft↗

arXiv2013

A general method to remove the stiffness of PDEs

A new method to remove the stiffness of partial differential equations is presented. Two terms are added to the right-hand-side of the PDE : the first is a damping term and is treated implicitly, the second is of the opposite sign and is treated explicitly. A criterion for absolute stability is found and the scheme is shown to be convergent. The method is applied with success to the mean curvature flow equation, the Kuramoto-Sivashinsky equation, and to the Rayleigh-Taylor instability in a Hele-Shaw cell, including the effect of surface tension.

physics.comp-ph↗

arXiv2013

Lifetimes and Lengthscales of Structural Motifs in a Model Glassformer

We use a newly-developed method to identify local structural motifs in a popular model glassformer, the Kob-Andersen binary Lennard-Jones mixture. By measuring the lifetimes of a zoo of clusters, we find that 11-membered bicapped square antiprisms, denoted as 11A, have longer lifetimes on average than other structures considered. Other long-lived clusters are similar in structure to the 11A cluster. These clusters group into ramified networks that are correlated with slow particles and act to retard the motion of neighbouring particles. The structural lengthscale associated with these networks does not grow as fast as the dynamical lengthscale $ξ_4$ as the system is cooled, in the range of temperatures our molecular dynamics simulations access. Thus we find a strong, but indirect, correlation between static structural ordering and slow dynamics.

cond-mat.soft↗

arXiv2013

Identification of long-lived clusters and their link to slow dynamics in a model glass former

We study the relationship between local structural ordering and dynamical heterogeneities in a model glass-forming liquid, the Wahnstrom mixture. A novel cluster-based approach is used to detect local energy minimum polyhedral clusters and local crystalline environments. A structure-specific time correlation function is then devised to determine their temporal stability. For our system, the lifetime correlation function for icosahedral clusters decays far slower than for those of similarly sized but topologically distinct clusters. Upon cooling, the icosahedra form domains of increasing size and their lifetime increases with the size of the domains. Furthermore, these long-lived domains lower the mobility of neighboring particles. These structured domains show correlations with the slow regions of the dynamical heterogeneities that form on cooling towards the glass transition. Although icosahedral clusters with a particular composition and arrangement of large and small particles are structural elements of the crystal, we find that most icosahedral clusters lack such order in composition and arrangement and thus local crystalline ordering makes only a limited contribution to this process. Finally, we characterize the spatial correlation of the domains of icosahedra by two structural correlation lengths and compare them with the four-point dynamic correlation length. All the length scales increase upon cooling, but in different ways.

cond-mat.soft↗

arXiv2011

Local structure of Liquid-Vapour Interfaces

The structure of a simple liquid may be characterised in terms of ground state clusters of small numbers of atoms of that same liquid. Here we use this sensitive structural probe to consider the effect of a liquid-vapour interface upon the liquid structure. At higher temperatures (above around half the critical temperature) we find that the predominant effect of the interface is to reduce the local density, which significantly suppresses the local cluster populations. At lower temperatures, however, pronounced interfacial layering is found. This appears to be connected with significant orientational ordering of clusters based on 3- and 5-membered rings, with the rings aligning perpendicular and parallel to the interface respectively. At all temperatures, we find that the population of five-fold symmetric structures is suppressed, rather than enhanced, close to the interface.

cond-mat.soft↗

arXiv2010

The effect of inter-cluster interactions on the structure of colloidal clusters

Colloidal systems present exciting opportunities to study clusters. Unlike atomic clusters, which are frequently produced at extremely low density, colloidal clusters may interact with one another. Here we consider the effect of such interactions on the intra-cluster structure in simulations of colloidal cluster fluids. A sufficient increase in density leads to a higher population of clusters in the ground state. In other words, inter-cluster interactions perturb the intra-cluster behaviour, such that each cluster may no longer be considered as an isolated system. Conversely, for dilute, weakly interacting cluster fluids little dependence on colloid concentration is observed, and we thus argue that it is reasonable to treat each cluster as an isolated system.

cond-mat.soft↗

arXiv2010

Geometric frustration in small colloidal clusters

We study the structure of clusters in a model colloidal system with competing interactions using Brownian dynamics simulations. A short-ranged attraction drives clustering, while a weak, long-ranged repulsion is used to model electrostatic charging in experimental systems. The former is treated with a short-ranged Morse attractive interaction, the latter with a repulsive Yukawa interaction. We consider the yield of clusters of specific structure as a function of the strength of the interactions, for clusters with m=3,4,5,6,7,10 and 13 colloids. At sufficient strengths of the attractive interaction (around 10 kT), the average bond lifetime approaches the simulation timescale and the system becomes nonergodic. For small clusters m<=5 where geometric frustration is not relevant, despite nonergodicity, for sufficient strengths of the attractive interaction the yield of clusters which maximise the number of bonds approaches 100%. However for $m=7$ and higher, in the nonergodic regime we find a lower yield of these structures where we argue geometric frustration plays a significant role. $m=6$ is a special case, where two structures, of octahedral and C2v symmetry compete, with the latter being favoured by entropic contributions in the ergodic regime and by kinetic trapping in the nonergodic regime. We believe that our results should be valid as far as the one-component description of the interaction potential is valid. A system with competing electrostatic repulsions and van der Waals attractions may be such an example. However, in some cases, the one-component description of the interaction potential may not be appropriate.

cond-mat.soft↗

arXiv2009

The blistering of a viscoelastic filament of a droplet of saliva

A fluid dynamics video of the break up of a droplet of saliva is shown. First a viscoelastic filament is formed and than the blistering of this filament is shown. Finally, a flow induced phase separation takes place nanometer sized solid fiber remains that consist out of the biopolymers.

physics.flu-dyn↗

arXiv2008

M-brane singularity formation

We derive self-similar string solutions in a graph representation, near the point of singularity formation, which can be shown to extend to point-like singularities on M-branes, as well as to the radially symmetric case.

hep-th↗

arXiv2008

The role of self-similarity in singularities of PDE's

We survey rigorous, formal, and numerical results on the formation of point-like singularities (or blow-up) for a wide range of evolution equations. We use a similarity transformation of the original equation with respect to the blow-up point, such that self-similar behaviour is mapped to the fixed point of a \textit{dynamical system}. We point out that analysing the dynamics close to the fixed point is a useful way of characterising the singularity, in that the dynamics frequently reduces to very few dimensions. As far as we are aware, examples from the literature either correspond to stable fixed points, low-dimensional centre-manifold dynamics, limit cycles, or travelling waves. For each "class" of singularity, we give detailed examples.

math-ph↗

arXiv2008

Rayleigh-Plateau instability causes the crown splash

The impact of a drop onto a liquid layer and the subsequent splash has important implications for diverse physical processes such as air-sea gas transfer, cooling, and combustion. In the {\it crown splash} parameter regime, the splash pattern is highly regular. We focus on this case as a model for the mechanism that leads to secondary droplets, and thus explain the drop size distribution resulting from the splash. We show that the mean number of secondary droplets is determined by the most unstable wavelength of the Rayleigh-Plateau instability. Variations from this mean are governed by the width of the spectrum. Our results for the crown splash will provide the basis for understanding more complicated splashes.

physics.flu-dyn↗

arXiv2008

Maximum size of drops levitated by an air cushion

Liquid drops can be kept from touching a plane solid surface by a gas stream entering from underneath, as it is observed for water drops on a heated plate, kept aloft by a stream of water vapor. We investigate the limit of small flow rates, for which the size of the gap between the drop and the substrate becomes very small. Above a critical drop radius no stationary drops can exist, below the critical radius two solutions coexist. However, only the solution with the smaller gap width is stable, the other is unstable. We compare to experimental data and use boundary integral simulations to show that unstable drops develop a gas "chimney" which breaks the drop in its middle.

physics.flu-dyn↗

arXiv2007

A catalogue of singularities

This paper is an attempt to classify finite-time singularities of PDEs. Most of the problems considered describe free-surface flows, which are easily observed experimentally. We consider problems where the singularity occurs at a point, and where typical scales of the solution shrink to zero as the singularity is approached. Upon a similarity transformation, exact self-similar behaviour is mapped to the fixed point of a {\it infinite dimensional dynamical system} representing the original dynamics. We show that the dynamics close to the fixed point is a useful way classifying the structure of the singularity. Specifically, we consider various types of stable and unstable fixed points, centre-manifold dynamics, limit cycles, and chaotic dynamics.

math.AP↗

arXiv2005

Contact line motion for partially wetting fluids

We study the flow close to an advancing contact line in the limit of small capillary number. To take into account wetting effects, both long and short-ranged contributions to the disjoining pressure are taken into account. In front of the contact line, there is a microscopic film corresponding to a minimum of the interaction potential. We compute the parameters of the contact line solution relevant to the matching to a macroscopic problem, for example a spreading droplet. The result closely resembles previous results obtained with a slip model.

physics.flu-dyn↗

arXiv2005

Instability of a moving contact line

We study a solid plate plunging into or being withdrawn from a liquid bath, to highlight the fundamental difference between the local behavior of an advancing or a receding contact line, respectively. It is assumed that the liquid partially wets the solid, making a finite contact angle in equilibrium. In our hydrodynamic description which neglects the presence of the outer gas atmosphere, an advancing dynamic wetting line persists to arbitrarily high speeds. The receding wetting line, on the other hand, vanishes at a critical speed set by the competition between viscous and surface tension forces. In the advancing case, we apply existing matching techniques to the plunging plate geometry, to significantly improve on existing theories. For the receding contact line, we demonstrate for the first time how the local contact line solution can be matched to the far-field meniscus. In doing so, we confirm our very recent criterion for the instability of the receding contact line. The results of both the advancing and the receding cases are tested against simulations of the full model equations.

physics.flu-dyn↗