Rheology of Suspensions of Flat Elastic Particles.

We consider a suspension of noninteracting flat elastic particles in a Newtonian fluid. We model a flat shape as three beads, carried along by the flow according to Stokes law, and connected by nonlinear springs, chosen such that the energy is quadratic in the area. In analogy with common dumbbell models involving two beads connected by linear springs, we solve the stochastic equations of motion exactly to compute the constitutive law for the stress tensor of a flat elastic particle suspension. A lower convected time derivative naturally arises as part of the constitutive law, but surprisingly the rheological response in strong extensional and strong contracting flows is similar to that of the classical Oldroyd-B model associated with dumbbell suspensions.

Path instability of an air bubble rising in water.

It has been documented since the Renaissance that an air bubble rising in water will deviate from its straight, steady path to perform a periodic zigzag or spiral motion once the bubble is above a critical size. Yet, unsteady bubble rise has resisted quantitative description, and the physical mechanism remains in dispute. Using a numerical mapping technique, we for the first time find quantitative agreement with high-precision measurements of the instability. Our linear stability analysis shows that the straight path of an air bubble in water becomes unstable to a periodic perturbation (a Hopf bifurcation) above a critical spherical radius of R = 0.926 mm, within 2% of the experimental value. While it was previously believed that the bubble's wake becomes unstable, we now demonstrate a new mechanism, based on the interplay between flow and bubble deformation.

Anomalous dimensions of the Smoluchowski coagulation equation.

The coagulation (or aggregation) equation was introduced by Smoluchowski in 1916 to describe the clumping together of colloidal particles through diffusion, but has been used in many different contexts as diverse as physical chemistry, chemical engineering, atmospheric physics, planetary science, and economics. The effectiveness of clumping is described by a kernel K(x,y), which depends on the sizes of the colliding particles x,y. We consider kernels K=(xy)^{γ}, but any homogeneous function can be treated using our methods. For sufficiently effective clumping 1≥γ>1/2, the coagulation equation produces an infinitely large cluster in finite time (a process known as the gel transition). Using a combination of analytical methods and numerics, we calculate the anomalous scaling dimensions of the main cluster growth. Apart from the solution branch which originates from the exactly solvable case γ=1, we find a branch of solutions near γ=1/2, which violates matching conditions for the limit of small cluster sizes, widely believed to hold on a universal basis.

Elastic Rayleigh-Plateau instability: dynamical selection of nonlinear states.

A slender thread of elastic hydrogel is susceptible to a surface instability that is reminiscent of the classical Rayleigh-Plateau instability of liquid jets. The final, highly nonlinear states that are observed in experiments arise from a competition between capillarity and large elastic deformations. Combining a slender analysis and fully three-dimensional numerical simulations, we present the phase map of all possible morphologies for an unstable neo-Hookean cylinder subjected to capillary forces. Interestingly, for softer cylinders we find the coexistence of two distinct configurations, namely, cylinders-on-a-string and beads-on-a-string. It is shown that for a given set of parameters, the final pattern is selected via a dynamical evolution. To capture this, we compute the dispersion relation and determine the characteristic wavelength of the dynamically selected profiles. The validity of the "slender" results is confirmed via simulations and these results are consistent with experiments on elastic and viscoelastic threads.

Fluid interfaces with very sharp tips in viscous flow.

When a fluid interface is subjected to a strong viscous flow, it tends to develop near-conical ends with pointed tips so sharp that their radius of curvature is undetectable. In microfluidic applications, tips can be made to eject fine jets, from which micrometer-sized drops can be produced. Here we show theoretically that the opening angle of the conical interface varies on a logarithmic scale as a function of the distance from the tip, owing to nonlocal coupling between the tip and the external flow. Using this insight we are able to show that the tip curvature grows like the exponential of the square of the strength of the external flow and to calculate the universal shape of the interface near the tip. Our experiments confirm the scaling of the tip curvature as well as of the interface's universal shape. Our analytical technique, based on an integral over the surface, may also have far wider applications, for example treating problems with electric fields, such as electrosprays.

How many ways a cell can move: the modes of self-propulsion of an active drop.

Numerous physical models have been proposed to explain how cell motility emerges from internal activity, mostly focused on how crawling motion arises from internal processes. Here we offer a classification of self-propulsion mechanisms based on general physical principles, showing that crawling is not the only way for cells to move on a substrate. We consider a thin drop of active matter on a planar substrate and fully characterize its autonomous motion for all three possible sources of driving: (i) the stresses induced in the bulk by active components, which allow in particular tractionless motion, (ii) the self-propulsion of active components at the substrate, which gives rise to crawling motion, and (iii) a net capillary force, possibly self-generated, and coupled to internal activity. We determine travelling-wave solutions to the lubrication equations as a function of a dimensionless activity parameter for each mode of motion. Numerical simulations are used to characterize the drop motion over a wide range of activity magnitudes, and explicit analytical solutions in excellent agreement with the simulations are derived in the weak-activity regime.

Curvature Regularization near Contacts with Stretched Elastic Tubes.

Inserting a rigid object into a soft elastic tube produces conformal contact between the two, resulting in contact lines. The curvature of the tube walls near these contact lines is often large and is typically regularized by the finite bending rigidity of the tube. Here, it is demonstrated using experiments and a Föppl-von Kármán-like theory that a second, independent, mechanism of curvature regularization occurs when the tube is axially stretched. In contrast with the effects of finite bending rigidity, the radius of curvature obtained increases with the applied stretching force and decreases with sheet thickness. The dependence of the curvature on a suitably rescaled stretching force is found to be universal, independent of the shape of the intruder, and results from an interplay between the longitudinal stresses due to the applied stretch and hoop stresses characteristic of curved geometry. These results suggest that curvature measurements can be used to infer the mechanical properties of stretched tubular structures.

Exact results for sheared polar active suspensions with variable liquid crystalline order.

We consider a confined sheared active polar liquid crystal with a uniform orientation and study the effect of variations in the magnitude of polarization. Restricting our analysis to one-dimensional geometries, we demonstrate that with asymmetric boundary conditions, this system is characterized, macroscopically, by a linear shear stress vs. shear strain relationship that does not pass through the origin: At a zero strain rate, the fluid sustains a non-zero stress. Analytic solutions for the polarization, density, and velocity fields are derived for asymptotically large or small systems and are shown by comparison with precise numerical solutions to be good approximations for finite-size systems.

Tractionless Self-Propulsion of Active Drops.

We report on a new mode of self-propulsion exhibited by compact drops of active liquids on a substrate which, remarkably, is tractionless, i.e., which imparts no mechanical stress locally on the surface. We show, both analytically and by numerical simulation, that the equations of motion for an active nematic drop possess a simple self-propelling solution, with no traction on the solid surface and in which the direction of motion is controlled by the winding of the nematic director field across the drop height. The physics underlying this mode of motion has the same origins as that giving rise to the zero viscosity observed in bacterial suspensions. This topologically protected tractionless self-propusion provides a robust physical mechanism for efficient cell migration in crowded environments like tissues.

Opposed flow focusing: evidence of a second order jetting transition.

We propose a novel microfluidic "opposed-flow" geometry in which the continuous fluid phase is fed into a junction in a direction opposite to the dispersed phase. This pulls out the dispersed phase into a micron-sized jet, which decays into micron-sized droplets. As the driving pressure is tuned to a critical value, the jet radius vanishes as a power law down to sizes below 1 µm. By contrast, the conventional "coflowing" junction leads to a first order jetting transition, in which the jet disappears at a finite radius of several µm, to give way to a "dripping" state, resulting in much larger droplets. We demonstrate the effectiveness of our method by producing the first microfluidic silicone oil emulsions with a sub micron particle radius, and utilize these droplets to produce colloidal clusters.

Bubble Bursting: Universal Cavity and Jet Profiles.

After a bubble bursts at a liquid surface, the collapse of the cavity generates capillary waves, which focus on the axis of symmetry to produce a jet. The cavity and jet dynamics are primarily controlled by a nondimensional number that compares capillary inertia and viscous forces, i.e., the Laplace number La=ργR_{0}/µ^{2}, where ρ, µ, γ, and R_{0} are the liquid density, viscosity, interfacial tension, and the initial bubble radius, respectively. In this Letter, we show that the time-dependent profiles of cavity collapse (tt_{0}) both obey a |t-t_{0}|^{2/3} inviscid scaling, which results from a balance between surface tension and inertia forces. Moreover, we present a scaling law, valid above a critical Laplace number, which reconciles the time-dependent scaling with the recent scaling theory that links the Laplace number to the final jet velocity and ejected droplet size. This leads to a self-similar formula which describes the history of the jetting process, from cavity collapse to droplet formation.

Active Suspensions have Nonmonotonic Flow Curves and Multiple Mechanical Equilibria.

We point out unconventional mechanical properties of confined active fluids, such as bacterial suspensions, under shear. Using a minimal model of an active liquid crystal with no free parameters, we predict the existence of a window of bacteria concentration for which a suspension of E. Coli effectively behaves, at steady-state, as a negative viscosity fluid and reach a quantitative agreement with experimental measurements. Our theoretical analysis further shows that a negative apparent viscosity is due to a nonmonotonic local velocity profile, and it is associated with a nonmonotonic stress versus strain rate flow curve. This implies that fixed stress and fixed strain rate ensembles are not equivalent for active fluids.

Pair creation, motion, and annihilation of topological defects in two-dimensional nematic liquid crystals.

We present a framework for the study of disclinations in two-dimensional active nematic liquid crystals and topological defects in general. The order tensor formalism is used to calculate exact multiparticle solutions of the linearized static equations inside a planar uniformly aligned state so that the total charge has to vanish. Topological charge conservation then requires that there is always an equal number of q=1/2 and q=-1/2 charges. Starting from a set of hydrodynamic equations, we derive a low-dimensional dynamical system for the parameters of the static solutions, which describes the motion of a half-disclination pair or of several pairs. Within this formalism, we model defect production and annihilation, as observed in experiments. Our dynamics also provide an estimate for the critical density at which production and annihilation rates are balanced.

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.

Validation of the Danish version of the Quick-Disabilities of Arm, Shoulder and Hand Questionnaire.

INTRODUCTION: The Quick-Disabilities of Arm, Shoulder and Hand (QuickDASH) questionnaire is an 11-item region-specific questionnaire used to measure the effect of clinical treatment of disorders and injuries to the upper extremity. During its original development, it was shown that the QuickDASH is a valid and reliable outcome measure. The purpose of this study was to validate the Danish version of the QuickDASH in patients with wrist fractures, using the Nottingham Health Profile (NHP) as an evaluation tool. METHODS: We included patients with wrist fractures. They all answered the QuickDASH and the NHP during their ambulatory follow-up. We investigated time to complete questionnaire. Internal consistency was tested with Cronbach's alpha and test-retest reliability was tested using the intra-class correlation coefficient, Bland-Altman's 95% limits of agreement and difference of mean. Convergent validity was calculated as correlation with the domains of Pain and Physical mobility in the NHP, and content validity was tested to reveal floor and ceiling effects. RESULTS: We included 61 patients. The time burden, Cronbach's alpha and the intra-class correlation coefficient were excellent. Pearson's correlation for convergent validity was high for both Pain and Physical mobility, and we recorded a divergent validity for the remaining domains of the NHP (Sleep and Social isolation). Furthermore, we found a good distribution of items showing no floor or ceiling effect. CONCLUSION: The Danish version of the QuickDASH is a valid and practical questionnaire for use in Danish wrist fracture patients. FUNDING: none. TRIAL REGISTRATION: not relevant.

Probing Colloidal Gels at Multiple Length Scales: 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.

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 glass former, 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 antiprisms, which are known to be a locally favored structure in the Lennard-Jones glass former. 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 is up to 40% higher relative to the reference system.

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 ≤ 13 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.

Blunting of conical tips by surface diffusion.

We study the evolution of an initially conical metal surface when it is heated. For all cone angles α from close to zero to 90 degrees, self-similar solutions with rounded tips are found, whose radius of curvature scales like (time)(1/4). For α>/~3°, theoretical profiles agree very well with experiment. For smaller cone angles, we find pronounced oscillations near the tip, which presumably are responsible for the experimentally observed fragility of such tips. The amplitude and wavelength of oscillations are characterized asymptotically.

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 Wahnström 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.