Growth kinetics of colloidal chains and labyrinths

Particles interacting by a combination of isotropic short-range attraction and long-range repulsion have been shown to form complex phases despite the apparent simplicity of the interparticle potential. Using computer simulations we study the behavior of two-dimensional systems of colloids with such an interaction, focusing on how area fraction and repulsion range at fixed repulsion gradient may be used to tune the resulting kinetics and nonequilibrium structure. While the short-range attraction leads to aggregation, the long-range repulsion encourages growth of chains of particles due to repulsive intercluster interactions. Depending on area fraction/ repulsion range we observe chain labyrinths, chain-compact aggregate coexistence, and connected networks of chains. The kinetics of cluster growth displays a sequence of connected networks and disconnected cluster or chain systems with increasing repulsion range, indicating the competing roles of connectivity of growing chains and repulsion-driven breakup of chains into compact aggregates. Chain-dominated systems show approximately logarithmic coarsening at late time that we interpret as the result of chains performing random walks in the randomly fluctuating potential landscape created by their neighbors, a situation reminiscent of glassy systems

A dynamical systems model of unorganised segregation

We consider Schelling's bounded neighbourhood model (BNM) of unorganised segregation of two populations from the perspective of modern dynamical systems theory. We derive a Schelling dynamical system and carry out a complete quantitative analysis of the system for the case of a linear tolerance schedule in both populations. In doing so, we recover and generalise Schelling's qualitative results. For the case of unlimited population movement, we derive exact formulae for regions in parameter space where stable integrated population mixes can occur. We show how neighbourhood tipping can be adequately explained in terms of basins of attraction. For the case of limiting population movement, we derive exact criteria for the occurrence of new population mixes and identify the stable cases. We show how to apply our methodology to nonlinear tolerance schedules, illustrating our approach with numerical simulations. We associate each term in our Schelling dynamical system with a social meaning. In particular we show that the dynamics of one population in the presence of another can be summarised as follows {rate of population change} = {intrinsic popularity of neighbourhood} - {finite size of neighbourhood} - {presence of other population} By approaching the dynamics from this perspective, we have a complementary approach to that of the tolerance schedule.Comment: 17 pages (inc references), 9 figure

Hot Brownian Motion

We derive the generalized Markovian description for the non-equilibrium Brownian motion of a heated particle in a simple solvent with a temperature-dependent viscosity. Our analytical results for the generalized fluctuation-dissipation and Stokes-Einstein relations compare favorably with measurements of laser-heated gold nano-particles and provide a practical rational basis for emerging photothermal technologies.Comment: 10 pages, 5 figure

Finding bridges in packings of colloidal spheres

We identify putative load-bearing structures (bridges) in experimental colloidal systems studied by confocal microscopy. Bridges are co-operative structures that have been used to explain stability and inhomogeneous force transmission in simulated granular packings with a range of densities. We show that bridges similar to those found in granular simulations are present in real experimental colloidal packings. We describe critically the bridge-finding procedure for real experimental data and propose a new criterion-Lowest Mean Squared Separation (LSQS)-for selecting optimum stabilisations

Jamming and unjamming of concentrated colloidal dispersions in channel flow

We investigated the pressure driven flow of concentrated colloidal dispersions in a converging channel geometry. Optical microscopy and image analysis were used to track tracer particles mixed into dispersions of sterically stabilized poly(methyl methacrylate) (PMMA) spheres. The dispersions were drawn into a round \unit[0.5]{mm} capillary at one of two pump speeds ($\equiv$ applied pressure): v_1=\unit[0.245]{ml\,\, min^{-1}} and v_2=\unit[0.612]{ml\,\, min^{-1}}. We observed that the dispersions at particle volume fractions $\phi\leqslant0.50$ followed Hagen-Poiseuille flow for a simple fluid; i.e. the mean flow rate $\langle V\rangle$ is approximately proportional to pressure drop (pump speed) and inversely proportional viscosity $\eta$. Above this concentration ($\phi\geqslant0.505$), the dispersions exhibit granular-like jamming behavior with $\langle V\rangle$ becoming independent of the pressure drop. However, at the highest applied pressure ($v_2$), the dispersions are able to unjam and switch from granular-like behaviour back to a simple hard-sphere liquid like system, due to the formation of rotating vortices in the spatial flow pattern. This mechanism is consistent with computer simulations of granular systems and supports for example proposed explanations of anomalously low friction in earthquake faults

Jamming, two-fluid behaviour and 'self-filtration' in concentrated particulate suspensions

We study the flow of model experimental hard sphere colloidal suspensions at high volume fraction $\Phi$ driven through a constriction by a pressure gradient. Above a particle-size dependent limit $\Phi_0$, direct microscopic observations demonstrate jamming and unjamming--conversion of fluid to solid and vice versa--during flow. We show that such a jamming flow produces a reduction in colloid concentration $\Phi_{x}$ downstream of the constriction. We propose that this `self-filtration' effect is the consequence of a combination of jamming of the particulate part of the system and continuing flow of the liquid part, i.e. the solvent, through the pores of the jammed solid. Thus we link the concept of jamming in colloidal and granular media with a 'two-fluid'-like picture of the flow of concentrated suspensions. Results are also discussed in the light of Osborne Reynolds' original experiments on dilation in granular materials.Comment: 4 pages, 3 figure

A dynamical systems model of unorganised segregation in two neighbourhoods

We present a complete analysis of the Schelling dynamical system [Haw2018] of two connected neighbourhoods, with or without population reservoirs, for different types of linear and nonlinear tolerance schedules. We show that stable integration is only possible when the minority is small and combined tolerance is large. Unlike the case of the single neighbourhood, limiting one population does not necessarily produce stable integration and may destroy it. We conclude that a growing minority can only remain integrated if the majority increases its own tolerance. Our results show that an integrated single neighbourhood may not remain so when a connecting neighbourhood is created.Comment: 26 pages, 13 figure