Correction: Sizing multimodal suspensions with differential dynamic microscopy.

Correction for 'Sizing multimodal suspensions with differential dynamic microscopy' by Joe J. Bradley et al., Soft Matter, 2023, 19, 8179-8192, https://doi.org/10.1039/D3SM00593C.

Sizing multimodal suspensions with differential dynamic microscopy.

Differential dynamic microscopy (DDM) can be used to extract the mean particle size from videos of suspensions. However, many suspensions have multimodal particle size distributions, for which a single 'mean' is not a sufficient description. After clarifying how different particle sizes contribute to the signal in DDM, we show that standard DDM analysis can extract the mean sizes of two populations in a bimodal suspension given prior knowledge of the sample's bimodality. Further, the use of the CONTIN algorithm obviates the need for such prior knowledge. Finally, we show that by selectively analysing portions of the DDM images, we can size a trimodal suspension where the large particles would otherwise dominate the signal, again without prior knowledge of the trimodality.

Mixed aqueous-and-oil foams in bulk.

HYPOTHESIS: Because particle-stabilised foams are extremely stable and have a yield stress, a particle-stabilised aqueous foam and a particle-stabilised oil foam can be mixed together to give a stable composite foam which brings together two immiscible liquids. EXPERIMENTS: We have developed a mixed foam system comprised of an olive oil foam with bubbles stabilised using partially fluorinated particles and an aqueous foam with bubbles stabilised using hydrophobic silica particles. The aqueous phase is a mixture of water and propylene glycol. We have studied this system using bulk observations, confocal microscopy and rheology as we vary the proportions of the two foams, the silica particles and the propylene glycol, and the sample age. FINDINGS: The composite foam resembles an emulsion of one foam within another and is stable for a week or more. The structure and flow properties depend on the proportions of the two phases and the quantities of both silica particles and propylene glycol. Inversion between water-in-oil and oil-in-water is observed, where both phases are foams, driven both by silica wettability and by adding increasing quantities of the dispersed foam. Composites formed at the inversion point are the least stable, showing significant phase separation in less than one week.

Impact of granular inclusions on the phase behavior of colloidal gels.

Colloidal gels formed from small attractive particles are commonly used in formulations to keep larger components in suspension. Despite extensive work characterising unfilled gels, little is known about how the larger inclusions alter the phase behavior and microstructure of the colloidal system. Here we use numerical simulations to examine how larger 'granular' particles can alter the gel transition phase boundaries. We find two distinct regimes depending on both the filler size and native gel structure: a 'passive' regime where the filler fits into already-present voids, giving little change in the transition, and an 'active' regime where the filler no longer fits in these voids and instead perturbs the native structure. In this second regime the phase boundary is controlled by an effective colloidal volume fraction given by the available free volume.

Flow-Switched Bistability in a Colloidal Gel with Non-Brownian Grains.

We show that mixing a colloidal gel with larger, non-Brownian grains generates novel flow-switched bistability. Using a combination of confocal microscopy and rheology, we find that prolonged moderate shear results in liquefaction by collapsing the gel into disjoint globules, whereas fast shear gives rise to a yield-stress gel with granular inclusions upon flow cessation. We map out the state diagram of this new "mechanorheological material" with varying granular content and demonstrate that its behavior is also found in separate mixture using different particles and solvents.

Rheological design of thickened alcohol-based hand rubs.

The handleability and sensory perception of hand sanitisers by consumers affect the hygiene outcome. Spillage may result in under-dosing and poor sensory properties can lead to under-utilisation. We first propose four principles (low runoff, spreadability, smoothness and non-stickiness) for designing the rheology of thickened alcohol-based hand rubs with acceptable handleability and hand feel. We then evaluate a commercial hand gel and a variety of simplified formulations thickened with microgels (Carbopol 974P, Carbopol Ultrez 20 and Sepimax Zen), or linear polymers (Jaguar HP 120 COS), and evaluate them against these design criteria. All four additives provide acceptable spreadability by shear thinning to η ≈ 10 - 1 Pa s at γ ˙ ∼ 10 3 s - 1 . Either the finite yield stress conferred by the microgels ( σ y ≳ 10 Pa ) or the increase in low-shear viscosity provided by the linear polymer ( η ≳ 1 Pa s at γ ˙ ≲ 0.1 s - 1 ) give rise to acceptably low runoff. However, the formulation using the linear polymer shows a filament breakage time of τ b ≈ 1 s in capillary rheology, which may result in stickiness and therefore a less than optimal hand feel.

Soft matter science and the COVID-19 pandemic.

Much of the science underpinning the global response to the COVID-19 pandemic lies in the soft matter domain. Coronaviruses are composite particles with a core of nucleic acids complexed to proteins surrounded by a protein-studded lipid bilayer shell. A dominant route for transmission is via air-borne aerosols and droplets. Viral interaction with polymeric body fluids, particularly mucus, and cell membranes controls their infectivity, while their interaction with skin and artificial surfaces underpins cleaning and disinfection and the efficacy of masks and other personal protective equipment. The global response to COVID-19 has highlighted gaps in the soft matter knowledge base. We survey these gaps, especially as pertaining to the transmission of the disease, and suggest questions that can (and need to) be tackled, both in response to COVID-19 and to better prepare for future viral pandemics.

Liquid Migration in Shear Thickening Suspensions Flowing through Constrictions.

Dense suspensions often become more dilute as they move downstream through a constriction. We find that as a shear-thickening suspension is extruded through a narrow die and undergoes such liquid migration, the extrudate maintains a steady concentration ϕ_{out}^{LM}, independent of time or initial concentration. At low volumetric flow rate Q, ϕ_{out}^{LM} is a universal function of Q/r_{d}^{3}, a characteristic shear rate in the die of radius r_{d}, and coincides with the critical input concentration for the onset of LM, ϕ_{in}^{crit}. We predict this function by coupling the Wyart-Cates model for shear thickening and the "suspension balance model" for solvent permeation through particles.

Rheological Behavior and in Situ Confocal Imaging of Bijels Made by Mixing.

Bijels (bicontinuous interfacially jammed emulsion gels) have the potential to be useful in many different applications due to their internal connectivity and the possibility of efficient mass transport through the channels. Recently, new methods of making the bijel have been proposed, which simplify the fabrication process, making commercial application more realistic. Here, we study the flow properties of bijels prepared by mixing alone using oscillatory rheology combined with confocal microscopy and also squeezing flow experiments. We found that the bijel undergoes a two-step yielding process where the first step corresponds to the fluidizing of the interface, allowing the motion of the structure, and the second step corresponds to the breaking of the structure. In the squeeze flow experiments, the yield stress of the bijel is observed to show a power law dependence on squeezing speed. However, when stress in excess of yield stress is plotted against shear rate, all the different squeeze flow data show a superposition.

Rheological Signature of Frictional Interactions in Shear Thickening Suspensions.

Colloidal shear thickening presents a significant challenge because the macroscopic rheology becomes increasingly controlled by the microscopic details of short ranged particle interactions in the shear thickening regime. Our measurements here of the first normal stress difference over a wide range of particle volume fractions elucidate the relative contributions from hydrodynamic lubrication and frictional contact forces, which have been debated. At moderate volume fractions we find N_{1}<0, consistent with hydrodynamic models; however, at higher volume fractions and shear stresses these models break down and we instead observe dilation (N_{1}>0), indicating frictional contact networks. Remarkably, there is no signature of this transition in the viscosity; instead, this change in the sign of N_{1} occurs while the shear thickening remains continuous. These results suggest a scenario where shear thickening is driven primarily by the formation of frictional contacts, with hydrodynamic forces playing a supporting role at lower concentrations. Motivated by this picture, we introduce a simple model that combines these frictional and hydrodynamic contributions and accurately fits the measured viscosity over a wide range of particle volume fractions and shear stress.

Rheology and dynamics of colloidal superballs.

Recent advances in colloidal synthesis make it possible to generate a wide array of precisely controlled, non-spherical particles. This provides a unique opportunity to probe the role that particle shape plays in the dynamics of colloidal suspensions, particularly at higher volume fractions, where particle interactions are important. We examine the role of particle shape by characterizing both the bulk rheology and micro-scale diffusion in a suspension of pseudo-cubic silica superballs. Working with these well-characterized shaped colloids, we can disentangle shape effects in the hydrodynamics of isolated particles from shape-mediated particle interactions. We find that the hydrodynamic properties of isolated superballs are marginally different from comparably sized hard spheres. However, shape-mediated interactions modify the suspension microstructure, leading to significant differences in the self-diffusion of the superballs. While this excluded volume interaction can be captured with a rescaling of the superball volume fraction, we observe qualitative differences in the shear thickening behavior of moderately concentrated superball suspensions that defy simple rescaling onto hard sphere results. This study helps to define the unknowns associated with the effects of shape on the rheology and dynamics of colloidal solutions.

Precisely cyclic sand: self-organization of periodically sheared frictional grains.

The disordered static structure and chaotic dynamics of frictional granular matter has occupied scientists for centuries, yet there are few organizational principles or guiding rules for this highly hysteretic, dissipative material. We show that cyclic shear of a granular material leads to dynamic self-organization into several phases with different spatial and temporal order. Using numerical simulations, we present a phase diagram in strain-friction space that shows chaotic dispersion, crystal formation, vortex patterns, and most unusually a disordered phase in which each particle precisely retraces its unique path. However, the system is not reversible. Rather, the trajectory of each particle, and the entire frictional, many-degrees-of-freedom system, organizes itself into a limit cycle absorbing state. Of particular note is that fact that the cyclic states are spatially disordered, whereas the ordered states are chaotic.

Droplet and cluster formation in freely falling granular streams.

Particle beams are important tools for probing atomic and molecular interactions. Here we demonstrate that particle beams also offer a unique opportunity to investigate interactions in macroscopic systems, such as granular media. Motivated by recent experiments on streams of grains that exhibit liquid-like breakup into droplets, we use molecular dynamics simulations to investigate the evolution of a dense stream of macroscopic spheres accelerating out of an opening at the bottom of a reservoir. We show how nanoscale details associated with energy dissipation during collisions modify the stream's macroscopic behavior. We find that inelastic collisions collimate the stream, while the presence of short-range attractive interactions drives structure formation. Parameterizing the collision dynamics by the coefficient of restitution (i.e., the ratio of relative velocities before and after impact) and the strength of the cohesive interaction, we map out a spectrum of behaviors that ranges from gaslike jets in which all grains drift apart to liquid-like streams that break into large droplets containing hundreds of grains. We also find a new, intermediate regime in which small aggregates form by capture from the gas phase, similar to what can be observed in molecular beams. Our results show that nearly all aspects of stream behavior are closely related to the velocity gradient associated with vertical free fall. Led by this observation, we propose a simple energy balance model to explain the droplet formation process. The qualitative as well as many quantitative features of the simulations and the model compare well with available experimental data and provide a first quantitative measure of the role of attractions in freely cooling granular streams.

High-speed tracking of rupture and clustering in freely falling granular streams.

Thin streams of liquid commonly break up into characteristic droplet patterns owing to the surface-tension-driven Plateau-Rayleigh instability. Very similar patterns are observed when initially uniform streams of dry granular material break up into clusters of grains, even though flows of macroscopic particles are considered to lack surface tension. Recent studies on freely falling granular streams tracked fluctuations in the stream profile, but the clustering mechanism remained unresolved because the full evolution of the instability could not be observed. Here we demonstrate that the cluster formation is driven by minute, nanoNewton cohesive forces that arise from a combination of van der Waals interactions and capillary bridges between nanometre-scale surface asperities. Our experiments involve high-speed video imaging of the granular stream in the co-moving frame, control over the properties of the grain surfaces and the use of atomic force microscopy to measure grain-grain interactions. The cohesive forces that we measure correspond to an equivalent surface tension five orders of magnitude below that of ordinary liquids. We find that the shapes of these weakly cohesive, non-thermal clusters of macroscopic particles closely resemble droplets resulting from thermally induced rupture of liquid nanojets.

Birth and growth of a granular jet.

The interaction between fine grains and the surrounding interstitial gas in a granular bed can lead to qualitatively new phenomena not captured in a simple, single-fluid model of granular flows. This is demonstrated by the granular jet formed by the impact of a solid sphere into a bed of loose, fine sand. Unlike jets formed by impact in fluids, this jet is actually composed of two separate components, an initial thin jet formed by the collapse of the cavity left by the impacting object stacked on top of a second, thicker jet which depends strongly on the ambient gas pressure. This complex structure is the result of an interplay between ambient gas, bed particles, and impacting sphere. Here we present the results of systematic experiments that combine measurements of the jet above the surface varying the release height, sphere diameter, container size, and bed material with x-ray radiography below the surface to connect the changing response of the bed to the changing structure of the jet. We find that the interstitial gas trapped by the low permeability of a fine-grained bed plays two distinct roles in the formation of the jet. First, gas trapped and compressed between grains prevents compaction, causing the bed to flow like an incompressible fluid and allowing the impacting object to sink deep into the bed. Second, the jet is initiated by the gravity driven collapse of the cavity left by the impacting object. If the cavity is large enough, gas trapped and compressed by the collapsing cavity can amplify the jet by directly pushing bed material upwards and creating the thick jet. As a consequence of these two factors, when the ambient gas pressure is decreased, there is a crossover from a nearly incompressible, fluidlike response of the bed to a highly compressible, dissipative response. Compaction of the bed at reduced pressure reduces the final depth of the impacting object, resulting in a smaller cavity and in the demise of the thick jet.

Gas-mediated impact dynamics in fine-grained granular materials.

Noncohesive granular media exhibit complex responses to sudden impact that often differ from those of ordinary solids and liquids. We investigate how this response is mediated by the presence of interstitial gas between the grains. Using high-speed x-ray radiography we track the motion of a steel sphere through the interior of a bed of fine, loose granular material. We find a crossover from nearly incompressible, fluidlike behavior at atmospheric pressure to a highly compressible, dissipative response once most of the gas is evacuated. We discuss these results in light of recent proposals for the drag force in granular media.

Wave-number selection by target patterns and sidewalls in Rayleigh-Bénard convection.

We present experimental results for patterns of Rayleigh-Bénard convection in a cylindrical container with static sidewall forcing. The fluid used was methanol, with a Prandlt number sigma=7.17 , and the aspect ratio was Gamma identical withR/d approximately 19 ( R is the radius and d the thickness of the fluid layer). In the presence of a small heat input along the sidewall, a sudden jump of the temperature difference DeltaT from below to slightly above a critical value Delta T(c) produced a stable pattern of concentric rolls (a target pattern) with the central roll (the umbilicus) at the center of the cell. A quasistatic increase of epsilon identical withDeltaT/Delta T(c) -1 beyond epsilon(1,c) approximately 0.8 caused the umbilicus of the pattern to move off center. As observed by others, a further quasistatic increase of epsilon up to epsilon=15.6 caused a sequence of transitions at epsilon(i,b) ,i=1,...,8 , each associated with the loss of one convection roll at the umbilicus. Each loss of a roll was preceded by the displacement of the umbilicus away from the center of the cell. After each transition the umbilicus moved back toward but never quite reached the center. With decreasing epsilon new rolls formed at the umbilicus when epsilon was reduced below epsilon(i,a) < epsilon(i,b) . When decreasing epsilon , large umbilicus displacements did not occur. In addition to quantitative measurements of the umbilicus displacement, we determined and analyzed the entire wave-director field of each image. The wave numbers varied in the axial direction, with minima at the umbilicus and at the cell wall and a maximum at a radial position close to 2Gamma/3 . The wave numbers at the maximum showed hysteretic jumps at epsilon(i,b) and epsilon(i,a) , but on average agreed well with the theoretical predictions for the wave numbers selected in the far field of an infinitely extended target pattern. To our knowledge there is as yet no prediction for the wave number selected by the umbilicus itself, or by the cell wall of the finite experimental system.