We report a simple correlation between microstructure and straindependent elasticity in colloidal gels by visualizing the evolution of cluster structure in high strain-rate flows. We control the initial gel microstructure by inducing different levels of isotropic depletion attraction between particles suspended in refractive index matched solvents. Contrary to previous ideas from mode coupling and micromechanical treatments, our studies show that bond breakage occurs mainly due to the erosion of rigid clusters that persist far beyond the yield strain. This rigidity contributes to gel elasticity even when the sample is fully fluidized; the origin of the elasticity is the slow Brownian relaxation of rigid, hydrodynamically interacting clusters. We find a power-law scaling of the elastic modulus with the stress-bearing volume fraction that is valid over a range of volume fractions and gelation conditions. These results provide a conceptual framework to quantitatively connect the flow-induced microstructure of soft materials to their nonlinear rheology.colloids | confocal microscopy | suspensions | shear flow C olloidal gels form sample-spanning networks (1) and are used to generate solid-like properties in a broad range of materials such as direct-write inks (2), nanoemulsions (3), tissue scaffolds (4), and membranes (5). When gels undergo large deformations, their network ruptures into clusters via a complex process. The ability to connect structural changes to suspension rheology is critical in understanding the mechanism of yielding. The network of clusters that makes up colloidal gels arises due to percolation, dynamic arrest, and phase separation, where the volume fraction and pair potential play an important part in their structure and rheology (6-8). Interparticle bonds rupture under a sufficiently large stress; the result is a flow-induced fluidization transition accompanied by the formation of voids and aggregates that continuously break and reform along the principal axes of flow (9, 10). A complex two-step yielding process has been observed in gels at intermediate volume fractions (0.05 ≤ ϕ ≤ 0.30) (11,12). Within this regime, a small number of bonds are broken in gels undergoing steady shear yielding (9, 10). Methods that track the evolution of ensemble-averaged structure, such as mode coupling theory (6) and light scattering, lack sensitivity to these subpopulations. On the other hand, micromechanical treatments directly model the contributions of local microstructure to the macroscopic elasticity of the material (13-15). However, experiments to connect the yield stress to different interparticle potentials, volume fractions, and particle sizes show little agreement. Presently, these theories can only provide estimates of colloidal rheology under specific conditions.We demonstrate that a simple, general correlation between microstructure and strain-dependent rheology exists for colloidal depletion gels undergoing large deformations at high shear rates. Our experiments harness confocal laser scanning mi...

Colloidal gels formed by arrested phase separation are found widely in agriculture, biotechnology, and advanced manufacturing; yet, the emergence of elasticity and the nature of the arrested state in these abundant materials remains unresolved. Here, the quantitative agreement between integrated experimental, computational, and graph theoretic approaches are used to understand the arrested state and the origins of the gel elastic response. The micro-structural source of elasticity is identified by the l -balanced graph partition of the gels into minimally interconnected clusters that act as rigid, load bearing units. The number density of cluster-cluster connections grows with increasing attraction, and explains the emergence of elasticity in the network through the classic Cauchy-Born theory. Clusters are amorphous and iso-static. The internal cluster concentration maps onto the known attractive glass line of sticky colloids at low attraction strengths and extends it to higher strengths and lower particle volume fractions.

To assess the role of particle roughness in the rheological phenomena of concentrated colloidal suspensions, we develop model colloids with varying surface roughness length scales up to 10% of the particle radius. Increasing surface roughness shifts the onset of both shear thickening and dilatancy towards lower volume fractions and critical stresses. Experimental data are supported by computer simulations of spherical colloids with adjustable friction coefficients, demonstrating that a reduction in the onset stress of thickening and a sign change in the first normal stresses occur when friction competes with lubrication. In the quasi-Newtonian flow regime, roughness increases the effective packing fraction of colloids. As the shear stress increases and suspensions of rough colloids approach jamming, the first normal stresses switch signs and the critical force required to generate contacts is drastically reduced. This is likely a signature of the lubrication films giving way to roughness-induced tangential interactions that bring about load-bearing contacts in the compression axis of flow. DOI: 10.1103/PhysRevLett.119.158001 Shear thickening is an increase in the viscosity η of a concentrated suspension of particles in a fluid as the shear stress σ or shear rate rises beyond a critical value [1]. When suspensions shear thicken at high volume fractions ϕ it is frequently accompanied by complex behavior that includes S-shaped flow curves [2,3] and slow stress decays [4]. The degree of shear thickening can range from a few fold to orders of magnitude increase in η as a function of σ. These distinctions are typically used as working definitions for continuous shear thickening (CST) and discontinuous shear thickening (DST) in the literature [5]. We define weak and strong thickening using the power β as the slope of logðηÞ plotted against logðσÞ [6], where weak thickening occurs at 0.1 ≤ β ≤ 0.7 and strong thickening occurs at 0.7 < β ≤ 1.0. These categories are convenient classifications of the magnitude of the rheological response rather than a fundamental physical transition. Shifting the value of demarcation between weak and strong thickening has no qualitative impact on the state diagrams presented.Dilatancy is sometimes observed with strong shear thickening. Reynolds showed that a dilatant suspension expands in volume because particles cannot otherwise find direct flow paths within the confined environment [7]. This tendency to expand generates a normal thrust, and causes the first normal stress difference N 1 to switch from negative to positive values if boundaries are spherical in shape and surface tension is negligible [5]. The onset stresses for shear thickening and dilatancy do not necessarily coincide [6,8]. Similarly, a sheared suspension that freely expands in volume will not shear thicken because of the lack of a confining stress [9,10].To date, neither hydrodynamics nor friction has successfully explained the full range of flow phenomena in concentrated suspensions. When particles are pushed into cl...

Gallium and its alloys react with oxygen to form a native oxide that encapsulates the liquid metal with a solid "skin". The viscoelasticity of this skin is leveraged in applications such as soft electronics, 3D printing, and components for microfluidic devices. In these applications, rheological characterization of the oxide skin is paramount for understanding and controlling liquid metals. Here, we provide a direct comparison of the viscoelastic properties for gallium-based liquid metals and illustrate the effect of different subphases and addition of a dopant on the elastic nature of the oxide skin. The du Nouÿ ring method is used to investigate the interfacial rheology of oxide skins formed by galliumbased liquid metal alloys. The results show that the oxide layer on gallium, eutectic gallium−indium, and Galinstan are viscoelastic with a yield stress. Furthermore, the storage modulus of the oxide layer is affected by exposure to water or when small amounts of aluminum dopant are added to the liquid metals. The former scenario decreases the interfacial storage modulus of the gallium by 35−85% while the latter increases the interfacial storage modulus by 25−45%. The presence of water also changes the chemical composition of the oxide skin. Scanning electron microscopy, energy-dispersive X-ray spectroscopy (EDS), and X-ray photoelectron spectroscopy suggest that a microstructural evolution of the interface occurs when aluminum preferentially migrates from the bulk to the surface. These studies provide guidance on selecting liquid metals as well as simple methods to optimize their rheological behavior for future applications.

The interplay between phase separation and kinetic arrest is important in supramolecular self-assembly, but their effects on emergent orientational order are not well understood when anisotropic building blocks are used. Contrary to the typical progression from disorder to order in isotropic systems, here we report that colloidal oblate discoids initially self-assemble into short, metastable strands with orientational order—regardless of the final structure. The model discoids are suspended in a refractive index and density-matched solvent. Then, we use confocal microscopy experiments and Monte Carlo simulations spanning a broad range of volume fractions and attraction strengths to show that disordered clusters form near coexistence boundaries, whereas oriented strands persist with strong attractions. We rationalize this unusual observation in light of the interaction anisotropy imparted by the discoids. These findings may guide self-assembly for anisotropic systems in which orientational order is desired, such as when tailored mechanical properties are sought.