Minimal conditions for solidification and thermal processing of colloidal gels.

Colloidal gelation is used to form processable soft solids from a wide range of functional materials. Although multiple gelation routes are known to create gels of different types, the microscopic processes during gelation that differentiate them remain murky. A fundamental question is how the thermodynamic quench influences the microscopic driving forces of gelation, and determines the threshold or minimal conditions where gels form. We present a method that predicts these conditions on a colloidal phase diagram, and mechanistically connects the quench path of attractive and thermal forces to the emergence of gelled states. Our method employs systematically varied quenches of a colloidal fluid over a range of volume fractions to identify minimal conditions for gel solidification. The method is applied to experimental and simulated systems to test its generality toward attractions with varied shapes. Using structural and rheological characterization, we show that all gels incorporate elements of percolation, phase separation, and glassy arrest, where the quench path sets their interplay and determines the shape of the gelation boundary. We find that the slope of the gelation boundary corresponds to the dominant gelation mechanism, and its location approximately scales with the equilibrium fluid critical point. These results are insensitive to potential shape, suggesting that this interplay of mechanisms is applicable to a wide range of colloidal systems. By resolving regions of the phase diagram where this interplay evolves in time, we elucidate how programmed quenches to the gelled state could be used to effectively tailor gel structure and mechanics.

Modeling colloidal interactions that predict equilibrium and non-equilibrium states.

Modulating the interaction potential between colloids suspended in a fluid can trigger equilibrium phase transitions as well as the formation of non-equilibrium "arrested states," such as gels and glasses. Faithful representation of such interactions is essential for using simulation to interrogate the microscopic details of non-equilibrium behavior and for extrapolating observations to new regions of phase space that are difficult to explore in experiments. Although the extended law of corresponding states predicts equilibrium phases for systems with short-ranged interactions, it proves inadequate for equilibrium predictions of systems with longer-ranged interactions and for predicting non-equilibrium phenomena in systems with either short- or long-ranged interactions. These shortcomings highlight the need for new approaches to represent and disambiguate interaction potentials that replicate both equilibrium and non-equilibrium phase behavior. In this work, we use experiments and simulations to study a system with long-ranged thermoresponsive colloidal interactions and explore whether a resolution to this challenge can be found in regions of the phase diagram where temporal effects influence material state. We demonstrate that the conditions for non-equilibrium arrest by colloidal gelation are sensitive to both the shape of the interaction potential and the thermal quench rate. We exploit this sensitivity to propose a kinetics-based algorithm to extract distinct arrest conditions for candidate potentials that accurately selects between potentials that differ in shape but share the same predicted equilibrium structure. The algorithm selects the candidate that best matches the non-equilibrium behavior between simulation and experiments. Because non-equilibrium behavior in simulation is encoded entirely by the interparticle potential, the results are agnostic to the particular mechanism(s) by which arrest occurs, and so we expect our method to apply to a range of arrested states, including gels and glasses. Beyond its utility in constructing models, the method reveals that each potential has a quantitatively distinct arrest line, providing insight into how the shape of longer-ranged potentials influences the conditions for colloidal gelation.

Promoting rotation, friction, and mixed lubrication for particles rolling on microstructured surfaces.

We investigate how the aspect ratio of micropillar or microwell arrays patterned on a surface affects the rolling and slipping motion of spheres under flooded conditions at low Reynolds numbers. We study arrays of rigid microstructures with aspect ratios varying over two orders of magnitude for surface coverages ranging from 0.04 to 0.96. We investigate how the surface features (dimensions, surface coverage, and geometry) individually impact the motion of the sphere. We find that increasing microstructure height results in higher rotational velocities on all studied surfaces. We then model the motion of the spheres using two physical parameters: an effective separation and a coefficient of friction between the sphere and the incline. We find that a simple superposition of resistance functions, previously shown to accurately predict the motion of spheres for different surface coverages and geometries, indeed shows good agreement with experimental outcomes for all microstructure heights studied. We also perform separate sliding friction measurements via a force microscope to measure the coefficient of friction between the sphere and incline, under identically flooded conditions. A comparison of the sliding friction measurements at different Hersey numbers suggests that the effect of the microstructure on the coefficient of friction becomes more important as the Hersey number increases.

Rolling Spheres on Bioinspired Microstructured Surfaces.

Microstructured surfaces, such as those inspired by nature, mediate surface interactions and are actively sought after to control wetting, adhesion, and friction. In particular, the rolling motion of spheres on microstructured surfaces in fluid environments is important for the transport of particles in microfluidic devices or in tribology. Here, we characterize the motion of smooth silicon nitride spheres (diameters 3-5 mm) as they roll down inclined planes decorated with hexagonal arrays of microwells and micropillars. For both types of patterned surfaces, we vary the area fraction of the micropatterned features from 0.04 to 0.96. We measure directly and independently the rotational and translational velocities of the spheres as they roll down planes with inclination angles that vary between 5 and 30°. For a given area fraction, we find that spheres have a higher translational and rotational velocity on surfaces with microwells than on micropillars. We rely on the model of Smart and Leighton [Phys. Fluids A 5, 13 (1993)] to obtain an effective gap width and coefficient of friction for all microstructured surfaces investigated. We find that the coefficient of friction is significantly higher for a surface with micropillars than that for one with microwells, likely due to the presence of interconnected drainage channels that provide additional paths for the fluid flow and favor solid-solid contact on the surface with micropillars. We find that while the effective gap width at a very low solid fraction is equal to the height of the patterned features, the effective separation decreases exponentially as the surface coverage of microstructures increases, with little measured differences between the two geometries. Superposition of resistance functions is used to relate the rapid decrease in the effective gap height with increase in the surface coverage observed in experiments.