Session G2: Suspensions: Gels and Soft Particles

A parsimonious hydrodynamic model for colloidal gelation

Colloidal gels are formed during arrested phase separation. Models for microstructural evolution during gelation have often struggled to match experimental results with long standing questions regarding the role of hydrodynamics. We hypothesize that long-ranged hydrodynamic interactions between the suspended particles are key for colloidal gelation. A simplified hydrodynamic model tests this hypothesis by including only long-ranged interactions via the Rotne-Prager-Yamakawa tensor. We show simulations of gelation with and without hydrodynamic interactions between the suspended particles executed in HOOMD-blue. The disparities between these simulations are striking. The hydrodynamic simulations agree with experimental observations, however. These results suggest that long-ranged hydrodynamic interactions are sufficient for establishing the gel boundary, structure and coarsening kinetics observed in experiments and more sophisticated simulation methods. Near the gel boundary, there exists a competition between compaction of individual aggregates which suppresses gelation and coagulation of aggregates which enhances it. The time scale for coagulation is greatly accelerated, leading to a shift in the gel boundary when compared to models that neglect hydrodynamic interactions.   

Delayed yield in reversible colloidal gels: a micro- mechanical perspective

We study via dynamic simulation the nonlinear response of a reversible colloidal gel undergoing deformation under fixed stress, with a view toward elucidating mechanisms of macroscopic yield at the level of particle dynamics. Under shear, such gels may flow but then regain solidlike behavior upon removal of the stress. The transition from solidlike to liquidlike behavior is a yielding process that is not instantaneous but rather occurs after a finite delay. The delay duration decreases as stress increases, but the underlying microstructural origins are not understood. Recent experiments reveal two regimes, suggesting multiple yield mechanisms. Theories advanced to link gel structure to this rheology hypothesize a competition between bond breakage and reconnection rates, but no such particle-scale dynamics have been directly observed -- or reconciled with ongoing structural evolution. To study these behaviors, we impose a step stress on a gel comprising 750,000 Brownian particles for a range of volume fraction, attraction strength, and imposed stress, monitoring displacement and particle velocity over time. A detailed connection between macroscopic response, microstructure, and particle dynamics leads to a phase map predicting nonlinear response of such gels to fixed stress.   

Transient yield in reversible colloidal gels: a micro-mechanical perspective

We study the nonlinear rheology of colloidal gels via large-scale dynamic simulation, with a view toward understanding the micro-mechanical origins of the transition from solid-like to liquid-like behavior during flow startup, and post-cessation relaxation, and its connection to energy storage and viscous dissipation. Such materials often exhibit an overshoot in the stress during startup, but the underlying microstructural origins of this behavior remain unclear. To understand this behavior, a fixed strain rate is imposed on a reversible colloidal gel, where thermal fluctuations enable quiescent gel aging. It has been suggested flow occurs only after clusters first break free from the network and then disintegrate, leading to two stress peaks that vary with age, flow strength, volume fraction, bond strength, and pre-strain history. However, our detailed studies of the microstructural evolution during startup challenge this view. We present a new model of stress development, relaxation, and microstructural evolution in reversible colloidal gels in which the ongoing age-coarsening process plays a central role.   

Deformation of ovalbumin-alginate capsules in a T-Junction

We study experimentally the flow-induced deformation of liquid-filled ovalbumin-alginate capsules in a T-junction. In applications, capsules/cells often negotiate branched networks with junctions thus experiencing large deformations. We investigate the constant volume-flux viscous flow of buoyancy-neutral thin-walled capsules close to the centreline of rectangular channels, by comparison to near-rigid gelled beads. The motion of the capsules in straight channels scales with the capillary number – the ration of viscous to elastic forces. However, the effect of elastic deformation on the motion is sufficiently weak that a rigid sphere model predicts the velocity of capsules with diameters of up to 70\% of that of the channel to within 5\%. In the T-junction, systematic selection of daughter channel (right-left) occurs outside a finite region around the channel centreline, by contrast with near-rigid gelled beads, where the actual centreline is the separator. We quantify the behaviour of capsules in terms of their longitudinal stretching (up to a factor of three without rupture). We show the large range of deformations encountered can be applied to the measurement of the elastic properties of capsules as well as to the geometric-induced sorting and manipulation of capsules.   

Soft particles at a fluid interface

Particles added to a fluid interface can be used as a surface stabilizer in the food, oil and cosmetic industries. As an alternative to rigid particles, it is promising to consider highly deformable particles that can adapt their conformation at the interface. In this study, we compute the shapes of soft elastic particles using molecular dynamics simulations of a cross-linked polymer gel, complemented by continuum calculations based on the linear elasticity. It is shown that the particle shape is not only affected by the Young's modulus of the particle, but also strongly depends on whether the gel is partially or completely wetting the fluid interface. We find that the molecular simulations for the partially wetting case are very accurately described by the continuum theory. By contrast, when the gel is completely wetting the fluid interface the linear theory breaks down and we reveal that molecular details have a strong influence on the equilibrium shape.   

Interplay of microdynamics and macrorheology in a suspension of fluid-filled soft particles

The microscopic dynamics of objects suspended in a fluid determines the macroscopic rheology of a suspension. As shown theoretically, the viscosity of a dilute suspension of vesicles is a non-monotonic function of the viscosity contrast (ratio between the viscosities of the encapsulated and the suspending fluids). By performing simulations, we recover this effect and demonstrate that it persists for a wide range of parameters such as the concentration, membrane deformability and the swelling degree. We also explain why other numerical and experimental studies lead to contradicting results. Furthermore, our simulations show that this effect even persists in non-dilute and confined suspensions, but that it becomes less pronounced at higher concentrations and for more swollen particles [Kaoui et al., Soft Matter 10, 4735 (2014)]. The interplay of inertia and deformability has also a substantial impact on rheological properties. When a suspension of soft particles is subjected to Poiseuille flow, at finite Reynolds numbers, the Segre-Silberberg effect is suppressed and a flow focusing effect emerges, which is accompanied by a non-monotonic behavior of the suspension viscosity [Krueger et al., J. Fluid Mech. 751, 725 (2014)].   

Buckling and its effect on the confined flow of a model capsule suspension

The rheology of confined flowing suspensions, such as blood, depend upon the dynamics of the components, which can be particularly rich when they are elastic capsules. Using boundary integral methods, we simulate a two-dimensional model channel through which flows a dense suspension of fluid-filled capsules. A parameter of principal interest is the equilibrium membrane perimeter, which ranges from round capsules to capsules with an elongated dog-bone-like equilibrium shape. It is shown that the minimum effective viscosity occurs for capsules with a biconcave equilibrium shape, similar to that of a red blood cell. The rheological behavior changes significantly over this range; transitions are linked to specific changes in the capsule dynamics. Most noteworthy is an abrupt change in behavior when capsules transition to a dog-bone-like equilibrium shape, which correlates with the onset of capsule buckling. The buckled capsules have a more varied orientation and make significant rotational (rotlet) contributions to the capsule--capsule interactions.   

Theory of margination in confined multicomponent suspensions

In blood flow, leukocytes and platelets tend to segregate near the vessel walls; this is known as margination. Margination of leukocytes and platelets is important in physiological processes, medical diagnostics and drug delivery. A mechanistic theory is developed to describe flow-induced segregation in confined multicomponent suspensions of deformable particles such as blood. The theory captures the essential features of margination by describing it in terms of two key competing processes in these systems at low Reynolds number: wall-induced migration and hydrodynamic pair collisions. The theory also includes the effect of physical properties of the deformable particles and molecular diffusion. Several regimes of segregation are identified, depending on the value of a “margination parameter” M. Moreover, there is a critical value of M below which a sharp “drainage transition” occurs: one component is completely depleted from the bulk flow to the vicinity of the walls. Direct hydrodynamic simulations also display this transition in suspensions where the components differ in size or flexibility. The developed mechanistic theory leads to substantial insight into the origins of margination and will help in guiding development of new technologies involving multicomponent suspensions.   

Simulations of the dynamics of soft particles of different shapes suspended in liquids under shear flow.

Soft particles of different shapes are found in several natural and industrial systems, examples including biological cells, elastic capsules, and microgels. When suspended in a flowing liquid, such deformable particles can exhibit complicated dynamics in response to the hydrodynamic forces exerted by the suspending fluid and, in turn, have a significant impact on the overall mechanical properties of the multiphase material. The behavior of suspensions of soft particles, both of spherical and non-spherical shape at rest, in Newtonian and viscoelastic fluids subjected to shear flow is studied through direct numerical simulations. In both Newtonian and viscoelastic matrices, initially spherical particles are found to deform and eventually migrate orthogonally to the flow, the direction and velocity of such migration being determined by the interplay of the geometrical and the rheological parameters of the system. Non-spherical particles have even more complex dynamics due to their non-trivial undeformed shape, which introduces additional parameters to the system.