RESUMEN
The rheology of noncolloidal suspensions under cyclic shear is studied numerically. The main findings are a strain amplitude (γ_{0}) dependent response in the shear stress and second normal stress difference (N_{2}). Specifically, we find a reduced viscosity, an enhanced intracycle shear thinning, the onset of a finite N_{2}, and its frequency doubling, all near a critical strain amplitude γ_{c} that scales with the volume fraction Ï as γ_{c}â¼Ï^{-2}. These rheological changes also signify a reversible-irreversible transition (RIT), dividing stroboscopic particle dynamics into a reversible absorbing phase (for γ_{0}<γ_{c}) and a persistently diffusing phase (for γ_{0}>γ_{c}). We explain the results based on two flow-induced mechanisms and elucidate their connection in the context of RIT through the underlying microstructure, which tends toward hyperuniformity near γ_{0}=γ_{c}. Overall, we expect this correspondence between rheology and emergent dynamics to hold in a wide range of settings where structural organizations are dominated by volume exclusions.
RESUMEN
Self-assembly of soft matter, such as droplets or colloids, has become a promising scheme to engineer novel materials, model living matter, and explore non-equilibrium statistical mechanics. In this article, we present detailed numerical simulations of few non-Brownian droplets in various flow conditions, specifically, focusing on their self-assembly within a short distance in a three-dimensional (3D) microfluidic channel, cf. [Shen et al., Adv. Sci., 2016, 3(6), 1600012]. Contrary to quasi two-dimensional (q2D) systems, where dipolar interaction is the key mechanism for droplet rearrangement, droplets in 3D confinement produce much less disturbance to the underlying flow, thus experiencing weaker dipolar interactions. Using confined simple shear and Poiseuille flows as reference flows, we show that the droplet dynamics is mostly affected by the shear-induced cross-stream migration, which favors chain structures if the droplets are under an attractive depletion force. For more compact clusters, such as three droplets in a triangular shape, our results suggest that an inhomogeneous cross-sectional inflow profile is further required. Overall, the accelerated self-assembly of a small-size droplet cluster results from the combined effects of strong depletion forces, confinement-mediated shear alignments, and fine-tuned inflow conditions. The deterministic nature of the flow-assisted self-assembly implies the possibility of large throughputs, though calibration of all different effects to directly produce large droplet crystals is generally difficult.
RESUMEN
We construct a boundary integral representation for the low-Reynolds-number flow in a channel in the presence of freely suspended particles (or droplets) of arbitrary size and shape. We demonstrate that lubrication theory holds away from the particles at horizontal distances exceeding the channel height and derive a multipole expansion of the flow which is dipolar to the leading approximation. We show that the dipole moment of an arbitrary particle is a weighted integral of the stress and the flow at the particle surface, which can be determined numerically. We introduce the equation of motion that describes hydrodynamic interactions between arbitrary, possibly different, distant particles, with interactions determined by the product of the mobility matrix and the dipole moment. Further, the problem of three identical interacting spheres initially aligned in the streamwise direction is considered and the experimentally observed "pair exchange" phenomenon is derived analytically and confirmed numerically. For nonaligned particles, we demonstrate the formation of a configuration with one particle separating from a stable pair. Our results suggest that in a dilute initially homogenous particulate suspension flowing in a channel the particles will eventually separate into singlets and pairs.