Structures and topological defects in pressure-driven lyotropic chromonic liquid crystals.

Lyotropic chromonic liquid crystals are water-based materials composed of self-assembled cylindrical aggregates. Their behavior under flow is poorly understood, and quantitatively resolving the optical retardance of the flowing liquid crystal has so far been limited by the imaging speed of current polarization-resolved imaging techniques. Here, we employ a single-shot quantitative polarization imaging method, termed polarized shearing interference microscopy, to quantify the spatial distribution and the dynamics of the structures emerging in nematic disodium cromoglycate solutions in a microfluidic channel. We show that pure-twist disclination loops nucleate in the bulk flow over a range of shear rates. These loops are elongated in the flow direction and exhibit a constant aspect ratio that is governed by the nonnegligible splay-bend anisotropy at the loop boundary. The size of the loops is set by the balance between nucleation forces and annihilation forces acting on the disclination. The fluctuations of the pure-twist disclination loops reflect the tumbling character of nematic disodium cromoglycate. Our study, including experiment, simulation, and scaling analysis, provides a comprehensive understanding of the structure and dynamics of pressure-driven lyotropic chromonic liquid crystals and might open new routes for using these materials to control assembly and flow of biological systems or particles in microfluidic devices.

Evaporation-Driven Cellular Patterns in Confined Hyperelastic Hydrogels.

When a hyperelastic hydrogel confined between two parallel glass plates begins to dry from a lateral boundary, the volume lost by evaporation is accommodated by an inward displacement of the air-hydrogel interface that induces an elastic deformation of the hydrogel. Once a critical front displacement is reached, we observe intermittent fracture events initiated by a geometric instability resulting in localized bursts at the interface. These bursts relax the stresses and irreversibly form air cavities that lead to cellular networks. We show that the spatial extent of the strain field prior to a burst, influenced by the air-hydrogel interfacial tension and the confinement of the gel, determines the characteristic size of the cavities.

Criteria for Crack Formation and Air Invasion in Drying Colloidal Suspensions.

The drying of sessile drops of aqueous colloidal suspensions leads to the formation of a close-packed particle deposit. As water evaporates, a solidification front propagates from the edge of the drop toward the center, leaving behind a thin disk-shaped deposit. For drops with sufficiently large particle volume fractions, the deposit eventually covers the entire wetted area. In this regime, the dynamics of the deposit growth is governed by volume conservation across a large range of particle volume fractions and drying times. During drying, water flows radially through the deposit to compensate for evaporation over the solid's surface, creating a negative pore pressure in the deposit which we rationalize with a hydrodynamic model. We show that the pressure inside the deposit controls both the onset of crack formation and the onset of air invasion. Two distinct regimes of air invasion occur, which we can account for using the same model that further provides a quantitative criterion for the crossover between the two regimes.

Yield precursor in primary creep of colloidal gels.

Colloidal gels under constant moderate stress flow only after a prolonged solid-like deformation. Predicting the time-dependent yielding of the gels would facilitate control of their mechanical stability and transport, but early detectable signs of such delayed solid-to-fluid transition remain unknown. We show that the shear rate of colloidal gels under constant stress can forecast an eventual yielding during the earliest stage of deformation known as primary creep. The shear rate before failure exhibits a characteristic power-law decrease as a function of time, distinct from the linear viscoelastic response. We model this early-stage behavior as a series of uncorrelated local plastic events that are thermally activated, which illuminates the exponential dependence of the yield time on the applied stress. By revealing underlying viscoplasticity, this precursor to yield in the macroscopic shear rate provides a convenient tool to predict the yielding of a gel well in advance of its actual occurrence.

Spectral Universality of Elastoinertial Turbulence.

Dissolving small amounts of polymer into a Newtonian fluid can dramatically change the dynamics of transitional and turbulent flows. We investigate the spatiotemporal dynamics of a submerged jet of dilute polymer solution entering a quiescent bath of Newtonian fluid. High-speed digital Schlieren imaging is used to quantify the evolution of Lagrangian features in the jet revealing a rich sequence of transitional and turbulent states. At high levels of viscoelasticity, we identify a new distinct transitional pathway to elastoinertial turbulence (EIT) that does not feature the conventional turbulent bursts and instead proceeds via a shear-layer instability that produces elongated filaments of polymer due to the nonlinear effects of viscoelasticity. Even though the pathways to the EIT state can be different, and within EIT the spatial details of the turbulent structures vary systematically with polymer microstructure and concentration, there is a universality in the power-law spectral decay of EIT with frequency, f^{-3}, independent of fluid rheology and flow parameters.

Growth morphology and symmetry selection of interfacial instabilities in anisotropic environments.

The displacement of a fluid by another less viscous one in a quasi-two dimensional geometry typically leads to complex fingering patterns. In an isotropic system, dense-branching growth arises, which is characterized by repeated tip-splitting of evolving fingers. When anisotropy is present in the interfacial dynamics, the growth morphology changes to dendritic growth characterized by regular structures. We introduce anisotropy by engraving a six-fold symmetric lattice of channels on a Hele-Shaw cell. We show that the morphology transition in miscible fluids depends not only on the previously reported degree of anisotropy set by the lattice topography, but also on the viscosity ratio between the two fluids, ηin/ηout. Remarkably, ηin/ηout and the degree of anisotropy also govern the global features of the dendritic patterns, inducing a systematic change from six-fold towards twelve-fold symmetric dendrites. Varying either control parameter provides a new method to tune the symmetry of complex patterns, which may also have relevance for analogous phenomena of gradient-driven interfacial dynamics, such as directional solidification or electrodeposition.

Crack morphologies in drying suspension drops.

A drop of an aqueous suspension of nanoparticles placed on a substrate forms a solid deposit as it dries. For dilute suspensions, particles accumulate within a narrow ring at the drop edge, whereas a uniform coating covering the entire wetted area forms for concentrated suspensions. In between these extremes, we report two additional regimes characterized by non-uniform deposit thicknesses and by distinct crack morphologies. We show that both the deposit shape and the number of cracks are controlled exclusively by the initial particle volume fraction. The different regimes share a common avalanche-like crack propagation dynamics, as a result of the delamination of the deposit from the substrate.

Emergence of Multiscale Dynamics in Colloidal Gels.

To gain insight into the kinetics of colloidal gel evolution at low particle volume fractions ϕ, we utilize differential dynamic microscopy to investigate particle aggregation, geometric percolation, and the subsequent transition to nonergodic dynamics. We report the emergence of unexpectedly rich multiscale dynamics upon the onset of nonergodicity, which separates the wave vectors q into three different regimes. In the high-q domain, the gel exhibits ϕ-independent internal vibrations of fractal clusters. The intermediate-q domain is dominated by density fluctuations at the length scale of the clusters, as evidenced by the q independence of the relaxation time τ. In the low-q domain, the scaling of τ as q^{-3} suggests that the network appears homogeneous. The transitions between these three regimes introduce two characteristic length scales, distinct from the cluster size.

Criterion for Fingering Instabilities in Colloidal Gels.

We sandwich a colloidal gel between two parallel plates and induce a radial flow by lifting the upper plate at a constant velocity. Two distinct scenarios result from such a tensile test: (i) stable flows during which the gel undergoes a tensile deformation without yielding, and (ii) unstable flows characterized by the radial growth of air fingers into the gel. We show that the unstable regime occurs beyond a critical energy input, independent of the gel's macroscopic yield stress. This implies a local fluidization of the gel at the tip of the growing fingers and results in the most unstable wavelength of the patterns exhibiting the characteristic scalings of the classical viscous fingering instability. Our work provides a quantitative criterion for the onset of fingering in colloidal gels based on a local shear-induced yielding in agreement with the delayed failure framework.

Designing allostery-inspired response in mechanical networks.

Recent advances in designing metamaterials have demonstrated that global mechanical properties of disordered spring networks can be tuned by selectively modifying only a small subset of bonds. Here, using a computationally efficient approach, we extend this idea to tune more general properties of networks. With nearly complete success, we are able to produce a strain between any two target nodes in a network in response to an applied source strain on any other pair of nodes by removing only ∼1% of the bonds. We are also able to control multiple pairs of target nodes, each with a different individual response, from a single source, and to tune multiple independent source/target responses simultaneously into a network. We have fabricated physical networks in macroscopic 2D and 3D systems that exhibit these responses. This work is inspired by the long-range coupled conformational changes that constitute allosteric function in proteins. The fact that allostery is a common means for regulation in biological molecules suggests that it is a relatively easy property to develop through evolution. In analogy, our results show that long-range coupled mechanical responses are similarly easy to achieve in disordered networks.

Airflows generated by an impacting drop.

A drop impacting a solid surface with sufficient velocity will splash and emit many small droplets. However, lowering the ambient air pressure suppresses splashing completely. This effect, robustly found for different liquid and substrate properties, raises the fundamental question of how air affects a spreading drop. In a combined experimental and numerical study we characterize the flow of air induced by the drop after it hits the substrate, using a modified Schlieren optics technique combined with high-speed video imaging and Lattice-Boltzmann simulations. Our experiments reveal the emergence of air structures on different length scales. On large scales, the airflow induced in the drop's wake leads to vortex structures due to interaction with the substrate. On smaller scales, we visualize a ring structure above the outer edge of the spreading liquid generated by the spreading of the drop. Our simulations reveal the interaction between the wake vorticity and the flows originating from the rapidly escaping air from below the impacting drop. We show that the vorticity is governed by a balance between inertial and viscous forces in the air, and is unrelated to the splashing threshold.

An island of stability in a sea of fingers: emergent global features of the viscous-flow instability.

The displacement of a more viscous fluid by a less viscous one in a quasi-two dimensional geometry leads to the formation of complex fingering patterns. This fingering has been characterized by a most unstable wavelength, λc, which depends on the viscosity difference between two immiscible fluids and sets the characteristic width of the fingers. How the finger length grows after the instability occurs is an equally important, but previously overlooked, aspect that characterizes the global features of the patterns. Long after the instability onset, once the fingers are growing in a nearly steady-state regime, there is a stable inner region where the outer fluid is completely displaced. We show that the ratio of the finger length to the radius of this stable region depends only on the viscosity ratio of the fluids and is decoupled from λc.

Crack densification in drying colloidal suspensions.

As sessile drops of aqueous colloidal suspensions dry, a close-packed particle deposit forms that grows from the edge of the drop toward the center. To compensate for evaporation over the solid's surface, water flows radially through the deposit, generating a negative pore pressure in the deposit associated with tensile drying stresses that induce the formation of cracks. As these stresses increase during drying, existing cracks propagate and additional cracks form, until the crack density eventually saturates. We rationalize the dynamics of crack propagation and crack densification with a local energy balance between the elastic energy released by the crack, the energetic cost of fracture, and the elastic energy released by previously formed cracks. We show that the final spacing between radial cracks is proportional to the local thickness of the deposit, while the aspect ratio of the crack segments depends on the shape of the deposit.

Fracture and relaxation in dense cornstarch suspensions.

Dense suspensions exhibit the remarkable ability to switch dynamically and reversibly from a fluid-like to a solid-like, shear-jammed (SJ) state. Here, we show how this transition has important implications for the propensity for forming fractures. We inject air into bulk dense cornstarch suspensions and visualize the air invasion into the opaque material using time-resolved X-ray radiography. For suspensions with cornstarch mass fractions high enough to exhibit discontinuous shear thickening and shear jamming, we show that air injection leads to fractures in the material. For high mass fractions, these fractures grow quasistatically as rough cavities with fractured interfaces. For lower mass fractions, remarkably, the fractures can relax to smooth bubbles that then rise under buoyancy. We show that the onset of the relaxation occurs as the shear rate induced by the air cavity growth decreases below the critical shear rate denoting the onset of discontinuous shear thickening, which reveals a structural signature of the SJ state.

Flow-induced periodic chiral structures in an achiral nematic liquid crystal.

Supramolecular chirality typically originates from either chiral molecular building blocks or external chiral stimuli. Generating chirality in achiral systems in the absence of a chiral input, however, is non-trivial and necessitates spontaneous mirror symmetry breaking. Achiral nematic lyotropic chromonic liquid crystals have been reported to break mirror symmetry under strong surface or geometric constraints. Here we describe a previously unrecognised mechanism for creating chiral structures by subjecting the material to a pressure-driven flow in a microfluidic cell. The chirality arises from a periodic double-twist configuration of the liquid crystal and manifests as a striking stripe pattern. We show that the mirror symmetry breaking is triggered at regions of flow-induced biaxial-splay configurations of the director field, which are unstable to small perturbations and evolve into lower energy structures. The simplicity of this unique pathway to mirror symmetry breaking can shed light on the requirements for forming macroscopic chiral structures.

Dendritic patterns from shear-enhanced anisotropy in nematic liquid crystals.

Controlling the growth morphology of fluid instabilities is challenging because of their self-amplified and nonlinear growth. The viscous fingering instability, which arises when a less viscous fluid displaces a more viscous one, transitions from exhibiting dense-branching growth characterized by repeated tip splitting of the growing fingers to dendritic growth characterized by stable tips in the presence of anisotropy. We controllably induce such a morphology transition by shear-enhancing the anisotropy of nematic liquid crystal solutions. For fast enough flow induced by the finger growth, the intrinsic tumbling behavior of lyotropic chromonic liquid crystals can be suppressed, which results in a flow alignment of the material. This microscopic change in the director field occurs as the viscous torque from the shear flow becomes dominant over the elastic torque from the nematic potential and macroscopically enhances the liquid crystal anisotropy to induce the transition to dendritic growth.

Local Mechanism Governs Global Reinforcement of Nanofiller-Hydrogel Composites.

We reveal the mechanism for the strong reinforcement of attractive nanofiller-hydrogel composites. Measuring the linear viscoelastic properties of hydrogels containing filler nanoparticles, we show that a significant increase of the modulus can be achieved at unexpectedly low volume fractions of nanofillers when the filler-hydrogel interactions are attractive. Using three-dimensional numerical simulations, we identify a general microscopic mechanism for the reinforcement, common to hydrogel matrices of different compositions and concentrations and containing nanofillers of varying sizes. The attractive interactions induce a local increase in the gel density around the nanofillers. The effective fillers, composed of the nanofillers and the densified regions around them, assemble into a percolated network, which constrains the gel displacement and enhances the stress coupling throughout the system. A global reinforcement of the composite is induced as the stresses become strongly coupled. This physical mechanism of reinforcement, which relies only on attractive filler-matrix interactions, provides design strategies for versatile composites that combine low nanofiller fractions with an enhanced mechanical strength.

Two modes of cluster dynamics govern the viscoelasticity of colloidal gels.

Colloidal gels formed by strongly attractive particles at low particle volume fractions are composed of space-spanning networks of uniformly sized clusters. We study the thermal fluctuations of the clusters using differential dynamic microscopy by decomposing them into two modes of dynamics, and link them to the macroscopic viscoelasticity via rheometry. The first mode, dominant at early times, represents the localized, elastic fluctuations of individual clusters. The second mode, pronounced at late times, reflects the collective, viscoelastic dynamics facilitated by the connectivity of the clusters. By mixing two types of particles of distinct attraction strengths in different proportions, we control the transition time at which the collective mode starts to dominate, and hence tune the frequency dependence of the linear viscoelastic moduli of the binary gels.

Single-Shot Quantitative Polarization Imaging of Complex Birefringent Structure Dynamics.

Polarization light microscopes are powerful tools for probing molecular order and orientation in birefringent materials. While a number of polarization microscopy techniques are available to access steady-state properties of birefringent samples, quantitative measurements of the molecular orientation dynamics on the millisecond time scale have remained a challenge. We propose polarized shearing interference microscopy (PSIM), a single-shot quantitative polarization imaging method, for extracting the retardance and orientation angle of the laser beam transmitting through optically anisotropic specimens with complex structures. The measurement accuracy and imaging performance of PSIM are validated by imaging a birefringent resolution target and a bovine tendon specimen. We demonstrate that PSIM can quantify the dynamics of a flowing lyotropic chromonic liquid crystal in a microfluidic channel at an imaging speed of 506 frames per second (only limited by the camera frame rate), with a field-of-view of up to 350 × 350 µm2 and a diffraction-limit spatial resolution of ~2 µm. We envision that PSIM will find a broad range of applications in quantitative material characterization under dynamical conditions.

Confinement-induced stabilization of the Rayleigh-Taylor instability and transition to the unconfined limit.

The prevention of hydrodynamic instabilities can lead to important insights for understanding the instabilities' underlying dynamics. The Rayleigh-Taylor instability that arises when a dense fluid sinks into and displaces a lighter one is particularly difficult to arrest. By preparing a density inversion between two miscible fluids inside the thin gap separating two flat plates, we create a clean initial stationary interface. Under these conditions, we find that the instability is suppressed below a critical plate spacing. With increasing spacing, the system transitions from the limit of stability where mass diffusion dominates over buoyant forces, through a regime where the gap sets the wavelength of the instability, to the unconfined regime governed by the competition between buoyancy and momentum diffusion. Our study, including experiment, simulation, and linear stability analysis, characterizes all three regimes of confinement and opens new routes for controlling mixing processes.