Collective chemomechanical oscillations in active hydrogels.

We report on the collective response of an assembly of chemomechanical Belousov-Zhabotinsky (BZ) hydrogel beads. We first demonstrate that a single isolated spherical BZ hydrogel bead with a radius below a critical value does not oscillate, whereas an assembly of the same BZ hydrogel beads presents chemical oscillation. A BZ chemical model with an additional flux of chemicals out of the BZ hydrogel captures the experimentally observed transition from oxidized nonoscillating to oscillating BZ hydrogels and shows this transition is due to a flux of inhibitors out of the BZ hydrogel. The model also captures the role of neighboring BZ hydrogel beads in decreasing the critical size for an assembly of BZ hydrogel beads to oscillate. We finally leverage the quorum sensing behavior of the collective to trigger their chemomechanical oscillation and discuss how this collective effect can be used to enhance the oscillatory strain of these active BZ hydrogels. These findings could help guide the eventual fabrication of a swarm of autonomous, communicating, and motile hydrogels.

Active Pulsatile Gels: From a Chemical Microreactor to a Polymeric Actuator.

We report on a synthesis protocol, experimental characterization, and theoretical modeling of active pulsatile Belousov-Zhabotinsky (BZ) hydrogels. Our two-step synthesis technique allows independent optimization of the geometry, the chemical, and the mechanical properties of BZ gels. We identify the role of the surrounding medium chemistry and gel radius for the occurrence of BZ gel oscillations, quantified by the Damköhler number, which is the ratio of chemical reaction to diffusion rates. Tuning the BZ gel size to maximize its chemomechanical oscillation amplitude, we find that its oscillatory strain amplitude is limited by the time scale of gel swelling relative to the chemical oscillation period. Our experimental findings are in good agreement with a Vanag-Epstein model of BZ chemistry and a Tanaka Fillmore theory of gel swelling dynamics.

Partition, Reaction, and Diffusion Coefficients of Bromine in Elastomeric Polydimethylsiloxane.

Experiments and models were used to determine the extent to which aqueous bromine permeated into, and reacted with, the elastomer polydimethylsiloxane (PDMS). Thin films of PDMS were immersed in bromine water, and the absorbance of bromine in the aqueous phase was measured as a function of time. Kinetics were studied as a function of mass and thickness of the immersed PDMS films. We attribute the decrease of bromine in solution to permeation into PDMS, followed by a combination of diffusion, reversible binding, and an irreversible reaction with PDMS. In order to decouple the irreversible reaction from the reversible processes, kinetics were also studied for bromine-passivated PDMS films. Fits of the models to a variety of experiments yielded the partition coefficient of bromine between the water and PDMS phases, the diffusion constant of bromine in PDMS, the irreversible reaction constant between bromine and PDMS, the molar concentration of the reactive sites within PDMS, and the on and off rates of reversible binding of bromine to PDMS. Developing a quantitative reaction-diffusion model accounting for the transport of bromine through PDMS is necessary for the design of microfluidic devices fabricated using PDMS, which are used in experimental studies of the nonlinear dynamics of reaction-diffusion networks containing Belousov-Zhabotinsky chemical oscillators.

Dynamics of Reaction-Diffusion Oscillators in Star and other Networks with Cyclic Symmetries Exhibiting Multiple Clusters.

We experimentally and theoretically investigate the dynamics of inhibitory coupled self-driven oscillators on a star network in which a single central hub node is connected to k peripheral arm nodes. The system consists of water-in-oil Belousov-Zhabotinsky ∼100 µm emulsion drops contained in storage wells etched in silicon wafers. We observed three dynamical attractors by varying the number of arms in the star graph and the coupling strength: (i) unlocked, uncorrelated phase shifts between all oscillators; (ii) locked, arm hubs synchronized in phase with a k-dependent phase shift between the arm and central hub; and (iii) center silent, a central hub stopped oscillating and the arm hubs oscillated without synchrony. We compare experiment to theory. For case (ii), we identified a logarithmic dependence of the phase shift on star degree, and were able to discriminate between contributions to the phase shift arising from star topology and oscillator chemistry.

Electroosmosis near surfactant laden liquid-air interfaces.

Generation of an electroosmostic (EO) flow near a liquid-gas interface covered with ionic surfactants is experimentally investigated. A combination of microscopic flow measurements with a molecular characterization of the interface by second harmonic generation (SHG) shows that under an electrical forcing, although a liquid flow is generated below the free surface, the surfactants remain immobile. The zeta potential was then determined and compared to the surfactant surface coverage. This combination of experimental techniques opens the route to simultaneously probe the liquid flow near a soapy interface and the corresponding surfactant repartition affecting the hydrodynamic boundary condition.

Electrokinetic transport in liquid foams.

Investigating electrokinetic transport in a liquid foam is at the confluence of two well developed research areas. On one hand, the study of electrokinetic flows (i.e. surface-driven flows generated close to a charged interface) is fairly well understood in regards the solid/liquid interface. On the other hand, the flow of liquid in a 3D deformable network, i.e a foam, under a volume force such as gravity has been thoroughly studied over the past decade. The overlapping zone of these two frameworks is of great interest for both communities as it gives rise to challenging new questions such as: what is the importance of the nature of the charged interface, created by mobile and soluble surfactants in the case of foam, on electrokinetic transport? How does a foam behave when submitted to a surface-driven flow? Can we compensate a volume-driven flow, i.e. gravity, by a surface-driven flow, i.e. electroosmosis? In this review, we will explore these questions on three different scales: a surfactant laden interface, a foam film and a macroscopic foam.

Avalanche precursors in a frictional model.

We present a one-dimensional numerical model based on elastically coupled sliders on a frictional incline of variable tilt. This very simple approach makes it possible to study the precursors to the avalanche and to provide a rationalization of different features that have been observed in experiments. We provide a statistical description of the model leading to master equations describing the state of the system as a function of the angle of inclination. Our central results are the reproduction of large-scale regular events preceding the avalanche, on the one hand, and an analytical approach providing an internal threshold for the outbreak of rearrangements before the avalanche in the system, on the other hand.

On-and-off dynamics of a creeping frictional system.

We report on the dynamics of a model frictional system submitted to minute external perturbations. The system consists of a chain of sliders connected through elastic springs that rest on an incline. By introducing cyclic expansions and contractions of the rest length of the springs, we induce the reptation of the chain. Decreasing the amplitude of the perturbation below a critical value, we observe an intermittent creep regime characterized by alternated periods of reptation (flowing state) and rest (quiescent state). A further decrease of the perturbation leads to the disappearance of the reptation. The width of the transition region between the continuous creep and the full stop (i.e., the range of excitation amplitudes where the intermittent creep is observed) is shown to depend on the difference between the static (µ(s)) and the dynamic (µ(d)) friction coefficients. For µ(s) = µ(d) the intermittent creep is not observed. Studying the statistical features of the intermittent creep regime for any given perturbation amplitude, we find that the time the system resides in each state (flowing or quiescent) suggests that: i) reptation events are uncorrelated, and ii) rest events are history dependent. We show that this latter history dependence is consistent with the aging of the stress state inside the chain of sliders during the quiescent periods.

Intrinsic creep of a granular column subjected to temperature changes.

Minute external perturbations, such as temperature variations, can lead to a creep of the fragile structures that are the granular piles. We report a study, resolved in space and time, of the dynamics associated with the slow compaction of a granular column submitted to thermal cycles. Avoiding the thermal dilations of the container, we observe that the material still creeps, even in the absence of external mechanical perturbations. The latter intrinsic creep of the material exhibits several surprising features: the compaction of the material is not homogeneous along the column height, and sudden collapses involve the entire system even if one could expect arches to screen the mechanical interaction between regions far apart from one another. In addition, the analysis of the dependence of the flow rate on the frequency of the temperature cycles suggests that the creep is mainly induced by the propagation of the temperature profile, slow temperature changes being less efficient than rapid ones in making the material flow.

Creep motion of a model frictional system.

We report on the dynamics of a model frictional system submitted to minute external perturbations. The system consists of a chain of sliders connected through elastic springs that rest on an incline. By introducing cyclic expansions and contractions of the springs we observe a reptation of the chain. We account for the average reptation velocity theoretically. The velocity of small systems exhibits a series of plateaus as a function of the incline angle. Due to elastic effects, there exists a critical amplitude below which the reptation is expected to cease. However, rather than a full stop of the creep, we observe in numerical simulations a transition between a continuous-creep and an irregular-creep regime when the critical amplitude is approached. The latter transition is reminiscent of the transition between the continuous and the irregular compaction of granular matter submitted to periodic temperature changes.