Self-propulsion of a droplet induced by combined diffusiophoresis and Marangoni effects.

Chemically active droplets display complex self-propulsion behavior in homogeneous surfactant solutions, often influenced by the interplay between diffusiophoresis and Marangoni effects. Previous studies have primarily considered these effects separately or assumed axisymmetric motion. To understand the full hydrodynamics, we investigate the motion of a two-dimensional active droplet under their combined influences using weakly nonlinear analysis and numerical simulations. The impact of two key factors, the Péclet number ( P e $Pe$ ) and the mobility ratio between diffusiophoretic and Marangoni effects ( m $m$ ), on droplet motion is explored. We establish a phase diagram in the P e - m $Pe-m$ space, categorizing the boundaries between four types of droplet states: stationary, steady motion, periodic/quasi-periodic motion, and chaotic motion. We find that the mobility ratio does not affect the critical P e $Pe$ for the onset of self-propulsion, but it significantly influences the stability of high-wavenumber modes as well as the droplet's velocity and trajectory. Scaling analysis reveals that in the high P e $Pe$ regime, the Marangoni and diffusiophoresis effects lead to distinct velocity scaling laws: U ∼ P e - 1 / 2 $U\sim Pe^{-1/2}$ and U ∼ P e - 1 / 3 $U\sim Pe^{-1/3}$ , respectively. When these effects are combined, the velocity scaling depends on the sign of the mobility ratio. In cases with a positive mobility ratio, the Marangoni effect dominates the scaling, whereas the negative diffusiophoretic effect leads to an increased thickness of the concentration boundary layer and a flattened scaling of the droplet velocity.

Hydrodynamic Anisotropy of Depletion in Nonequilibrium.

Active colloids in a bath of inert particles of smaller size cause anisotropic depletion. The active hydrodynamics of this nonequilibrium phenomenon, which is fundamentally different from its equilibrium counterpart and passive particles in an active bath, remains scarcely understood. Here we combine mesoscale hydrodynamic simulation as well as theoretical analysis to examine the physical origin for the active depletion around a self-propelled noninteractive colloid. Our results elucidate that the variable hydrodynamic effect critically governs the microstructure of the depletion zone. Three characteristic states of anisotropic depletion are identified, depending on the strength and stress of activity. This yields a state diagram of depletion in the two-parameter space, captured by developing a theoretical model with the continuum kinetic theory and leading to a mechanistic interpretation of the hydrodynamic anisotropy of depletion. Furthermore, we demonstrate that such depletion in nonequilibrium results in various clusters with ordered organization of squirmers, which follows a distinct principle contrary to that of the entropy scenario of depletion in equilibrium. The findings might be of immediate interest to tune the hydrodynamics-mediated anisotropic interactions and active nonequilibrium organizations in the self-propulsion systems.

Electroconvective Flow in Liquid Electrolytes Containing Oligomer Additives.

Metal electrodeposition in batteries is fundamentally unstable and affected by different instabilities depending on operating conditions and electrolyte chemistry. Particularly, at high charging rates, a hydrodynamic instability loosely termed electroconvection sets in, which complicates all electrochemical processes by creating a nonuniform ion flux and preferential deposition at the electrode. Here, we isolate and study electroconvection by experimentally investigating how oligomer additives in liquid electrolytes interact with the hydrodynamic instability at a cation selective interface. From electrochemical measurements and direct visualization experiments, we find that electroconvection is delayed and suppressed at all voltages in the presence of oligomers. The underlying mechanism is revealed to involve formation of an oligomer ad-layer at the interface, which in response to perturbation is believed to exert an opposing body force on the surrounding fluid to preserve the ad-layer structure and in so doing suppresses electroconvection. Our results therefore reveal that in battery electrolytes without obvious sources of bulk elasticity, surface forces produced by adsorbed polymers can be used to advantage for suppressing instability.

Structure and Dynamics of Electric-Field-Driven Convective Flows at the Interface between Liquid Electrolytes and Ion-Selective Membranes.

At voltages above a certain critical value, Vc ≈ 20 kT/e, a space charge layer forms near ion-selective interfaces in liquid electrolytes. Interactions between the space charge and an imposed electric field drives a hydrodynamic instability known as electroconvection. Through particle tracking velocimetry we experimentally study the structure and dynamics of the resultant electroconvective flow. Consistent with previous numerical simulations, we report that, following imposition of a sufficiently large voltage, electroconvection develops gradually as pairs of counter-rotating vortices, which nucleate at the interface between an ion-selective substrate and a liquid electrolyte. Depending on the imposed voltage and cell geometry, the vorticies grow to length scales of hundreds of micrometers. Electroconvective flows are also reported to be structured and multiscale, with the size ratio of the largest to the smallest observable vortices inversely proportional to the Debye screening length.

Suppression of dendrite growth by cross-flow in microfluidics.

Formation of rough, dendritic deposits is a critical problem in metal electrodeposition processes and could occur in next-generation, rechargeable batteries that use metallic electrodes. Electroconvection, which originates from the coupling of the imposed electric field and a charged fluid near an electrode surface, is believed to be responsible for dendrite growth. However, few studies are performed at the scale of fidelity where root causes and effective strategies for controlling electroconvection and dendrite growth can be investigated in tandem. Using microfluidics, we showed that forced convection across the electrode surface (cross-flow) during electrodeposition reduced metal dendrite growth (97.7 to 99.4%) and delayed the onset of electroconvective instabilities. Our results highlighted the roles of forced convection in reducing dendrite growth and electroconvective instabilities and provided a route toward effective strategies for managing the consequences of instability in electrokinetics-based processes where electromigration dominates ion diffusion near electrodes.

Structure, Rheology, and Electrokinetics of Soft Colloidal Suspension Electrolytes.

When ion transport in a binary liquid electrolyte is driven at potentials above the thermal voltage, an extended space charge region forms at the electrolyte/electrode interface and triggers the hydrodynamic instability termed electroconvection. We experimentally show that this instability can be completely arrested in soft colloidal suspension electrolytes composed of low concentrations of polymer-grafted nanoparticles in a liquid host. The mechanism is revealed by means of X-ray scattering, Brownian dynamics calculations, and linear stability analysis to involve overlap of the soft particles at low particle fractions to create a jammed, nanoporous medium that resists convective flow by a Darcy-Brinkman like drag on the electrolyte solvent.

Designing Polymeric Interphases for Stable Lithium Metal Deposition.

Reactive metals are known to electrodeposit with irregular morphological features on planar substrates. A growing body of work suggest that multiple variables: composition, mechanics, structure, ion transport properties, reductive stability, and interfacial energy of interphases, formed either spontaneously or by design on the metal electrode play important but differentiated roles in regulating these morphologies. We examine the effect of fluorinated thermoset polymer coatings on Li deposition by means of experiment and theoretical linear stability analysis. By tuning the chemistry of the polymer backbone and side chains, we investigate how physical and mechanical properties of polymeric interphases influence Li electrodeposit morphology. It is found that an interplay between elasticity and diffusivity leads to an optimum interphase thickness and that higher interfacial energy augments elastic stresses at a metal electrode to prevent out-of-plane deposition. These findings are explained using linear stability analysis of electrodeposition and provide guidelines for designing polymer interphases to stabilize metal anodes in rechargeable batteries.

Spontaneous and field-induced crystallographic reorientation of metal electrodeposits at battery anodes.

The propensity of metal anodes of contemporary interest (e.g., Li, Al, Na, and Zn) to form non-planar, dendritic morphologies during battery charging is a fundamental barrier to achievement of full reversibility. We experimentally investigate the origins of dendritic electrodeposition of Zn, Cu, and Li in a three-electrode electrochemical cell bounded at one end by a rotating disc electrode. We find that the classical picture of ion depletion-induced growth of dendrites is valid in dilute electrolytes but is essentially irrelevant in the concentrated (≥1 M) electrolytes typically used in rechargeable batteries. Using Zn as an example, we find that ion depletion at the mass transport limit may be overcome by spontaneous reorientation of Zn crystallites from orientations parallel to the electrode surface to dominantly homeotropic orientations, which appear to facilitate contact with cations outside the depletion layer. This chemotaxis-like process causes obvious texturing and increases the porosity of metal electrodeposits.

Electroconvection in a Viscoelastic Electrolyte.

Direct numerical simulations of a liquid electrolyte with polymer additives demonstrate that viscoelasticity promotes an earlier transition from steady to unsteady electroconvective flow. Viscoelasticity also decreases the overlimiting current resulting from convection by up to 40%. Both of these effects would reduce the time-averaged spatial variability of ion flux suggesting that polymeric fluids may inhibit dendrite growth. Polymer relaxation near a surface destabilizes the flow structures and decreases the time duration of high current fluxes. This mechanism of polymer-induced flux reduction is general to wall bounded flows with transfer of mass, heat or momentum.

Stabilizing electrochemical interfaces in viscoelastic liquid electrolytes.

Electrodeposition is a widely practiced method for creating metal, colloidal, and polymer coatings on conductive substrates. In the Newtonian liquid electrolytes typically used, the process is fundamentally unstable. The underlying instabilities have been linked to failure of microcircuits, dendrite formation on battery electrodes, and overlimiting conductance in ion-selective membranes. We report that viscoelastic electrolytes composed of semidilute solutions of very high-molecular weight neutral polymers suppress these instabilities by multiple mechanisms. The voltage window ΔV in which a liquid electrolyte can operate free of electroconvective instabilities is shown to be markedly extended in viscoelastic electrolytes and is a power-law function, ΔV : η1/4, of electrolyte viscosity, η. This power-law relation is replicated in the resistance to ion transport at liquid/solid interfaces. We discuss consequences of our observations and show that viscoelastic electrolytes enable stable electrodeposition of many metals, with the most profound effects observed for reactive metals, such as sodium and lithium. This finding is of contemporary interest for high-energy electrochemical energy storage.

Hydrodynamic interaction of swimming organisms in an inertial regime.

We numerically investigate the hydrodynamic interaction of swimming organisms at small to intermediate Reynolds number regimes, i.e., Re∼O(0.1-100), where inertial effects are important. The hydrodynamic interaction of swimming organisms in this regime is significantly different from the Stokes regime for microorganisms, as well as the high Reynolds number flows for fish and birds, which involves strong flow separation and detached vortex structures. Using an archetypal swimmer model, called a "squirmer," we find that the inertial effects change the contact time and dispersion dynamics of a pair of pusher swimmers, and trigger hydrodynamic attraction for two pullers. These results are potentially important in investigating predator-prey interactions, sexual reproduction, and the encounter rate of marine organisms such as copepods, ctenophora, and larvae.

Collective Motion of Microorganisms in a Viscoelastic Fluid.

We study the collective motion of a suspension of rodlike microswimmers in a two-dimensional film of viscoelastic fluids. We find that the fluid elasticity has a small effect on a suspension of pullers, while it significantly affects the pushers. The attraction and orientational ordering of the pushers are enhanced in viscoelastic fluids. The induced polymer stresses break down the large-scale flow structures and suppress velocity fluctuations. In addition, the energy spectra and induced mixing in the suspension of pushers are greatly modified by fluid elasticity.

Hydrodynamic interaction of microswimmers near a wall.

The hydrodynamics of an archetypal low-Reynolds number swimmer, called "squirmer," near a wall has been numerically studied. For a single squirmer, depending on the swimming mechanism, three different modes are distinguished: (a) the squirmer escaping from the wall, (b) the squirmer swimming along the wall at a constant distance and orientation angle, and (c) the squirmer swimming near the wall in a periodic trajectory. The role of inertial effects on the near-wall motion of the squirmer is quantified. The dynamics of multiple squirmers swimming between two walls is found to be very different from a single squirmer. Near-wall accumulation of squirmers are observed. At a relatively small concentration c = 0.1, around 60-80% of the squirmers are accumulated near the walls and attraction of pushers and pullers toward the wall is stronger than neutral squirmers. Near-wall squirmers orient normal to the wall, while in the bulk region, the squirmers are mostly oriented parallel to the wall. At a high concentration c = 0.4, the percentage of the near-wall squirmers is around 40%. The orientation angle of squirmers in the bulk region is more uniformly distributed at high concentrations. In the near-wall region, pullers repel each other, while pushers are attracted to each other and form clusters.