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Time-varying fields drive the motion of magnetic particles adsorbed on liquid drops due to interfacial constraints that couple magnetic torques to capillary forces. Such magneto-capillary particle dynamics and the associated fluid flows are potentially useful for propelling drop motion, mixing drop contents, and enhancing mass transfer between phases. The design of such functions benefits from the development and validation of predictive models. Here, we apply methods of Bayesian data analysis to identify and validate a dynamical model that accurately predicts the field-driven motion of a magnetic particle adsorbed at the interface of a spherical droplet. Building on previous work, we consider candidate models that describe particle tilting at the interface, field-dependent contributions to the magnetic moment, gravitational forces, and their combinations. The analysis of each candidate is informed by particle tracking data for a magnetic Janus sphere moving in a precessing field at different frequencies and angles. We infer the uncertain parameters of each model, criticize their ability to describe and predict experimental data, and select the most probable candidate, which accounts for gravitational forces and the tilting of the Janus sphere at the interface. We show how this favored model can predict complex particle trajectories with micron-level accuracy across the range of driving fields considered. We discuss how knowledge of this “best” model can be used to design experiments that inform accurate parameter estimates or achieve desired particle trajectories. 

Membraneless organelles within the living cell use phase separation of biomolecules coupled with enzymatic reactions to regulate cellular processes. The diverse functions of these biomolecular condensates motivate the pursuit of simpler in vitro models that exhibit primitive forms of self-regulation based on internal feedback mechanisms. Here, we investigate one such model based on complex coacervation of the enzyme catalase with an oppositely charge polyelectrolyte DEAE-dextran to form pH-responsive catalytic droplets. Upon addition of hydrogen peroxide “fuel”, enzyme activity localized within the droplets causes a rapid increase in the pH. Under appropriate conditions, this reaction-induced pH change triggers coacervate dissolution owing to its pH-responsive phase behavior. Notably, this destabilizing effect of the enzymatic reaction on phase separation depends on droplet size owing to the diffusive delivery and removal of reaction components. Reaction-diffusion models informed by the experimental data show that larger drops support larger changes in the local pH thereby enhancing their dissolution relative to smaller droplets. Together, these results provide a basis for achieving droplet size control based on negative feedback between pH-dependent phase separation and pH-changing enzymatic reactions. 

Lipid vesicles immersed in solute gradients are predicted to migrate from regions of high to low solute concentration due to osmotic flows induced across their semipermeable membranes. This process─known as osmophoresis─is potentially relevant to biological processes such as vesicle trafficking and cell migration; however, there exist significant discrepancies (several orders of magnitude) between experimental observations and theoretical predictions for the vesicle speed. Here, we seek to reconcile predictions of osmophoresis with observations of vesicle motion in osmotic gradients. We prepare quasi-steady solute gradients in a microfluidic chamber using density-matched solutions of sucrose and glucose to eliminate buoyancy-driven flows. We quantify the motions of giant DLPC vesicles and Brownian tracer particles in such gradients using Bayesian analysis of particle tracking data. Despite efforts to mitigate convective flows, we observe directed motion of both lipid vesicles and tracer particles in a common direction at comparable speeds of order 10 nm/s. These observations are not inconsistent with models of osmophoresis, which predict slower motion at ca. 1 nm/s; however, experimental uncertainty and the confounding effects of fluid convection prohibit a quantitative comparison. In contrast to previous reports, we find no evidence for anomalously fast osmophoresis of lipid vesicles when fluid convection is mitigated and quantified. We discuss strategies for enhancing the speed of osmophoresis using high permeability membranes and geometric confinement. 

We derive a perturbation solution to the one-dimensional Poisson–Nernst–Planck (PNP) equations between parallel electrodes under oscillatory polarization for arbitrary ionic mobilities and valences. Treating the applied potential as the perturbation parameter, we show that the second-order solution yields a nonzero time-average electric field at large distances from the electrodes, corroborating the recent discovery of Asymmetric Rectified Electric Fields (AREFs) via numerical solution to the full nonlinear PNP equations [Hashemi Amrei et al. , Phys. Rev. Lett. , 2018, 121 , 185504]. Importantly, the first-order solution is analytic, while the second-order AREF is semi-analytic and obtained by numerically solving a single linear ordinary differential equation, obviating the need for full numerical solutions to the PNP equations. We demonstrate that at sufficiently high frequencies and electrode spacings the semi-analytical AREF accurately captures both the complicated shape and the magnitude of the AREF, even at large applied potentials. 

Microfluidic gradient generators are used to study the movement of living cells, lipid vesicles, and colloidal particles in response to spatial variations in their local chemical environment. Such gradient driven motions are often slow (less than 1 μm s −1 ) and therefore influenced or disrupted by fluid flows accompanying the formation and maintenance of the applied gradient. Even when external flows are carefully eliminated, the solute gradient itself can drive fluid motions due to combinations of gravitational body forces and diffusioosmotic surface forces. Here, we develop a microfluid gradient generator based on the in situ formation of biopolymer membranes and quantify the fluid flows induced by steady solute gradients. The measured velocity profiles agree quantitatively with those predicted by analytical approximations of relevant hydrodynamic models. We discuss how the speed of gradient-driven flows depends on system parameters such as the gradient magnitude, the fluid viscosity, the channel dimensions, and the solute type. These results are useful in identifying and mitigating undesired flows within microfluidic gradient systems. 

Active colloids are a class of microparticles that ‘swim’ through fluids by breaking the symmetry of the force distribution on their surfaces. Our ability to direct these particles along complex trajectories in three-dimensional (3D) space requires strategies to encode the desired forces and torques at the single particle level. Here, we show that spherical colloids with metal patches of low symmetry self-propel along non-linear 3D trajectories when powered remotely by an alternating current (AC) electric field. In particular, particles with triangular patches of approximate mirror symmetry trace helical paths along the axis of the field. We demonstrate that the speed and shape of the particle’s trajectory can be tuned by the applied field strength and the patch geometry. We show that helical motion can enhance particle transport through porous materials with implications for the design of microrobots that can navigate complex environments.

 

Traveling waves of mechanical actuation provide a versatile strategy for locomotion and transport in both natural and engineered systems across many scales. These rhythmic motor patterns are often orchestrated by systems of coupled oscillators such as beating cilia or firing neurons. Here, we show that similar motions can be realized within linear arrays of conductive particles that oscillate between biased electrodes through cycles of contact charging and electrostatic actuation. The repulsive interactions among the particles along with spatial gradients in their natural frequencies lead to phase-locked states characterized by gradients in the oscillation phase. The frequency and wavelength of these traveling waves can be specified independently by varying the applied voltage and the electrode separation. We demonstrate how traveling wave synchronization can enable the directed transport of material cargo. Our results suggest that simple energy inputs can coordinate complex motions with opportunities for soft robotics and colloidal machines.

 

Contact charge electrophoresis (CCEP) uses steady electric fields to drive the oscillatory motion of conductive particles and droplets between two or more electrodes. In contrast to traditional forms of electrophoresis and dielectrophoresis, CCEP allows for rapid and sustained particle motions driven by low-power dc voltages. These attributes make CCEP a promising mechanism for powering active components for mobile microfluidic technologies. This Feature Article describes our current understanding of CCEP as well as recent strategies to harness it for applications in microfluidics and beyond.