Oscillations of flagella and cilia play an important role in biology, which motivates the idea of functional mimicry as part of bio-inspired applications. Nevertheless, it still remains challenging to drive their artificial counterparts to oscillate via a steady, homogeneous stimulus. Combining theory and simulations, we demonstrate a strategy to achieve this goal by using an elasto-electro-hydrodynamic instability. In particular, we show that applying a uniform DC electric field can produce self-oscillatory motion of a microrobot composed of a dielectric particle and an elastic filament. Upon tuning the electric field and filament elasticity, the microrobot exhibits three distinct behaviors: a stationary state, undulatory swimming and steady spinning, where the swimming behavior stems from an instability emerging through a Hopf bifurcation. Our results imply the feasibility of engineering self-oscillations by leveraging the elasto-viscous response to control the type of bifurcation and the form of instability. We anticipate that our strategy will be useful in a broad range of applications imitating self-oscillatory natural phenomena and biological processes.
Under a steady DC electric field of sufficient strength, a weakly conducting dielectric sphere in a dielectric solvent with higher conductivity can undergo spontaneous spinning (Quincke rotation) through a pitchfork bifurcation. We design an object composed of a dielectric sphere and an elastic filament. By solving an elasto-electro-hydrodynamic (EEH) problem numerically, we uncover an EEH instability exhibiting diverse dynamic responses. Varying the bending stiffness of the filament, the composite object displays three behaviours: a stationary state, undulatory swimming and steady spinning, w…
A new model for the interaction of an electric pulse with a lipid membrane is proposed. Using this model we show that when a DC electric pulse is applied to an insulating lipid membrane separating fluids with different conductivities, the capacitive charging current through the membrane drives electrohydrodynamic flow that destabilizes the membrane. The instability is transient and decays as the membrane charges. The bulk conductivity mismatch plays an essential role in this instability because it results in a different rate of charge accumulation on the membrane's physical surfaces. Shearing …
For the first time the electrohydrodynamic convection (EHC) of nematic liquid crystals is studied via fully nonlinear simulation. As a system of rich pattern-formation the EHC is mostly studied with negative nematic liquid crystals experimentally, and sometimes with the help of theoretical instability analysis in the linear regime. Up to now there is only weakly nonlinear simulation for a step beyond the emergence of steady convection rolls. In this work we modify the liquid crystal stochastic rotational model (LC SRD) [Lee et al., J. Chem. Phys., 2015, 142, 164110] to incorporate the field al…
Active droplets can swim spontaneously in viscous flows as a result of the non-linear convective transport of a chemical solute produced at their surface by the Marangoni and/or phoretic flows generated by this solute's inhomogeneous distribution, provided the ratio of convective-to-diffusive solute transport, or Péclet number $\mbox{Pe}$ is large enough. As the result of their net buoyancy, active drops typically evolve at a small finite distance $d$ from rigid boundaries. Yet, existing models systematically focus on unbounded flows, ignoring the effect of the wall proximity on the intrisical…
We combine experiments with simulations to investigate the fluid-structure interaction of a flexible helical rod rotating in a viscous fluid, under low Reynolds number conditions. Our analysis takes into account the coupling between the geometrically nonlinear behavior of the elastic rod with a non-local hydrodynamic model for the fluid loading. We quantify the resulting propulsive force, as well as the buckling instability of the originally helical filament that occurs above a critical rotation velocity. A scaling analysis is performed to rationalize the onset of this instability. A universal…
We investigate the self-propulsive motion of a drop containing an active polar field. The drop demonstrates spontaneous symmetry breaking from a uniform orientational order into a splay or bend instability depending on the types of active stress, namely, contractile or extensile, respectively. We develop the analytical theory of the mechanism of this instability, which has been observed only in numerical simulations. We show that both contractile and extensile active stress result in the instability and self-propulsive motion. We also discuss asymmetry between contractile and extensile stress,…
The swimming of cells, far from any boundary, can arise in the absence of long-range liquid-crystalline order within the cytoplasm, but simple models of this effect are lacking. Here we present a two-dimensional model of droplet self-propulsion involving two scalar fields, representing the cytoplasm and a contractile cortex. An active stress results from coupling between these fields; self-propulsion results when rotational symmetry is spontaneously broken. The swimming speed is predicted, and shown numerically, to vary linearly with the activity parameter and with the droplet area fraction. T…
The influence of an electric field on a poorly conductive membrane such as a lipid bilayer is studied theoretically. The unbalanced electric stress created by an ionic current across a non-perfectly flat membrane gives rise to a destabilizing surface energy enhancing undulations. The deformation of a membrane attached to a frame and the subsequent force on the frame are derived and the electrohydrodynamic instability of a free floating membrane is also studied. We find a most unstable mode of undulation, of wavelength in the $μm$ range, connected to the crossover between membrane and solvent d…
Phoretic mechanisms, whereby gradients of chemical solutes induce surface-driven flows, have recently been used to generate directed propulsion of patterned colloidal particles. When the chemical solutes diffuse slowly, an instability further provides active but isotropic particles with a route to self-propulsion by spontaneously breaking the symmetry of the solute distribution. Here we show theoretically that, in a mechanism analogous to Bénard-Marangoni convection, phoretic phenomena can create spontaneous and self-sustained wall-driven mixing flows within a straight, chemically-uniform acti…
In experiments, an individual chemically active liquid crystal (LC) droplet submerged in the bulk of a surfactant solution may self-propel along a straight, helical, or random trajectory. In this paper, we develop a minimal model capturing all three types of self-propulsion trajectories of a drop in the case of a nematic LC with homeotropic anchoring at LC-fluid interface. We emulate the director field within the drop by a single preferred polarization vector that is subject of two reorientation mechanisms, namely, the internal flow-induced displacement of the hedgehog defect and the droplet's…
Self-propulsion of a Janus droplet in a solution of surfactant, which reacts on a half of a drop surface, is studied theoretically. The droplet acts as a catalytic motor creating a concentration gradient, which generates its surface-tension-driven motion; the self-propulsion speed is rather high, $60\; {\rm μm/s}$ and more. This catalytic motor has several advantages over other micromotors: simple manufacturing, easily attained neutral buoyancy. In contrast to a single-fluid droplet, which demonstrates a self-propulsion as a result of symmetry breaking instability, for Janus one no stability t…
We demonstrate that active rotations in chemically signalling particles, such as autochemotactic {\it E. coli} close to walls, create a route for pattern formation based on a nonlinear yet deterministic instability mechanism. For slow rotations, we find a transient persistence of the uniform state, followed by a sudden formation of clusters contingent on locking of the average propulsion direction by chemotaxis. These clusters coarsen, which results in phase separation into a dense and a dilute region. Faster rotations arrest phase separation leading to a global travelling wave of rotors with …
We study a simple two-dimensional model for motion of an elastic filament subject to internally generated stresses and show that wave-like propagating shapes which can propel the filament can be induced by a self-organized mechanism via a dynamic instability. The resulting patterns of motion do not depend on the microscopic mechanism of the instability but only of the filament rigidity and hydrodynamic friction. Our results suggest that simplified systems, consisting only of molecular motors and filaments could be able to show beating motion and self-propulsion.
Swimmers and self-propelled particles are physical models for the collective behaviour and motility of a wide variety of living systems, such as bacteria colonies, bird flocks and fish schools. Such artificial active materials are amenable to physical models which reveal the microscopic mechanisms underlying the collective behaviour. Here we study colloids in a DC electric field. Our quasi-two-dimensional system of electrically-driven particles exhibits a rich and exotic phase behaviour. At low field strengths, electrohydrodynamic flows lead to self-organisation into crystallites with hexagona…
Since the historical experiments of Crookes, the direct manipulation of matter by light has been both a challenge and a source of scientific debate. Here we show that laser illumination allows to displace a vial of nanoparticle solution over centimetre-scale distances. Cantilever-based force measurements show that the movement is due to millisecond long force spikes, which are synchronised with a sound emission. We observe that the nanoparticles undergo negative thermophoresis, while ultrafast imaging reveals that the force spikes are followed by the explosive growth of a bubble in the solutio…
Motivated by recent experiments on colloidal suspensions, we study analytically and numerically a microscopic model for self-propelled particles lacking alignment interactions. In this model, even for purely repulsive interactions, a dynamical instability leading to phase separation has been reported. Starting from the many-body Smoluchowski equation, we develop a mean-field description based on a novel closure scheme and derive the effective hydrodynamic equations. We demonstrate that the microscopic origin of the instability is a force imbalance due to an anisotropic pair distribution leadin…
We present a comprehensive study of a model system of repulsive self-propelled disks in two dimensions with ferromagnetic and nematic velocity alignment interactions. We characterize the phase behavior of the system as a function of the alignment and self-propulsion strength, featuring orientational order for strong alignment and Motility-Induced Phase Separation (MIPS) at moderate alignment but high enough self-propulsion. We derive a microscopic theory for these systems yielding a close set of hydrodynamic equations from which we perform a linear stability analysis of the homogenous disorder…
Growing, Buckling, and Swirling: motility from polymerization
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（国际理论科学中心，塔塔基础研究所）；Center for Computational Biology, Flatiron Institute（计算生物学中心，平顿研究所）；Courant Institute of Mathematical Sciences, New York University（纽约大学库朗数学科学研究所）
Liquid shells (e.g. double emulsions, vesicles etc.) are susceptible to interfacial instability and rupturing when driven out of mechanical equilibrium. This poses a significant challenge for the design of liquid shell based micro-machines, where the goal is to maintain stability and dynamical control in combination with motility. Here we present our solution to this problem with controllable self-propelling liquid shells, which we have stabilized using the soft topological constraints imposed by a nematogen oil. We demonstrate, through experiments and simulations, that anisotropic elasticity …
We derive a dynamical field theory for self-propelled particles subjected to generic torques and forces by explicitly coarse-graining their microscopic dynamics, described by a many-body Fokker-Planck equation. The model includes both intrinsic torques inducing self-rotation, as well as interparticle torques leading to, for instance, the local alignment of particles' orientations. Within this approach, although the functional form of the pairwise interactions does not need to be specified, one can directly map the parameters of the field theory onto the parameters of particle-based models. We …
