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The dynamics of a spherical particle undergoing Quincke electrorotation in the vicinity of a planar electrode are investigated. Using a multipole representation of the electric field, the influence of the electrode is incorporated through the method of images. Starting from the Taylor–Melcher leaky dielectric model and enforcing conservation of linear and angular momentum, we derive the evolution equations for the electric multipole moments and the particle trajectory. As the first step, a simplified scenario that neglects motion normal to the electrode is considered. Linear stability analysis of this reduced model reveals that the presence of the nearby boundary raises the threshold for Quincke electrorotation and the onset of chaotic dynamics. Numerical simulations of the simplified setting reveal that increasing the electric field induces a transition from steady rolling to periodic and then chaotic oscillations, with the onset threshold depending on the particle–surface gap and particle inertia. Full simulations that also allow normal motion of the particle show that electrostatic attraction reduces the gap, which in turn suppresses chaotic behavior and reestablishes a steady rolling state. 

Bacterial motility is strongly influenced by confinement. Here, we derive an asymptotic solution for the flow about a microswimmer enclosed in a weakly deformable Hele-Shaw drop—a drop sandwiched between two solid planes. For a microswimmer modelled as a dipole, we explore the swimmer’s trajectory, the evolution of the droplet interface and the drop velocity. The results show that at steady state, the dipole induces droplet translation with a velocity independent of the dipole location and in the same direction as the dipole orientation. The trajectory of the swimming dipole is significantly affected by droplet deformability. This article is part of the theme issue ‘Biological fluid dynamics: emerging directions’. 

Uncovering the rules governing the nonequilibrium dynamics of the membranes that define biological cells is of central importance to understanding the physics of living systems. We theoretically and computationally investigate the behavior of flexible quasispherical vesicles that exchange membrane constituents, internal volume, and heat with an external reservoir. The excess chemical potential and osmotic pressure difference imposed by the reservoir act as generalized thermodynamic driving forces that modulate vesicle morphology. We show that the renormalization of membrane mechanical properties by nonequilibrium driving gives rise to a morphological transition between a weakly driven regime, in which growing vesicles remain quasispherical, and a strongly driven regime, in which vesicles accommodate rapid membrane uptake by developing surface wrinkles. Additionally, we propose a minimal vesicle growth-shape law, derived using insights from stochastic thermodynamics, that robustly describes vesicle growth dynamics even in strongly driven, far-from-equilibrium regimes. 

The impact of interfacial deformations on the hydrodynamic force and torque exerted on a spherical particle with surface slip moving along a gas-liquid interface is investigated. Following a two-parameter asymptotic modeling approach, we perturb the interface from its planar state and apply the Lorentz reciprocal theorem to the zeroth- and first-order approximations to analytically calculate the drag and torque on the particle. This allows us to explicitly account for the effect of physical parameters like the three-phase contact angle, the Bond number, and the slip coefficient on the particle motion. In addition, we study the interactions between two translating and rotating particles at a large separation. The interaction forces and torques exerted by the flow-induced deformations are calculated via the linear superposition approximation, where the interaction forces are identified as dipolar in terms of the azimuthal angle. 

The encapsulation of active particles, such as bacteria or active colloids, inside a droplet gives rise to a non-trivial shape dynamics and droplet displacement. To understand this behaviour, we derive an asymptotic solution for the fluid flow about a deformable droplet containing an active particle, modelled as a Stokes-flow singularity, in the case of small shape distortions. We develop a general solution for any Stokes singularity and apply it to compute the flows and resulting droplet velocity due to common singularity representations of active particles, such as Stokeslets, rotlets and stresslets. The results show that offsetting of the active particle from the centre of the drop breaks symmetry and excites a large number of generally non-axisymmetric shape modes as well as particle and droplet motion. In the case of a swimming stresslet singularity, a run-and-tumble locomotion results in superdiffusive droplet displacement. The effect of interfacial properties is also investigated. Surfactants adsorbed at the droplet interface counteract the internal flow and arrest the droplet motion for all Stokes singularities except the Stokeslet. Our results highlight strategies to steer the flows of active particles and create autonomously navigating containers. 

Dense suspensions of Quincke random walkers exhibit turbulent-like flows mimicking those of bacterial suspensions. 

Nonlinear electrokinetic phenomena, where electrically driven fluid flows depend nonlinearly on the applied voltage, are commonly encountered in aqueous suspensions of colloidal particles. A prime example is the induced-charge electro-osmosis, driven by an electric field acting on diffuse charge induced near a polarizable surface. Nonlinear electrohydrodynamic flows also occur in non-polar fluids, driven by the electric field acting on space charge induced by conductivity gradients. Here, we analyse the flows about a charge-neutral spherical solid particle in an applied uniform electric field that arise from conductivity dependence on local field intensity. The flow pattern varies with particle conductivity: while the flow about a conducting particle has a quadrupolar pattern similar to induced-charge electro-osmosis, albeit with opposite direction, the flow about an insulating particle has a more complex structure. We find that this flow induces a force on a particle near an electrode that varies non-trivially with particle conductivity: while it is repulsive for perfectly insulating particles and particles more conductive than the suspending medium, there exists a range of particle conductivities where the force is attractive. The force decays as the inverse square of the distance to the electrode and thus can dominate the dielectrophoretic attraction due to the image dipole, which falls off with the fourth power with the distance. This electrohydrodynamic lift opens new possibilities for colloidal manipulation and driven assembly by electric fields. 

Abstract Living cells can adapt their shape in response to their environment, a process driven by the interaction between their flexible membrane and the activity of the underlying cytoskeleton. However, the precise physical mechanisms of this coupling remain unclear. Here we show how cytoskeletal forces acting on a biomimetic membrane affect its deformations. Using a minimal cell model that consists of an active network of microtubules and molecular motors encapsulated inside lipid vesicles, we observe large shape fluctuations and travelling membrane deformations. Quantitative analysis of membrane and microtubule dynamics demonstrates how active forces set the temporal scale of vesicle fluctuations, giving rise to fluctuation spectra that differ in both their spatial and temporal decays from their counterparts in thermal equilibrium. Using simulations, we extend the classical framework of membrane fluctuations to active cytoskeleton-driven vesicles, demonstrating how correlated activity governs membrane dynamics and the roles of confinement, membrane material properties and cytoskeletal forces. Our findings provide a quantitative foundation for understanding the shape-morphing abilities of living cells.