Petia M. Vlahovska

We theoretically investigate the thermally-driven curvature and lipid density fluctuations of a quasi-spherical vesicle, accounting for the dissipation due to monolayer viscosity and intermonolayer friction. The theory predicts that membrane curvature makes long-wavelength undulations sensitive to membrane viscosity and speeds up the relaxation of the lipid density fluctuations. Implications for the dynamic roughness and Dynamic Structure Factor measurements of submicron liposomes on nano-second time scales are discussed. Specifically, a clear stretched-exponential relaxation regime may not exist, in contrast to the behavior of planar membranes for which an anomalous diffusion exponent of 2/3 has been predicted [Zilman and Granek, Phys. Rev. Lett. (1996)].

We theoretically investigate the thermally-driven curvature and lipid density fluctuations of a quasi-spherical vesicle, accounting for the dissipation due to monolayer viscosity and intermonolayer friction. The theory predicts that membrane curvature makes long-wavelength undulations sensitive to membrane viscosity and speeds up the relaxation of the lipid density fluctuations. Implications for the dynamic roughness and Dynamic Structure Factor measurements of submicron liposomes on nano-second time scales are discussed. Specifically, a clear stretched-exponential relaxation regime may not exist, in contrast to the behavior of planar membranes for which an anomalous diffusion exponent of 2/3 has been predicted [Zilman and Granek, Phys. Rev. Lett. (1996)].

For almost 30 years, the Zilman–Granek stretched exponential [Zilman & Granek (1996). Phys. Rev. Lett. 77 , 4788–4791] has been used to obtain bending rigidities of membranes in lipid and surfactant vesicles from neutron spin echo data. However, with the advent of improved spectrometers that can easily measure Fourier times up to some 100 ns and even 1 µs, more subtle effects become visible in the data, which requires a refined theory. Recently, we published a framework for analysing such neutron spin echo data [Granek et al. (2024). Eur. Phys. J. E 47 , 12]. Here, we apply this framework to different model membranes. The purpose of this paper is twofold. We intend to elucidate some often overlooked parameters, such as vesicle diffusion, size, lamellarity and membrane tension, that limit the quantitative interpretation of bending modulus values from NSE data. We also present some future opportunities to better understand the membrane dynamics and major sources of dissipation at the nanoscale uniquely probed with NSE.

A new theory for the thermally driven shape fluctuations of a quasi-spherical vesicle, accounting for dissipation due to membrane viscosity.

The linear stability of a lipid membrane under a DC electric field, applied perpendicularly to the interface, is investigated in the electrokinetic framework, taking account to the dynamics of the Debye layers formed near the membrane. The perturbed charge in the Debye layer redistributes and destabilizes the membrane via electrical surface stress interior and exterior to the membrane. The instability is suppressed as the difference in the electrolyte concentration of the solutions separated by the membrane increases, due to a weakened base state electric field near the membrane. This result contrasts with the destabilizing effect predicted using the leaky dielectric model in cases of asymmetric conductivity. We attribute this difference to the varying assumptions about the perturbation amplitude relative to the Debye length, which result in different regimes of validity for the linear stability analysis within these two frameworks.

The hydrodynamic force and torque exerted on a moving spherical particle with surface slip and a three-phase contact angle on a gas-liquid interface is investigated. Perturbation theory is employed to estimate the drag and torque on the particle in the limit of small capillary number and small deviations of the contact angle from 90 degrees. The interactions between two translating and rotating particles at a large separation distance are also examined.

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'.

The physical properties of lipid membranes are essential to cellular function, with membrane fluidity playing a key role in the mobility of embedded biomolecules. Fluidity is governed by the membrane's phase state, which is known to depend on composition and temperature. However, in living cells, the transmembrane electric potential may also influence membrane fluidity. In this study, we use giant unilamellar vesicles composed of dimyristoylphosphatidylcholine (DMPC) to examine the membrane's response to electric fields near its main phase transition temperature. Below the transition temperature, the vesicle remains undeformed indicating a bilayer in the gel phase. However, near the transition, the vesicle elongates into an ellipsoid and the evolution of the aspect ratio exhibits a two-step response: an initial rapid increase followed by a slower elongation. Electrodeformation experiments at various temperatures relative to the transition temperature Tm reveal that the duration of the fast step increases as the temperature approaches Tm , and the slow step vanishes for a bilayer the fluid phase. We attribute the initial rapid response to the fluid phase and the subsequent slow response to a thermal expansion induced by Joule heating from the electric field.

An isolated charge-neutral drop suspended in an unbounded medium does not migrate in a uniform DC electric field. A nearby wall breaks the symmetry and causes the drop to drift towards or away from the boundary, depending on the electric properties of the fluids and the wall. In the case of an electrically insulating wall and an electric field applied tangentially to the wall, the interaction of the drop with its electrostatic image gives rise to repulsion by the wall. However, the electrohydrodynamic flow causes either repulsion for a drop with $\mathrm{R/P}<1$, where $\mathrm{R}$ and $\mathrm{P}$ are the drop-to-medium ratios of conductivity and permittivity, respectively, or attraction for $\mathrm{R/P}>1$. We experimentally measure droplet trajectories and quantify the wall-induced electrohydrodynamic lift in the case $\mathrm{R/P}<1$. Numerical simulations using the boundary integral method agree well with the experiment and also explore the $\mathrm{R/P}>1$ case. The results show that the lateral migration of a drop in a uniform electric field applied parallel to an insulating wall is dominated by the long-range flow due to the image stresslet.

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.

Cells and cellular organelles are encapsulated by nanometrically thin membranes whose main component is a lipid bilayer. In the presence of electric fields, the ion-impermeable lipid bilayer acts as a capacitor and supports a potential difference across the membrane. We analyze the charging dynamics of a planar membrane separating bulk solutions with different electrolyte concentrations upon the application of an applied uniform dc electric field. The membrane is modeled as a zero-thickness capacitive interface. The evolution of the electric potential and ion distributions in the bulk are solved for using the Poisson-Nernst-Planck equations. Asymptotic solutions are derived in the limit of thin Debye layers and weak fields (compared to the thermal electric potential).

An isolated charge-neutral drop suspended in an unbounded medium does not migrate in a uniform DC electric field. A nearby wall breaks the symmetry and causes the drop to drift towards or away from the boundary, depending on the electric properties of the fluids and the wall. In the case of an electrically insulating wall and an electric field applied tangentially to the wall, the interaction of the drop with its electrostatic image gives rise to repulsion by the wall. However, the electrohydrodynamic flow causes either repulsion for a drop with $\mathrm{R/P}&lt;1$, where $\mathrm{R}$ and $\mathrm{P}$ are the drop-to-medium ratios of conductivity and permittivity, respectively, or attraction for $\mathrm{R/P}&gt;1$. We experimentally measure droplet trajectories and quantify the wall-induced electrohydrodynamic lift in the case $\mathrm{R/P}&lt;1$. Numerical simulations using the boundary integral method agree well with the experiment and also explore the $\mathrm{R/P}&gt;1$ case. The results show that the lateral migration of a drop in a uniform electric field applied parallel to an insulating wall is dominated by the long-range flow due to the image stresslet.

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.

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.

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 bacterial suspensions exhibit turbulent-like flows at low Reynolds numbers, driven by the activity of the microswimmers. In this study, we develop a model system to examine these dynamics using motile colloids that mimic bacterial locomotion. The colloids are powered by the Quincke instability, which causes them to spontaneously roll in a random-walk pattern when exposed to a square-wave electric field. We experimentally investigate the flow dynamics in dense suspensions of these Quincke random walkers under quasi two-dimensional conditions, where the particle size is comparable to the gap between the electrodes. Our results reveal an energy spectrum scaling at high wavenumbers as $ \sim k^{-4}$, which holds across a broad range of activity levels -- controlled by the field strength -- and particle concentrations. We observe that velocity time correlations decay within a single period of the square-wave field, yet an anti-correlation appears between successive field applications, indicative of a dynamic structural memory of the ensemble.

at high wavenumbers, observed consistently across activity levels and particle concentrations. We observe that velocity time correlations decay within a single period of the square-wave field, yet an anti-correlation appears between successive field applications, indicative of a dynamic structural memory of the ensemble.

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.

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 analyze 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 particle and particles more conductive than the suspending medium, there exists a range of particle conductivities where the force is attractive. The force decays as 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.

The biological function of membranes is closely related to their softness, which is often studied through the membranes' thermally driven fluctuations. Typically, the analysis assumes that the relaxation rate of a pure bending deformation is determined by the competition between membrane bending rigidity and viscous dissipation in the surrounding medium. Here, we reexamine this assumption and demonstrate that viscous flows within the membrane dominate the dynamics of bending fluctuations of nonplanar membranes with a radius of curvature smaller than the Saffman-Delbrück length. Using flickering spectroscopy of giant vesicles made of dipalmitoylphosphatidylcholine, DPPC:cholesterol mixtures and pure diblock-copolymer membranes, we experimentally detect the signature of membrane dissipation in curvature fluctuations. We show that membrane viscosity can be reliably obtained from the short time behavior of the shape time correlations. The results indicate that the DPPC:cholesterol membranes behave as a Newtonian fluid, while the polymer membranes exhibit more complex rheology. Our study provides physical insights into the time scales of curvature remodeling of biological and synthetic membranes.

The dynamics of colloid-size particles trapped at a liquid interface is an extensively studied problem owing to its relevance to a wide range of engineering applications. Here we investigate 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. 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.

As a core component of biological and synthetic membranes, lipid bilayers are key to compartmentalizing chemical processes. Bilayer morphology and mechanical properties are heavily influenced by electric fields, such as those caused by biological ion concentration gradients. We present atomistic simulations exploring the effects of electric fields applied normally and laterally to lipid bilayers. We find that normal fields decrease membrane tension, while lateral fields increase it. Free energy perturbation calculations indicate the importance of dipole-dipole interactions to these tension changes, especially for lateral fields. We additionally show that membrane area compressibilities can be related to their cohesive energies, allowing us to estimate changes in membrane bending rigidity under applied fields. We find that normal and lateral fields decrease and increase bending rigidity, respectively. These results point to the use of directed electric fields to locally control membrane stiffness, thereby modulating associated cellular processes.

The encapsulation of active particles, such as bacteria or active colloids, inside a droplet gives rise to nontrivial shape dynamics and droplet motility. To understand this behavior, we derive an asymptotic solution for the fluid flow about a deformable droplet containing an active particle, modeled as a Stokes-flow singularity, in the case of small shape distortions. Offsetting of the active particle from the center of the drop breaks symmetry and leads to excitation of large number of shape modes as well as particle and drop displacement. Flows due to common singularity representations of active particles, such as Stokeslets, rotlets, and stresslets, are computed and compared to results for non-deformable droplets enclosing active particles. The effect of interfacial properties is also investigated. Surfactants adsorbed at the droplet interface immobilize the interface and arrest the droplet motion. Our results highlight strategies to steer the flows of active particles and create autonomously navigating containers.

We conduct a systematic exploration of the energy landscape of vesicle morphologies within the framework of the Helfrich model. Vesicle shapes are determined by minimizing the elastic energy subject to constraints of constant area and volume. The results show that pressurized vesicles can adopt higher-energy spindle-like configurations that require the action of point forces at the poles. If the internal pressure is lower than the external one, multilobed shapes are predicted. We utilize our results to rationalize experimentally observed spindle shapes of giant vesicles in a uniform AC electric field.

Biological cells exhibit the remarkable ability to adapt their shape in response to their environment, a phenomenon that hinges on the intricate interplay between their deformable membrane and the underlying activity of their cytoskeleton. Yet, the precise physical mechanisms of this coupling remain mostly elusive. Here, we introduce a synthetic cell model, comprised of an active cytoskeletal network of microtubules, crosslinkers and molecular motors encapsulated inside giant vesicles. Remarkably, these active vesicles exhibit large shape fluctuations and life-like morphing abilities. Active forces from the encapsulated cytoskeleton give rise to large-scale traveling membrane deformations. Quantitative analysis of membrane and microtubule fluctuations shows how the intricate coupling of confinement, membrane material properties and cytoskeletal forces yields fluctuation spectra whose characteristic scales in space and time are distinctly different from passive vesicles. We demonstrate how activity leads to uneven probability fluxes between fluctuation modes and hence sets the temporal scale of membrane fluctuations. Using simulations and theoretical modelling, we extend the classical approach to membrane fluctuations to active cytoskeleton-driven vesicles, highlighting the effect of correlated activity on the dynamics of membrane deformations and paving the way for quantitative descriptions of the shape-morphing ability typical of living systems.

The interaction of fluids and electric fields is at the heart of natural phenomena such as disintegration of raindrops in thunderstorms and many applications such as ink-jet printing, microfluidics, crude oil demulsification, and electrosprays. Many of these processes involve droplets and there has been a long-standing interest in understanding drop electrohydrodynamics. While an isolated drop in applied electric fields has been extensively studied, the behavior of many drops is largely unexplored. Even the pair-wise drop interactions have received scant attention and existing models are limited to axisymmetric and two-dimensional geometries. In three dimensions, the electrohydrodynamic interactions can be quite complex and non-trivial. For example, in an applied uniform electric field, instead of chaining along the field direction, drops can initially attract in the direction of the field and move towards each other, but then separate in the transverse direction [1]. Using a combination of numerical simulations based on a boundary integral formulation and an analytical theory assuming small drop deformations, we study the dynamics of a drop pair in an applied uniform electric field at arbitrary orientation of their line-of-centers relative to the applied field direction. For identical drops covered with insoluble surfactant [2], we find that the surfactant weakens the electrohydrodynamic flow and thus dielectrophoretic interactions play more prominent role in the dynamics of surfactant-covered drops compared to clean drops. If drop conductivity is the same as the suspending fluid, a nondiffusing surfactant can arrest the drops' relative motion thereby effectively preventing coalescence. Drop dissimilarity can also have profound effect on the pair dynamics: we find that in some cases droplets can form a stable pair (tandem) that “swims” either parallel or perpendicular to the applied field direction [3]. If time permits, I will discuss particle-particle and particle-wall interactions driven by electrohydrodynamic flows due to the Onsager effect.

2 MoreReceived 21 June 2023DOI:https://doi.org/10.1103/PhysRevFluids.8.089901©2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasContact line dynamicsFluid-particle interactionsLow Reynolds number flowsFluid Dynamics

, 034607]. Here, we investigate the effect of a second boundary because of its common occurrence in practical applications. We consider a spherical particle suspended between two parallel walls and subjected to a uniform electric field, applied in a direction either normal or tangential to the surfaces. All media are modeled as leaky dielectrics, thus allowing for the accumulation of free charge at interfaces, while bulk media remain charge-free. The Laplace equation for the electric potential is solved using a multipole expansion and the boundaries are accounted for by a set of images. The results show that in the case of a normal electric field, which corresponds to a particle between two electrodes, the force is always attractive to the nearer boundary and, in general, weaker that the case of only one wall. Intriguingly, for a given particle-wall separation we find that the force may vary nonmonotonically with confinement and its magnitude may exceed the one-wall value. In the case of tangential electric field, which corresponds to a particle between insulating boundaries, the force follows the same trends but it is always repulsive.