Michael J. Miksis

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.

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).

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 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.

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.

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

Stephen H. Davis (1939–2021) was an applied mathematician, fluid dynamicist, and materials scientist who lead the field in his contributions to interfacial dynamics, thermal convection, thin films, and solidification for over 50 years. Here, we briefly review his personal and professional life and some of his most significant contributions to the field.

, 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.