Lattice Boltzmann Simulations of Multiphase Dielectric Fluids.

The dynamic effect of an electric field on dielectric liquids is called liquid dielectrophoresis. It is widely used in several industrial and scientific applications, including inkjet printing, microfabrication, and optical devices. Numerical simulations of liquid-dielectrophoresis are necessary to understand the fundamental physics of the phenomenon, but also to explore situations that might be difficult or expensive to implement experimentally. However, such modeling is challenging, as one needs to solve the electrostatic and fluid dynamics equations simultaneously. Here, we formulate a new lattice-Boltzmann method capable of modeling the dynamics of immiscible dielectric fluids coupled with electric fields within a single framework, thus eliminating the need of using separate algorithms to solve the electrostatic and fluid dynamics equations. We validate the numerical method by comparing it with analytical solutions and previously reported experimental results. Beyond the benchmarking of the method, we study the spreading of a droplet using a dielectrowetting setup and quantify the mechanism driving the variation of the apparent contact angle of the droplet with the applied voltage. Our method provides a useful tool to study liquid-dielectrophoresis and can be used to model dielectric fluids in general, such as liquid-liquid and liquid-gas systems.

Near Axisymmetric Partial Wetting Using Interface-Localized Liquid Dielectrophoresis.

The wetting of solid surfaces can be modified by altering the surface free energy balance between the solid, liquid, and vapor phases. Liquid dielectrophoresis (L-DEP) can produce wetting on normally nonwetting surfaces, without modification of the surface topography or chemistry. L-DEP is a bulk force acting on the dipoles of a dielectric liquid and is not normally considered to be a localized effect acting at the interface between the liquid and a solid or other fluid. However, if this force is induced by a nonuniform electric field across a solid-liquid interface, it can be used to enhance and control the wetting of a dielectric liquid. Recently, it was reported theoretically and experimentally that this approach can cause a droplet of oil to spread along parallel interdigitated electrodes thus forming a stripe of liquid. Here we show that by using spiral-shaped electrodes actuated with four 90° successive phase-shifted signals, a near axisymmetric spreading of droplets can be achieved. Experimental observations show that the induced wetting can achieve film formation, an effect not possible with electrowetting. We show that the spreading is reversible thus enabling a wide range of partial wetting droplet states to be achieved in a controllable manner. Furthermore, we find that the cosine of the contact angle has a quadratic dependence on applied voltage during spreading and deduce a scaling law for the dependence of the strength of the effect on the electrode size.

Dielectrophoresis-driven spreading of immersed liquid droplets.

In recent years electrowetting-on-dielectric (EWOD) has become an effective tool to control partial wetting. EWOD uses the liquid-solid interface as part of a capacitive structure that allows capacitive and interfacial energies to adjust by changes in wetting when the liquid-solid interface is charged due to an applied voltage. An important aspect of EWOD has been its applications in microfluidics in chemistry and biology and in optical devices and displays in physics and engineering. Many of these rely on the use of a liquid droplet immersed in a second liquid due to the need either for neutral buoyancy to overcome gravity and shield against impact shocks or to encapsulate the droplet for other reasons, such as in microfluidic-based DNA analyses. Recently, it has been shown that nonwetting oleophobic surfaces can be forcibly wetted by nonconducting oils using nonuniform electric fields and an interface-localized form of liquid dielectrophoresis (dielectrowetting). Here we show that this effect can be used to create films of oil immersed in a second immiscible fluid of lower permittivity. We predict that the square of the thickness of the film should obey a simple law dependent on the square of the applied voltage and with strength dependent on the ratio of difference in permittivity to the liquid-fluid interfacial tension, Δε/γ(LF). This relationship is experimentally confirmed for 11 liquid-air and liquid-liquid combinations with Δε/γ(LF) having a span of more than two orders of magnitude. We therefore provide fundamental understanding of dielectrowetting for liquid-in-liquid systems and also open up a new method to determine liquid-liquid interfacial tensions.

Weak-anchoring effects in a thin pinned ridge of nematic liquid crystal.

A theoretical investigation of weak-anchoring effects in a thin two-dimensional pinned static ridge of nematic liquid crystal resting on a flat solid substrate in an atmosphere of passive gas is performed. Specifically, we solve a reduced version of the general system of governing equations recently derived by Cousins et al. [Proc. R. Soc. A 478, 20210849 (2022)10.1098/rspa.2021.0849] valid for a symmetric thin ridge under the one-constant approximation of the Frank-Oseen bulk elastic energy with pinned contact lines to determine the shape of the ridge and the behavior of the director within it. Numerical investigations covering a wide range of parameter values indicate that the energetically preferred solutions can be classified in terms of the Jenkins-Barratt-Barbero-Barberi critical thickness into five qualitatively different types of solution. In particular, the theoretical results suggest that anchoring breaking occurs close to the contact lines. The theoretical predictions are supported by the results of physical experiments for a ridge of the nematic 4^{'}-pentyl-4-biphenylcarbonitrile (5CB). In particular, these experiments show that the homeotropic anchoring at the gas-nematic interface is broken close to the contact lines by the stronger rubbed planar anchoring at the nematic-substrate interface. A comparison between the experimental values of and the theoretical predictions for the effective refractive index of the ridge gives a first estimate of the anchoring strength of an interface between air and 5CB to be (9.80±1.12)×10^{-6}Nm^{-1} at a temperature of (22±1.5)^{∘}C.

Diffraction grating with suppressed zero order fabricated using dielectric forces.

An electric-field-assisted method to produce diffractive optical devices is demonstrated. A uniform film of liquid UV curable resin was produced as a drying ring from an organic solvent. Dielectrophoresis forces maintained the stability of the thin film and also imprinted a periodic corrugation deformation of pitch 20 µm on the film surface. Continuous in situ voltage-controlled adjustment of the optical diffraction pattern was carried out simultaneously with UV curing. A fully cured solid phase grating was produced with the particular voltage-selected tailored optical property that the zero transmitted order was suppressed for laser light at 633 nm.

Controlling the breakup of toroidal liquid films on solid surfaces.

The breakup of a slender filament of liquid driven by surface tension is a classical fluid dynamics stability problem that is important in many situations where fine droplets are required. When the filament is resting on a flat solid surface which imposes wetting conditions the subtle interplay with the fluid dynamics makes the instability pathways and mode selection difficult to predict. Here, we show how controlling the static and dynamic wetting of a surface can lead to repeatable switching between a toroidal film of an electrically insulating liquid and patterns of droplets of well-defined dimensions confined to a ring geometry. Mode selection between instability pathways to these different final states is achieved by dielectrophoresis forces selectively polarising the dipoles at the solid-liquid interface and so changing both the mobility of the contact line and the partial wetting of the topologically distinct liquid domains. Our results provide insights into the wetting and stability of shaped liquid filaments in simple and complex geometries relevant to applications ranging from printing to digital microfluidic devices.

Not spreading in reverse: The dewetting of a liquid film into a single drop.

Wetting and dewetting are both fundamental modes of motion of liquids on solid surfaces. They are critically important for processes in biology, chemistry, and engineering, such as drying, coating, and lubrication. However, recent progress in wetting, which has led to new fields such as superhydrophobicity and liquid marbles, has not been matched by dewetting. A significant problem has been the inability to study the model system of a uniform film dewetting from a nonwetting surface to a single macroscopic droplet-a barrier that does not exist for the reverse wetting process of a droplet spreading into a film. We report the dewetting of a dielectrophoresis-induced film into a single equilibrium droplet. The emergent picture of the full dewetting dynamics is of an initial regime, where a liquid rim recedes at constant speed and constant dynamic contact angle, followed by a relatively short exponential relaxation of a spherical cap shape. This sharply contrasts with the reverse wetting process, where a spreading droplet follows a smooth sequence of spherical cap shapes. Complementary numerical simulations and a hydrodynamic model reveal a local dewetting mechanism driven by the equilibrium contact angle, where contact line slip dominates the dewetting dynamics. Our conclusions can be used to understand a wide variety of processes involving liquid dewetting, such as drop rebound, condensation, and evaporation. In overcoming the barrier to studying single film-to-droplet dewetting, our results provide new approaches to fluid manipulation and uses of dewetting, such as inducing films of prescribed initial shapes and slip-controlled liquid retraction.

Surface-stabilized ferroelectric liquid-crystal diffraction gratings with micrometer-scale pitches.

The first-order diffraction efficiency eta1 of surface-stabilized ferroelectric liquid-crystal (SSFLC) phase gratings is calculated for device thicknesses in the range d = 1 to 5 microm and for pitches p of 5 to 20 microm assuming incident light at 633 nm. The peak value of eta1 as a function of d has negligible dependence on the incoming polarization when p = 20 microm. For smaller pitch values the peak value of eta1 decreases and becomes increasingly dependent on the orientation of the incoming polarization owing to the influence of the domain walls that occur between the SSFLC pixels.

Calculation of the efficiency of polarization-insensitive surface-stabilized ferroelectric liquid-crystal diffraction gratings.

A rigorous analysis is presented of the diffraction efficiency of a polarization-insensitive surface-stabilized ferroelectric liquid-crystal (SSFLC) phase grating, taking full account of the internal structure of the ferroelectric liquid-crystal layer. When no field is applied, the twisted director profile in the relaxed state gives an optimum diffraction efficiency for a device thickness between the half-wave-plate and the full-wave-plate conditions. The influence of the magnitude of the spontaneous polarization and applied ac fields are investigated, and it is shown that the diffraction efficiency of a binary SSFLC phase grating can be strongly enhanced with the technique of ac stabilization.