Capillary-driven horseshoe vortex forming around a micro-pillar.

HYPOTHESIS: Horseshoe vortices are known to emerge around large-scale obstacles, such as bridge pillars, due to an inertia-driven adverse pressure gradient forming on the upstream-side of the obstacle. We contend that a similar flow structure can arise in thin-film Stokes flow around micro-obstacles, such as used in textured surfaces to improve wettability. This could be exploited to enhance mixing in microfluidic devices, typically limited to creeping-flow regimes. EXPERIMENTS: Numerical simulations based on the Navier-Stokes equations are carried out to elucidate the flow structure associated with the wetting dynamics of a liquid film spreading around a 50 µm diameter micro-pillar. The employed multiphase solver, which is based on the volume of fluid method, accurately reproduces the wetting dynamics observed in current and previous (Mu et al., Langmuir, 2019) experiments. FINDINGS: The flow structure within the liquid meniscus forming at the foot of the micro-pillar evinces a horseshoe vortex wrapping around the obstacle, notwithstanding that the Reynolds number in our system is extremely low. Here, the adverse pressure gradient driving flow reversal near the bounding wall is caused by capillarity instead of inertia. The horseshoe vortex is entangled with other vortical structures, leading to an intricate flow system with high-potential mixing capabilities.

Thermoelectric instabilities in a circular Couette flow.

The stability of a non-isothermal circular Couette flow is analyzed when subjected to a dielectrophoretic force field. Outward and inward heating configurations are considered when the inner cylinder is rotating and the outer cylinder is at rest. In addition, an alternating voltage is applied between the two cylinders to induce a radial electric buoyancy that acts on the dielectric fluid. The linear stability analysis provides the threshold for the first transition to instability, as well as the corresponding wavenumber and frequency of the modes. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (part 1)'.

Linear stability of a circular Couette flow under a radial thermoelectric body force.

The stability of the circular Couette flow of a dielectric fluid is analyzed by a linear perturbation theory. The fluid is confined between two concentric cylindrical electrodes of infinite length with only the inner one rotating. A temperature difference and an alternating electric tension are applied to the electrodes to produce a radial dielectrophoretic body force that can induce convection in the fluid. We examine the effects of superposition of this thermoelectric force with the centrifugal force including its thermal variation. The Earth's gravity is neglected to focus on the situations of a vanishing Grashof number such as microgravity conditions. Depending on the electric field strength and of the temperature difference, critical modes are either axisymmetric or nonaxisymmetric, occurring in either stationary or oscillatory states. An energetic analysis is performed to determine the dominant destabilizing mechanism. When the inner cylinder is hotter than the outer one, the circular Couette flow is destabilized by the centrifugal force for weak and moderate electric fields. The critical mode is steady axisymmetric, except for weak fields within a certain range of the Prandtl number and of the radius ratio of the cylinders, where the mode is oscillatory and axisymmetric. The frequency of this oscillatory mode is correlated with a Brunt-Väisälä frequency due to the stratification of both the density and the electric permittivity of the fluid. Under strong electric fields, the destabilization by the dielectrophoretic force is dominant, leading to oscillatory nonaxisymmetric critical modes with a frequency scaled by the frequency of the inner-cylinder rotation. When the outer cylinder is hotter than the inner one, the instability is again driven by the centrifugal force. The critical mode is axisymmetric and either steady under weak electric fields or oscillatory under strong electric fields. The frequency of the oscillatory mode is also correlated with the Brunt-Väisälä frequency.

Heat transfer in the thermo-electro-hydrodynamic convection under microgravity conditions.

This article deals with the thermal convection in a dielectric fluid confined in a finite-length plane capacitor with a temperature gradient under microgravity conditions. The dielectrophoretic force resulting from differential polarization of the fluid plays the role of buoyancy force associated with an electric effective gravity. It induces the convection when the Rayleigh number based on this electric gravity exceeds a critical value. Two-dimensional numerical simulation for a geometry with a large aspect ratio is used to determine the convective flow in the saturated state. The Nusselt number Nu is computed for a wide range of Prandtl number (0.01 ≤ Pr ≤ 10(3)) and its dependence on the distance from the critical condition is determined. A correlation between Nu and Pr in the vicinity of criticality is obtained and compared with that of the Rayleigh-Bénard convection. The behavior of the convection is analyzed in detail from an energetic viewpoint: electrostatic energy, power inputs by different components of the electric gravity and viscous and thermal dissipations are computed.

Dielectrophoretic Rayleigh-Bénard convection under microgravity conditions.

Thermal convection in a dielectric fluid layer between two parallel plates subjected to an alternating electric field and a temperature gradient is investigated under microgravity conditions. A thermoelectric coupling resulting from the thermal variation of the electric permittivity of the fluid produces the dielectrophoretic (DEP) body force, which can be regarded as thermal buoyancy due to an effective gravity. This electric gravity can destabilize a stationary conductive state of the fluid to develop convection. The similarity of the DEP thermal convection with the Rayleigh-Bénard (RB) convection is examined by considering its behavior in detail by a linear stability theory and a two-dimensional direct numerical simulation. The results are analyzed from an energetic viewpoint and in the framework of the Ginzburg-Landau (GL) equation. The stabilizing effects of a thermoelectric feedback make the critical parameters different from those in the RB instability. The nonuniformity of the electric gravity arising from the finite variation of permittivity also affects the critical parameters. The characteristic constants of the GL equation are comparable with those for the RB convection. The heat transfer in the DEP convection is weaker than in the RB convection as a consequence of the feedback that impedes the convection.

Pattern formation in bubbles emerging periodically from a liquid free surface.

Patterns formed by centimeter scale bubbles on the free surface of a viscous liquid are investigated in a cylindrical container. These bubbles emerge periodically at the surface and interact with each other in the central zone. Their radial emission, due to interaction and radial surface flow, leads to the formation of a variety of patterns. Different star-like and spiral patterns appear spontaneously by increasing the bubble emergence frequency. It is found that these patterns are due to a constant angular shift in the bubble emission direction. Measurements of this angular shift show a supercritical bifurcation accompanied by a transition from a pattern of two opposed straight arms to spiral patterns. By applying the tools and concepts from the study of leaf arrangement in botany (phyllotaxis), the recognized patterns and the mechanism of the pattern formation are discussed. Close similarities to the leaf arrangement are found in the behavior of the angular shift and the patterns. These findings suggest that the observed patterns are formed by a packing mechanism of successively appearing elements (bubbles), which is similar to that of the leaves at the earliest stage of phyllotaxis.

Bubble splitting in oscillatory flows on ground and in reduced gravity.

The stability of centimeter scale air bubbles is studied in quiescent suspending liquid under an imposed oscillatory acceleration field. Experiments were performed in reduced- and normal-gravity environments. A strong acceleration resulted in an instability leading to the breakups of the bubbles in both gravity environments. The breakup onset was investigated and found to be characterized by a critical acceleration a (cr). The influence of the liquid viscosity and the gravitational environment was studied. Empirical correlations for the onset are presented and discussed with the intention to reveal splitting mechanism. The inertial mechanism often deemed to cause the breakup of drops subjected to a rapid gas stream is shown to give explanations consistent with the experiments. A breakup criterion for both gravitational environments is proposed through discussions from an energetic point of view.