Session B53: Drops, Bubbles and Interfacial Fluid Mechanics

Acoustical vortices on a Chip for 3D single particle manipulation and vorticity control.

Surface acoustic waves offer most of the basic functions required for on-chip actuation of fluids at small scales: efficient flow mixing, integrated pumping, particles separation, droplet displacement, atomization, division and fusion. Nevertheless some more advanced functions such as 3D particles manipulation and vorticity control require the introduction of some specific kind of waves called acoustic vortices. These helical waves propagate spinning around a phase singularity called the dark core. On the one hand, the beam angular momentum can be transferred to the fluid and create point-wise vorticity for confined mixing, and on the other the dark core can trap individual particles in an acoustic well for single object manipulation. In this presentation, I will show how acoustical vortices on-a-chip can be synthesized with a programmable electronics and an array of transducers \footnote{A. Riaud, J.-L. Thomas, E. Charron, A. Bussonniere, O. Bou Matar, M. Baudoin Phys. Rev. Applied 4, 034004 (2015)}. I will then highlight how some of their specificities \footnote{A. Riaud, J.-L. Thomas, O. Bou Matar, M. Baudoin Phys. Rev. E - Accepted for publication} can be used for acoustical tweezing and twisting.   

\textbf{Coalescence-induced jumping of nanoscale droplets on super-hydrophobic surfaces}

The coalescence-induced jumping of tens of microns size droplets on super-hydrophobic surfaces has been observed in both experiments and simulations. However, whether the coalescence-induced jumping would occur for smaller, particularly nanoscale droplets, is an open question. Using molecular dynamics simulations, we demonstrate that in spite of the large internal viscous dissipation, coalescence of two nanoscale droplets on a super-hydrophobic surface can result in a jumping of the coalesced droplet from the surface with a speed of a few m/s. Similar to the coalescence-induced jumping of microscale droplets, we observe that the bridge between the coalescing nano-droplets expands and impacts the solid surface, which leads to an acceleration of the coalesced droplet by the pressure force from the solid surface. We observe that the jumping velocity decreases with the droplet size and its ratio to the inertial-capillary velocity is a constant of about 0.126, which is close to the minimum value of 0.111 predicted by continuum-level modeling of Enright et al. [R. Enright, N. Miljkovic, J. Sprittles, K. Nolan, R. Mitchell, and E. N. Wang, ACS Nano 8, 10352 (2014)].   

Droplet climbing on a pre-wetted conical fibre

We study the motion of a droplet on a wet conical fibre. The conical fibres are fabricated with a glass-puller, with tip diameters of several $\mu$m. With liquid is fed through the hollow fibre and travels up the outside of the cone, forming a droplet, which is initially attached near the tip. This drop grows in size and then detaches and moves on the fibre, at velocities up to 0.25 m/s. We focus on the regime with small Bond number $Bo=\rho g R^2 / \sigma$ and capillary number $Ca=\mu U / \sigma$, where the droplet motion is driven by the pressure gradient due to the continuous curvature change along the conical fibre. High-speed imaging and numerical simulations via the Gerris code are employed to investigate the dynamics of the droplet detachment and climbing. Our focus is on the interface profile near the tip, the mechanism of droplet formation and climbing, and the velocity field in the thin liquid layer on the cone.   

Electro-osmotic flow in bicomponent fluids

The electroosmotic flow (EOF) is a widely used technique that uses the action of external electric fields on solvated ions to move fluids around in microfluidics devices. For homogeneous fluids, the characteristics of the flow can be well approximated by simple analytical models, but in multicomponent systems such as oil-in-water droplets one has to rely to numerical simulations. The purpose of this study is to investigate physical properties of the EOF in a bicomponent fluid by solving the coupled equations of motions of explicit ions in interaction with a continuous model of the flow. To do so we couple the hydrodynamics equations as solved by a Shan-Chen Lattice-Boltzmann method\footnote{X. Shan, and H. Chen, Phys. Rev. E, 47, 1815-1819 (1993)} to the molecular dynamics of the ions\footnote{M. Sega, M. Sbragaglia, S. S. Kantorovich and A. Ivanov, Soft Matter, 9, 10092-10107 (2013)}. The presence of explicit ions allows us to go beyond the simple Poisson-Boltzmann approximations, and investigate a variety of EOF regimes.   

Electrohydrodynamics of toroidal droplets

Toroidal droplets are unstable and always transform into spherical droplets due to surface tension. This can happen via Rayleigh-Plateau instabilities, or via the shrinking of the handle. Interestingly, charging a toroidal droplet can cause expansion, rather than shrinking, of the handle. In this talk, we will discuss the use of particle image velocimetry to obtain the velocity profile inside both neutral and charged toroidal droplets as they transform into the spherical shape. In particular, we quantify the effect of surface stresses on the velocity field and, consequently, on the shape of the interface as the droplet evolves by either shrinking or expanding.   

Study of the $(1+1)$D Long Wavelength Steady States of the B\'{e}nard Problem For Ultrathin Films

We investigate the stationary states of the $(1+1)$D equation $h_t + \left [h^3h_{xxx}+h^2\gamma_x (h)\right]_x=0$ for thin films of thickness $h(x,t)$ where $x$ is the spatial variable and $t$ is time. The variable $\gamma(h)$, denotes the surface tension along the gas/liquid interface of the slender bilayer confined between two substrates enforcing thermal conduction within the gap. Equilibrium solutions include flat films, droplets, trenches/ridges and positive periodic steady states (PPSS), the latter conveniently parameterized by a generalized interfacial pressure and the global extremum in shape. We derive perturbative solutions describing PPSS shapes near the stability threshold including their minimal period, average height and free energy. Weakly nonlinear analysis confirms that flat films always undergo a supercritical unstable pitch-fork bifurcation. Globally, our numerical simulations indicate at most one non-trivial PPSS per given period and volume. The free energy of droplet states is also always lower than the relevant corresponding PPSS, suggesting that initial flat films tend to redistribute mass into droplet-like configurations. By solving the linearized eigenvalue problem, we also confirm the unstable nature of PPSS solutions far from the stability threshold.   

Collective oscillations and coupled modes in confined microfluidic droplet arrays

Microfluidic droplets have a wide range of applications ranging from analytic assays in cellular biology to controlled mixing in chemical engineering. Ensembles of microfluidic droplets are interesting model systems for non-equilibrium many-body phenomena. When flowing in a microchannel, trains of droplets can form microfluidic crystals whose dynamics are governed by long-range hydrodynamic interactions and boundary effects. In this contribution, excitation mechanisms for collective waves in dense and confined microfluidic droplet arrays are investigated by experiments and computer simulations. We demonstrate that distinct modes can be excited by creating specific `defect' patterns in flowing droplet trains. While longitudinal modes exhibit a short-lived cascade of pairs of laterally displacing droplets, transversely excited modes form propagating waves that behave like microfluidic phonons. We show that the confinement induces a coupling between longitudinal and transverse modes. We also investigate the life time of the collective oscillations and discuss possible mechanisms for the onset of instabilities. Our results demonstrate that microfluidic phonons can exhibit effects beyond the linear theory, which can be studied particularly well in dense and confined systems.   

Drop impact on inclined superhydrophobic surfaces

We report an empirical study and dimensional analysis on the impact patterns of water drops on inclined superhydrophobic surfaces. While the classic Weber number determines the spreading and recoiling dynamics of a water drop on a horizontal / smooth surface, for a superhydrophobic surface, the dynamics depends on two distinct Weber numbers, each calculated using the length scale of the drop or of the pores on the surface. Impact on an inclined superhydrophobic surface is even more complicated, as the velocity that determines the Weber number is not necessarily the absolute speed of the drop but the velocity components normal and tangential to the surface. We define six different Weber numbers, using three different velocities (absolute, normal and tangential velocities) and two different length scales (size of the drop and of the texture). We investigate the impact patterns on inclined superhydrophobic surfaces with three different types of surface texture: (i) posts, (ii) ridges aligned with and (iii) ridges perpendicular to the impact direction. Results suggest that all six Weber numbers matter, but affect different parts of the impact dynamics, ranging from the Cassie-Wenzel transition, maximum spreading, to anisotropic deformation.   

Spreading of water nanodroplets on graphene

Understanding the wetting of 2D materials is central to the successful application of these materials in a variety of disciplines that involve the interaction of a liquid with such layered substrates. Recent studies focusing on wetting statics and contact angle selection on graphene-coated solids indicate a wetting translucent behavior of graphene. However, little research has been done on the wetting dynamics of graphene-coated systems. Here, we simulate the wetting dynamics of water drops on free-standing graphene layers using a molecular dynamics framework. We employ the extended simple point charge (SPC/E) model to simulate the water drops. Our simulations are validated against the experimental results of water drop contact angles on graphite. Unlike many existing MD studies, we obtain the results starting from a physical consideration of spherical water drops. We observe the half power law for the spreading dynamics, i.e., r\textasciitilde t\textasciicircum (1/2) (r is the spreading radius and t is the spreading time). Identical spreading laws have been identified for Lennard Jones (LJ) nanodroplets on non-layered surfaces; therefore, we establish that the change in the nature of the substrate (non-layered to 2D) and the liquid (LJ to water) does not alter the physics of wetting dynamics of nanodroplets.   

Domain and rim growth kinetics in stratifying foam films

Foam films are freely standing thin liquid films that typically consist of two surfactant-laden surfaces that are \textasciitilde 5 nm -- 10 micron apart. Sandwiched between these interfacial layers is a fluid that drains primarily under the influence of viscous and interfacial forces, including disjoining pressure. Interestingly, a layered ordering of micelles inside the foam films (thickness \textless 100 nm) leads to a stepwise thinning phenomena called stratification, which results in a thickness-dependent variation in reflected light intensity, visualized as progressively darker shades of gray. Thinner, darker domains spontaneously grow within foam films. During the initial expansion, a rim forms near the contact line between the growing thinner domain and the surrounding region, which influences the dynamics of domain growth as well as stratification Using newly developed interferometry digitial imaging optical microscopy (IDIOM) technique, we capture the rim evolution dynamics. Finally, we also develop a theoretical model to describe both rim evolution and domain growth dynamics.   

Drop formation, pinch-off dynamics and liquid transfer of simple and complex fluids

Liquid transfer and drop formation processes underlying jetting, spraying, coating, and printing -- inkjet, screen, roller-coating, gravure, nanoimprint hot embossing, 3D -- often involve formation of unstable columnar necks. Capillary-driven thinning of such necks and their pinchoff dynamics are determined by a complex interplay of inertial, viscous and capillary stresses for simple, Newtonian fluids. Micro-structural changes in response to extensional flow field that arises within the thinning neck give rise to additional viscoelastic stresses in complex, non- Newtonian fluids. Using FLOW-3D, we simulate flows realized in prototypical geometries (dripping and liquid bridge stretched between two parallel plates) used for studying pinch-off dynamics and influence of microstructure and viscoelasticity. In contrast with often-used 1D or 2D models, FLOW-3D allows a robust evaluation of the magnitude of the underlying stresses and extensional flow field (both uniformity and magnitude). We find that the simulated radius evolution profiles match the pinch-off dynamics that are experimentally-observed and theoretically-predicted for model Newtonian fluids and complex fluids.   

Simulations of high and low viscosity micro-scale droplets splashing on a dry surface

When a droplet hits a dry surface at atmospheric pressure with a high enough impact velocity, it splashes and breaks apart into many smaller droplet. However, when the ambient gas pressure is reduced, splashing is suppressed. This is contrary to intuition, which suggest a more violent splash should occur at lower gas densities due to reduced drag forces. Although splashes of high and low viscosity liquids visually look very different, they also obey the pressure effect. In this study the effect of viscosity on splashing is investigated, to get a better understanding of the pressure effect in general. Simulation results are presented comparing splashing of low viscosity ethanol with high viscosity silicone oil in air. The droplets are several hundred microns large. The simulations are 2D, and are performed using a Volume Of Fluid approach. The contact line is described using the Generalized Navier Boundary Condition. Both the gas phase and the liquid phase are assumed to be incompressible. The results of the simulations show good agreement with experiments, including reproduction of the pressure effect, and suggest that the same scaling laws that apply to lamella formation in simple drop deposition, also apply to splashing droplets.   

Dynamics of Wetting and Wicking on Rough Surfaces

Micro/nano engineering of surfaces to enhance the performance of phase-change heat transfer processes has recently gained wide interest. Interfacial phenomena at the micro/nanoscale play an important role in defining the dynamic wetting and wicking characteristics of the surfaces. Here we report experiments that characterize the dynamic wetting and wicking processes on microstructured silicon surfaces. We investigated cylindrical micropillar arrays in a square pattern with various diameter, pitch, and height to characterize key interfacial behavior over a wide range of surface roughness. The experiments were performed by dipping the microstructured sample vertically into a reservoir of de-ionized water and the spreading dynamics were captured with a high speed camera. We observed that both wetting and wicking exhibit a power law dependence on time, however they occur at different time scales. The instantaneous (\textasciitilde 10-100 ms) wetting behavior occurs due to the interfacial tensions, and the resultant force acting at the three-phase contact line. The longer time scale (\textgreater 100 ms) wicking behavior results from the balance of the capillary pressure generated within the microstructure and the viscous pressure loss from flow through the micropillar array. We develop analytical models to predict these different time scale behavior and compare them to experimental results. This work provides insight into key dynamic processes affecting micro/nanostructure enhanced phase-change heat transfer devices.