Session P12: Surface Tension Effects: Interfacial Phenomena (3:10pm - 3:55pm CST)

Self-similar draining near a vertical edge

When a liquid film drains on a vertical plate, the film becomes nonuniform near the vertical edge. Here we experimentally report the three-dimensional (3D) self-similar shape of this film. Based on the well-known 2D self-similar solution of a draining film far from the edge, we identify a new 3D self-similar scaling, which converts the PDE for the film thickness with three independent variables into an ODE. Interferometry is performed to measure the film thickness as a function of position and time, and the results are in excellent agreement with the theoretical predictions.   

Theory of bubble tips in strong viscous flows

A drop or bubble, placed in a strong viscous flow (such that viscous forces overwhelm surface tension), develops ends with very sharp tips. Here we show that the shape of the ends, non-dimensionalized by the tip curvature, is governed by a universal similarity solution, which we describe theoretically. The shape of the similarity solution is close to a cone, but whose slope varies with the square root of the logarithmic distance from the tip. With this insight, we are able to show that the curvature grows exponentially with the square of the flow strength. We show that for the case of a drop in a hyperbolic flow the similarity solution matches previous slender-body analyses, thus providing a complete description of the drop shape. Our theoretical results agree well with numerical simulations of the Stokes equation.   

Jet Break-Up in Drop-on-Demand Inkjet Printing in the Presence of Surfactants

The rapid development of new applications for inkjet printing and increasing complexity of the inks has created a demand for in-silico optimisation of the ink jetting performance. Surfactants are often added to aqueous inks to modify the surface tension. However, the rapid expansion of the free surface during the fast jetting process means local areas of the surface will be depleted of surfactants leading to surface tension gradients. We present numerical simulations of inkjet break-up and drop formation in the presence of surfactants investigating both the surfactant transport on the interface and the influence of Marangoni forces on break-up dynamics. In particular, the initial phase of a “pull-push-pull” drive waveform leads to a concentration of surfactants at the front of the main drop with the trailing ligament being almost surfactant free. The resulting Marangoni stresses act to delay and can even prevent the break-off of the main drop from the ligament. The presence of surfactants also reduces the mobility of the surface of the droplet, modifying the internal flow within the droplet and enhancing the viscous dissipation.   

Hindered thermally driven migration of a drop on a chemically patterned solid wall.

A drop in a thermal gradient migrates to the hot side since surface tension is usually a decreasing function of temperature. If the drop is attached to a surface with a temperature gradient, the motion is more complicated. The drop either moves to the hot side or cold side, depending on the contact angle and viscosity ratio. If the surface with a temperature gradient is patterned, the wettability is different for different patches and here we show, using numerical simulations of two-dimensional flows, that is certain cases the drop can be brought to a halt, even if the drop moves in one direction when it occupies one patch only. Two quantities are defined to judge whether the patterned surface can hinder the thermally driven migration of a drop, namely, defect strength and minimum defect strength. The patterned surface can hinder the drop migration only when the defect strength is larger than the minimum defect strength. The minimum defect strength increases with the Marangoni number but decreases with the viscosity ratio. These results are summarized in a phase diagram. The force analysis is conducted to explain the above results.   

Influence of Marangoni-Induced Flows on Solidification Process in Horizontal Ribbon Growth Crystallization

Using the horizontal ribbon growth (HRG) technique, sheets of single-crystal silicon can be efficiently produced with desired thicknesses, without incurring the losses that are inherent in conventional crystallization procedures. However, recent experimental observations have shown that current theoretical models of the HRG process have not accounted for all the physical processes involved. Due to high temperature variations in the molten pool in contact with the solidified ribbon and the strong dependency of silicon surface tension to temperature, Marangoni-induced flows can play a significant role in the formation of the ribbon. In this study, the HRG process is simulated numerically using an accurate \textit{hp-}finite element procedure. It is observed that the Marangoni effect results in a strong flow close to the edge of the solidified ribbon, which forms a series of stationary vortices in conjunction with buoyancy flows. The vortices, which are a strong function of the underlying parameters such as the depth of the pool, the ribbon pull speed, and the cooling heat fluxes, can thin the ribbon and limit the maximum achievable pull speed. Moreover, it is observed that the flow field becomes unsteady at certain combinations of the governing parameters.   

Dynamics of a surface tension driven vortex ring

When an ethanol droplet is deposited on water surface, the surface tension difference between the ethanol and the water ($\Delta\sigma$) spreads a part of the drop as a thin film on the water surface. A buoyant vortex ring is found to expand beneath the spreading film such that the vortex ring radius (R), varies with time as $t^{1/4}$, similar to the film radius($r_{f}$). We study the generation and expansion of this buoyant vortex ring below the surface of a deep water layer. We propose a scaling for the vorticity generation at the interface, which we verify using 2-D PIV velocity measurements. The proposed scaIing needs the presence of a small length scale, proportional to $r_f$, across which $\Delta\sigma$ occurs. We explore the possible presence of such a length scale in the peripheral instability of the spreading film. This flower shaped instability is seen to occur when the Weber number based on $r_f$ becomes order one. The observed wavelengths and amplitudes of the instability are studied and compared with Rayleigh-Taylor instability as well as Vortex instability.   

Effects of Surfactant Solubility on the Hydrodynamics of a Viscous Drop in a DC Electric Field

The physico-chemistry of surfactants (amphiphilic surface active agents) is often used to control the dynamics of viscous drops and bubbles. Surfactant sorption kinetics has been shown to play a critical role in the deformation of drops in extensional and shear flows, yet to the best of our knowledge these kinetics effects on a viscous drop in an electric field have not been accounted for. In this talk we present numerical results from investigating the effects of sorption kinetics on a surfactant-covered viscous drop in an electric field. We focus on the dependence of deformation and flow on dimensionless physical parameters that characterize the extent of surfactant exchange between the drop surface and the bulk. At high surfactant coverage, we found that surfactants favor oblate drop shapes and change the circulation pattern at equilibrium.   

Folds on soap films

In this talk we report on experimental findings of fold formation on a surface of evolving soap films and relate it to the known effect of shock wave appearance. Theoretical explanation for the fold formation is provided and compared quantitatively with experimental measurements.   

Capillary Machines for Manipulating Small Objects

Machines that can operate on small objects in a programmable, scalable, and simple way are an attractive solution to many problems. To make such machines, we take advantage of the repulsive capillary interactions between millimeter-scale polymer ``floats'' pinned at an interface and the wetting walls of a decimeter-scale 3D-printed device. In this talk, we discuss the experimental techniques necessary to use these repulsive interactions in conjunction with the vertical motion of the device to guide objects along complex 3D paths. These techniques include defining serializable operations to programmably manipulate floats and using device geometry and contact angle hysteresis to simplify complicated motions. We then apply these techniques to the problems of twisting and braiding micrometer-scale wires, which are difficult to manipulate with typical braiding machines.   

Open siphon on a capillary channel

A conventional siphon is an everyday device for transferring liquids that consists of a tube with inverted U shape. Flow up and over can be established and maintained only if the tube is closed so air does not enter and break the line. Here we describe a siphoning mechanism that operates when entirely open to the atmosphere by exploiting surface tension effects. This capillary siphoning is demonstrated by hanging paper or fabric over the edge of a glass or tub of water, and we conduct experiments on a more subtle and controlled version that involves a single groove-like and curved capillary channel. The dependence of flow rate on the siphon geometry is well accounted for by a model that solves for the spatially-dependent shape of the fluid interface, speed and pressure.   

Capillary Machines for Manipulating Small Objects: Theory

Capillary interfaces can robustly assemble geometrically non-trivial structures at milli- and microscales. We apply the principles of capillary assembly to enable the design of arbitrary 3D paths for particles bound to 2D interfaces. Specifically, we consider flat polymer "floats'' which are repeatedly raised and lowered through a 3D-printed device. Repulsive capillary interactions between the floats and the device walls translate and rotate the floats. In this talk, we discuss and verify a simple numerical method to elucidate the design principles of the corresponding experimental results. These include a ratcheted twisting effect due to contact angle hysteresis, and the formation of a microscale 3-stranded braid. Our designs enable a gentle yet robust method to programmatically assemble thin fibers into braided topologies.   

Pressure-Actuated Influx and Outflow of Aqueous NaCl in Hydrophobic Nanopores

Compression of water in hydrophobic pores has been established as a viable mechanism for conversion of mechanical work to interfacial free energy as new form of energy storage or absorption. Reducing the hysteresis of the influx/outflow cycle is imperative for efficient energy recovery. Nanoporosity and addition of concentrated electrolytes are critical for improved storage density and lower kinetic barriers to the liquid expulsion. Our molecular simulations provide a theoretical perspective into the mechanisms involved in the process, and underlying structures and interactions in compressed nanoconfined solutions. Specifically, we consider aqueous NaCl in planar confinements of widths of 1-2 nm and pressures of up to 3 kbar. Open ensemble Monte Carlo simulations with fractional exchanges of ions are utilized in conjunction with pressure-dependent chemical potentials of bulk phases under pressure. Confinements open to pressurized bulk electrolyte phases show improved reversibility enabled by significant increases in the solid/liquid interfacial tension in narrower pores and associated infiltration and expulsion pressures. These changes are consistent with a strong desalination effects observed in the nanopores irrespective of external pressure and initial concentration.   

Interfacial Tension Hysteresis in Oxidizing Eutectic Gallium-Indium

Eutectic gallium-indium (EGaIn), a room-temperature liquid metal alloy, has the largest interfacial tension of any liquid at room temperature. Under an applied voltage in an electrolytic bath, the anodization of the EGaIn lowers its interfacial tension by orders of magnitude. We observe that the interfacial tension depends not only on the applied potential and the concentration of the sodium hydroxide bath, but also exhibits history-dependence when subjected to voltage sweeps. We examine the origins of these effects as arising from the dissolution rate of the oxide and the reaction rate (measured via current density). We identify four distinct regimes in the interfacial tension's dependence on electric potential, arising from the formation of different oxide species and configurations, and present a model that describes the voltage-dependence of the interfacial tension.   

Circular hydraulic jumps due to surface tension

We report {\bf the first computations to our knowledge} of circular hydraulic jumps created purely due to surface tension at small length scales. The existence of such jumps was shown more than a decade ago in \textit{M. Mathur et. al. Phys. Rev. Lett., 98(16), 2005}. Using the open-source code basilisk (basilisk.fr), we obtain such hydraulic jumps from Direct Numerical Simulations of the axisymmetric Navier-Stokes equations with surface tension of near air-water values, with and without gravity. In our simulation, a hydraulic jump forms from an impinging jet of water of radius $\mathcal{O}(1)$ microns. This causes a jump at a steady-state radius of $\approx 9$ microns. At these small scales where surface tension is expected to dominate over gravity, we find that the location of the jump is nearly insensitive to the presence or absence of gravity in the simulations. However, we also observe that even at these small scales, the film thickness downstream of the jump and the shape of the jump itself are influenced by gravity quite severely. Notably, the existence of the jump itself does not require gravity. Comparison with theory will be presented at the conference.   

Interface Equation For Slender Capillary Flow in 3D Curvy V Grooves

Capillary driven flow of wetting liquids in microstructures containing V-shaped surface grooves is an especially robust and rapid means of fluid transport in gravity free environments or in miniature flow circuits characterized by negligible Bond number. Such flows are routinely used for propellant management in space applications, lab-on-a-chip devices and cooling of 3D integrated electronic chips. The low-order, inertia-free interface model first developed independently by Romero and Yost (1996) and Weislogel (1996) elucidates the capillary-viscous mechanism driving the flow of a slender layer of Newtonian liquid within a straight V groove. Using differential geometry, we extend their approach to develop the nonlinear interface equation for flow in a 3D curvy V groove in the limit where the radius of curvature of the groove backbone exceeds the film thickness. A first-order perturbation analysis of the governing conservation equation yields an explicit form for the thin film equation in the inertia-free limit. The resulting nonlinear equation, which we demonstrate can describe very complex flows, will allow rapid design of determininistic trajectories for the wicking and transport of thin films in 3D curvy V groove networks.   

Theory, simulations and experiments for the slip on surfactant-contaminated superhydrophobic gratings in laminar flows

Surfactants have recently been established as a key factor affecting the drag reduction of laminar flows over superhydrophobic surfaces (SHS). Trace amounts of surfactants, unavoidable in practical applications, induce Marangoni forces that can completely negate slip and any associated drag reduction (Peaudecerf et al. PNAS, 2017; Song et al. PRF, 2018). A quantitative theory has recently been developed for two-dimensional flow (Landel et al. JFM, 2020). Here, we present a theory for the practically important case of three-dimensional flow over an SHS comprising long gratings aligned with the flow. The finite length of the gratings must be included in the model in order to capture the relevant surfactant physics. We test our theory by running three-dimensional numerical simulations inclusive of surfactant, and by performing microPIV measurements in microchannel experiments using confocal microscopy. Our theory yields expressions for the slip and drag as a function of ten dimensionless quantities, revealing the most effective routes to optimize the performance of SHS in practice.