Shear flow over a liquid drop adhering to a solid surface

The liquid drop captured at the capillary end, which is observed in capillary valve and pendant drop technique, is investigated theoretically and experimentally. Because of contact line pinning of the lower meniscus, the lower contact angle is able to rise from the intrinsic contact angle (θ*) so that the external force acting on the drop can be balanced by the capillary force. In the absence of contact angle hysteresis (CAH), the upper contact angle remains at θ*. However, in the presence of CAH, the upper contact angle can descend to provide more capillary force. The coupling between the lower and upper contact angles determines the equilibrium shape of the captured drop. In a capillary valve, the pinned contact line can move across the edge as the pressure difference exceeds the valving pressure, which depends on the geometrical characteristic and wetting property of the valve opening. When CAH is considered, the valving pressure is elevated because the capillary force is enhanced by the receding contact angle. For a pendant drop under gravity, the maximal capillary force is achieved as the lower contact angle reaches 180° in the absence of CAH. However, in the presence of CAH, four regimes can be identified by three critical drop volumes. The lower contact angle can exceed 180°, and therefore the drop takes on the shape of a light bulb, which does not exist in the absence of CAH. The comparisons between Surface Evolver simulations and experiments are quite well.

Breakup of drops in simple shear flows with high-confinement geometry

Static nanodroplets and dynamic contact line (CL) movements were visualized by an in situ transmission electron microscope (TEM) liquid cell technique at nanometer spatial resolution. Crawling and sliding movements of nanoscale CL were observed. The crawling happened at a capillary number (Ca) range of ∼10-9 to ∼10-8, and the sliding happened at a Ca range of ∼10-8 to ∼10-7. Three dimensional (3D) image construction had been employed to study static and dynamic contact angles (CAs) at nanoscale. CA hysteresis at nanoscale was observed in the sliding but not in the crawling. The energies associated with sliding were analyzed to investigate the CA hysteresis. An empirical model of the relationship between nanoscale CAs and Ca was developed. Both the experimental observation and the empirical analysis suggested that the competition among substrate defect, CL elastic, and molecular activation energies dictated different CL movements at nanoscale.

The effects of surface active agents on contact angle hysteresis is examined by photographing sessile drops at the point of incipient motion on an inclined solid. For solutions of anionic and cationic fluorocarbon surfactants Zonyl FSA and FSC and nonionic surfactant octanol on Teflon, contact angle hysteresis is substantially higher than that for pure water. Hydrophobic bonding of the surfactant molecules at the solid—liquid interface appears to be responsible for this change. Although inhomegeneities on the Teflon surface cause the advancing and receding contact angles to vary at a fixed surfactant concentration, their difference displays significantly lower scatter, indicating that hysteresis is a more reproducible material property than the individual contact angles. Experimental dimensionless sessile drop volumes at the critical inclination angle are compared to an analytical prediction by E. B. Dussan. ( J. Fluid Mech. 151, 1 (1985)). For the cationic and anionic surfactant solutions these volumes are between three and four times the prediction from the analysis. This disagreement is especially surprising because the analysis represents a force balance on the drop at the critical configuration, and a reasonable match was obtained for pure liquids by H. V. Nguyen et al. ( J. Colloid Interface Sci. 115, 410 (1987)). For solutions of the weak surfactant 1-octanol, the experimentally observed drop volumes at the critical inclination angle match the analytical predictions, indicating that the surfactant strength has an important bearing on the results. One possible explanation is that as the solid substrate is tilted from the horizontal, the sessile drop morphology is modified and the contact line shape changes from circular to one with parallel sides. Such a change must be accompanied by fluid motion. The presence of strong surfactants imposes some hydrodynamic rigidity to the solution—vapor interface and opposes this movement. Therefore, for a fixed drop volume, the inclination angle required for the drop to achieve its critical shape is greater than that predicted by the analysis.

Numerical contact line behavior prediction for droplet-wall impact by the modified Hoffman-function-based dynamic contact angle model

On the effect of static and dynamic contact angles on humid air condensation heat transfer

Numerical simulations are presented of shear flow past two-dimensional droplets adhering to a wall, at moderate Reynolds numbers. The results were obtained using a level-set method to track the interface, with measures to eliminate any errors in the conservation of mass of droplets. First, the case of droplets whose contact lines are pinned is considered. Data are presented for the critical value of the dimensionless shear rate (Weber number, $\hbox{\it We}$), beyond which no steady state is found, as a function of Reynolds number, $\hbox{\it Re}$. $\hbox{\it We}$ and $\hbox{\it Re}$ are based on the initial height of the droplet and shear rate; the range of Reynolds numbers simulated is $\hbox{\it Re} \leq 25$. It is shown that, as $\hbox{\it Re}$ is increased, the critical value $\hbox{\it We}_c$ changes from $\hbox{\it We}_c\propto \hbox{\it Re}$ to $\hbox{\it We}_c\approx$ const., and that the deformation of droplets at $\hbox{\it We}$ just above $\hbox{\it We}_c$ changes fundamentally from a gradual to a sudden dislodgement. In the second part of the paper, drops are considered whose contact lines are allowed to move. The contact-line singularity is removed by using a Navier-slip boundary condition. It is shown that macroscale contact angles can be defined that are primarily functions of the capillary number based on the contact-line speed, instead of the value of $\hbox{\it We}$ of the shear flow. It is shown that a Cox–Voinov-type expression can be used to describe the motion of the downstream contact line. A qualitatively different relation is tested for the motion of the upstream contact line. In a third part of this paper, results are presented for droplets moving on a wall with position-dependent sliplength or contact-angle hysteresis window, in an effort to stabilize or destabilize the drop.

In order to study emulsification phenomena, devices generating well‐defined flow conditions are essential. Thus, emulsification of drop collectives under laminar shear flow is commonly performed in cylindrical Couette or Searle devices. In these devices, the flow conditions in the shear gap and in the volume underneath the rotor are often different, which can lead to inhomogeneous product properties and may complicate sample taking. Here, a novel cone‐cone shear cell is presented to study emulsification processes. The flow inside the device is examined using numerical simulations. The numerical simulations indicate that simple shear flow is realized all over the sample volume in the cone‐cone shear cell. The experimental results show that the drop breakup in the cone‐cone shear cell is equivalent to the breakup under simple shear realized in the shear gap of a conventional device, i.e., the Searle device. Critical capillary numbers are calculated from the experimental data and show breakup behavior as predicted by single‐drop experiments. Thus, the cone‐cone shear cell proved to be suitable to study emulsification mechanisms in simple shear flow.

Arbitrary Lagrangian-Eulerian finite element method for liquid sloshing with contact angle hysteresis in microgravity

The present study evaluated the contact angles (CAs) of four denture base materials subjected to different surface treatments using deionized water and saliva substitutes. A total of 32 rectangular specimens were manufactured using four different denture base materials: heat-cured compression molded Lucitone 199 (C), milled Lucitone 199 (M), Formlabs Denture Base RP (P), and SR Ivocap High Impact (I). The CA of the surface of the unaltered, mechanically polished, and sandblasted surface specimens was evaluated after the application of five saliva substitutes: Biotene, VEGA, Spry, Moi-Stir, Dentilube, and ionized water. Ten droplet measurements were obtained for each group, with each droplet analyzed for advancing contact angle (ACA), receding contact angle (RCA), and the contact angle hysteresis (CAH) was calculated. The data of the experiment was analyzed using 2-way ANOVA, (α=0.05) with Tukey's test. CAH was demonstrated to have statistically significant differences among the denture bases (p<0.05), with unaltered 3D printed exhibiting the largest CAH, followed by unaltered milled. The unaltered denture bases exhibited higher CAH than the polished, and there were no significant differences in CAH among the polished denture bases (p>0.05). Sandblasting increased the ACA of the milled and conventional bases. The saliva substitutes exhibited differences in ACA, with Spry and VEGA having the highest ACA, and Biotene had the lowest CA of all the saliva substitutes evaluated. The manufacturing methods of denture bases influences the CAH, while the chemical composition of the denture base specimens does not appear to affect CAH. Sandblasting increases the ACA for the milled and conventional groups. Saliva substitutes do impact the ACA. Drawing from previous research, it is hypothesized that a 3D-printed denture base or sandblasting a milled denture base may offer greater resistance to dislodgement.

Drying of porous media is governed by a combination of evaporation and movement of the liquid phase within the porous structure. Contact angle hysteresis induced by surface roughness is shown to influence multi-phase flows, such as contact line motion of droplet, phase distribution during drainage and coffee ring formed after droplet drying in constant contact radius mode. However, the influence of contact angle hysteresis on liquid drying in porous media is still an unanswered question. Lattice Boltzmann model (LBM) is an advanced numerical approach increasingly used to study phase change problems including drying. In this paper, based on a geometric formulation scheme to prescribe contact angle, we implement a contact angle hysteresis model within the framework of a two-phase pseudopotential LBM. The capability and accuracy of prescribing and automatically measuring contact angles over a large range are tested and validated by simulating droplets sitting on flat and curved surfaces. Afterward, the proposed contact angle hysteresis model is validated by modeling droplet drying on flat and curved surfaces. Then, drying of two connected capillary tubes is studied, considering the influence of different contact angle hysteresis ranges on drying dynamics. Finally, the model is applied to study drying of a dual-porosity porous medium, where phase distribution and drying rate are compared with and without contact angle hysteresis. The proposed model is shown to be capable of dealing with different contact angle hysteresis ranges accurately and of capturing the physical mechanisms during drying in different porous media including flat and curved geometries.

The effect of liquid properties to contact angle hysteresis

We use molecular dynamics (MD) simulations to investigate the dynamic wetting of nanoscale water droplets on moving surfaces. The density and hydrogen bonding profiles along the direction normal to the surface are reported, and the width of the water depletion layer is evaluated first for droplets on three different static surfaces: silicon, graphite, and a fictitious superhydrophobic surface. The advancing and receding contact angles, and contact angle hysteresis, are then measured as a function of capillary number on smooth moving silicon and graphite surfaces. Our results for the silicon surface show that molecular displacements at the contact line are influenced greatly by interactions with the solid surface and partly by viscous dissipation effects induced through the movement of the surface. For the graphite surface, however, both the advancing and receding contact angles values are close to the static contact angle value and are independent of the capillary number; i.e., viscous dissipation effects are negligible. This finding is in contrast with the wetting dynamics of macroscale water droplets, which show significant dependence on the capillary number.

High Reynolds number oscillating contact lines

Synergistic effects in flows of mixtures of wormlike micelles and hydroxyethyl celluloses with or without hydrophobic modifications