Session J19: Drops: Recoil, Spreading and Contact Line

Modeling moving contact lines during drop spreading over a textured substrate

Contact line movement during spreading of low viscosity liquid drops has been addressed in the literature using a contact angle model that connects the interfacial slope with the contact line velocity. Here, we present such a contact angle model that is general enough to hold for a variety of surfaces, starting from non-hysteretic superhydrophobic all the way to highly sticky, hysteretic hydrophobic surfaces. The surface-related characteristics of spreading, such as friction and pinning appear as parameters in the contact angle model. The model is simulated along with the conservation equations to yield drop spreading details such as the instantaneous drop height, footprint and timescales, along with possible recoil and capillary waves are derived. Further, these details are compared with experimental data recorded from high-speed imaging experiments where the match is seen to be quite good. The contact angle model is then tested against experiments related to electrowetting over a dielectric and simulations are shown to be in good agreement with experiments. In a second application, the proposed contact angle model is tested via simulations for drop spreading over a surface with microscale pillar arrays. The match against experiments reported in the literature is shown to be quite good. Simulations show that the equilibrium drop shape as well as Cassie-Wenzel transitions depend on the spreading dynamics and cannot be specified in advance. The success of the model is related to correctly resolving multiple surface waves propagating over the gas-liquid interface. It being extended to account for droplet impact on textured surfaces.   

Spontaneous charge separation at receding contact lines causes contact angle hysteresis

Contact angle hysteresis is one of the most important phenomena in wetting. Despite many known contributions and corresponding theories, some observations still remain unexplained. In recent years, slide electrification – the spontaneous charge separation at receding contact lines – has sparked increased interest. Here, we show that electrostatic interactions between the liquid surface and the deposited surface charge on the dewetted substrate can decrease the receding contact angle and thus cause contact angle hysteresis exceeding 10°. This occurs even for grounded liquids and can thus not be explained by electrowetting. We propose an analytical model for this mechanism and experimentally confirm the predicted dependency on drop size. We further demonstrate this universal effect for various salt solutions and substrates. Our results uncover electrostatic interactions at receding contact lines as a fundamental and until now overlooked phenomenon in wetting.   

Dynamic hysteresis of an oscillating contact line

The behavior of contact line is conventionally described by the single-valued dependence between the dynamic contact angle θ_d  and contact line velocity U_CL. However, by experimentally investigating the mobile contact line of a sessile droplet supported by a vertically vibrating substrate, a distinct multivalued contact line relation is found on fluorosilane coated surface.

To understand the cause of the multivaluedness, we first evaluate the dynamic contact line (DCL) friction coefficient μ_f, which is quantified by balancing the work done by the unbalanced Young's force and the frictional dissipation on DCL. Using this metric, we gauge μ_f of different systems. It is found that both surface coating (molecule species, chain length) and liquid properties (viscosity) have impact on the DCL friction. The results suggest that μ_f is a complex phenomenological parameter, which incorporates the dissipative effects from both molecular interaction and viscous resistance in the vicinity of DCL. Moreover, instead of being a constant, μ_f is found to increase dramatically as DCL decelerates, indicating the transition between dynamic and static friction regimes.

Finally, the multivaluedness in the contact line relation is attributed to the asymmetry in μ_f  distribution between approaching and leaving the turning points. To validate this relevance, we incorporate dynamical μ_f model in the DCL mobility relation in volume of fluid simulation, expecting to reproduce the multivaluedness in the numerical solution.   

Mocha Diffusion: The Art of Spreading Miscible Liquids

Mocha diffusion is a technique in ceramic surface decoration known to produce radial, fern-like patterns. The veined designs are made by dripping a dark dye solution onto a miscible wet clay slip covering the pottery. These dye solutions commonly include additives like acidic tobacco tea, alkaline stale urine, or surfactants. We investigate the underlying mechanisms of this pattern formation by exploring various additives for dye solutions, such as propylene glycol, ammonia, citric acid, and isopropanol, as well as various sub-fluids. In our experiments, dyes are dropped onto a variety of viscous sub-fluids, including sodium alginate, corn syrup, acrylic paint, and sugar water solutions. We observe a large variety of dendritic patterns, meaning there are many ways to design mocha diffusion art. We find that a highly non-linear relationship between water concentration and shear viscosity in the sub-fluid is a key feature needed for mocha diffusion. Contrary to prior conclusions from our group, sub-fluids do not need to be shear-thinning. Our data suggests that partial diffusion of the dye solution into the sub-fluid lowers the local viscosity, creating a channelizing effect. When combined with surface tension gradients (Marangoni flow) in the dye solution that drive the spreading process, dendritic patterns form only when the dye solution has sufficient time for diffusion. This influences the initial formation of fingering patterns and distinguishes mocha diffusion from conventional fluid spreading.   

Rim recoil of impacted drops with pinned contact lines

When a liquid drop impacts a surface with sufficient speed, it initially spreads to form a thin lamellar disk of liquid surrounded by a relatively thick rim, quickly reaching a maximum spreading diameter before recoiling to minimize the droplet's total energy. While the spreading phase is dominated by inertia, the recoil dynamics depend intimately on the receding contact angle and the fluid rheology. The present work investigates the recoil of rims formed in drop impact where the contact line is 'pinned'. Experiments are performed using drops of water, glycerol mixtures, and a shear-thinning yield stress fluid impacting on clean glass slides at varying speeds, resulting in a pinned contact line for varying degrees of maximum spreading diameter and fluid viscosity. The experiments show that while the recoil rate of rim is initially fast, it quickly slows as the recession progresses. Incorporating a rate-dependent viscosity further slows the recoil. An energy model is constructed to investigate the roles of the maximum spreading extent and the lamella thickness on the recession rate. Increasing either the maximum spreading extent or lamella thickness leads to a slower recoil for a fixed total volume due to a lower rate of energy minimization. In the limiting case of no lamella, an energy minimum appears early in the recession and the rim will remain stable as a toroidal cap.   

Human blood drop impact and retraction driven by ambient humidity

Although the receding (retraction) of a drop after its impact on a solid substrate is an important phenomenon, it has received less attention than spreading. We investigated the receding dynamics for a drop of whole human blood with different impact velocities for both varnished and unvarnished wooden floors. The effect of the room's relative humidity and temperature were considered by performing experiments under different surroundings conditions. The obtained results show that the receding phenomena occurred on the varnished wooden floor (smooth substrate) and were absent on the unvarnished wooden floor (rough substrate). For the smooth substrate, the retraction occurred only at low relative humidity. This is explained by the decrease in the surface tension with relative humidity level. In this presentation, the obtained results on the blood drop receding after impact are provided by discussing its dynamics and the influence of relative humidity.   

Can the tails of bloodstain help forensic investigation?

In the field of forensic science, elongated elliptical stains, called spatter stains, provide valuable insights into the oblique impact of blood droplets. For low-impact angles, the stain can include an asymmetric tail that bloodstain analysts can use qualitatively to establish directionality. However, quantitative analysis of these bloodstain tails, and any insight that they can provide in the impact dynamics, is lacking. Here we carry out systematic experiments in which small human blood droplets impact a horizontal surface at impact angles ranging from 16 to 65 degrees. High-speed imagery confirms that the tail is not part of a prompt splashing event, but rather forms at the last moments of spreading. For each stain, we link the tail length and elliptical geometry to the blood drop size and impact velocity vector that created it. Additionally, we report a power-law correlation of the dimensionless tail length with the angle and Weber and Reynolds numbers, and we describe how this correlation in conjunction with other existing correlations can improve reconstruction of the droplet size and impact velocity.   

Investigation of microdroplet trajectories in respiratory airways

Investigations motivated by respiratory health requirements have been focusing on the inhalation and transport processes of pollutant particles via the human respiratory system. Similar issues arise in the studies of transmission of infectious diseases by respiratory droplets. The understanding of the motion of particles or droplets through the air and their interactions with the mouth, throat, and upper airways has improved as a result of studies on micro- and nanoparticle transport and deposition over the past few decades. However, several aspects of interaction of droplets with air flow in this context are still not well understood. In order to investigate the trajectories and deposition of microdroplets in the respiratory airways, we used an imposed velocity profile of air flow that accounts for both motion of inhaled/exhaled air and evaporation from the wall of the respiratory airway. We track droplet motion depending on their initial location and velocity and investigate the effects of viscous drag and the Saffman force on the microparticle deposition. Application of the general framework we developed to droplets that experience phase change is also discussed.