Effect of Surfactants on the Splashing Dynamics of Drops Impacting Smooth Substrates.

We present the results of a systematic study elucidating the role that dynamic surface tension has on the spreading and splashing dynamics of surfactant-laden droplets during the impact on hydrophobic substrates. Using four different surfactants at various concentrations, we generated a range of solutions whose dynamic surface tension were characterized to submillisecond timescales using maximum bubble-pressure tensiometry. Impact dynamics of these solutions were observed by high-speed imaging with subsequent quantitative image processing to determine the impact parameters (droplet size and speed) and dynamic wetting properties (dynamic contact angle). Droplets were slowly formed by dripping to allow the surfactants to achieve equilibrium at the free surface prior to impact. Our results indicate that while only the fastest surfactants appreciably affect the maximum spreading diameter, the droplet morphology during the initial stages of spreading is different to water for all surfactant solutions studied. Moreover, we show that surfactant-laden droplets splash more easily than pure liquid (water). Based on the association of the splashing ratio to our tensiometry measurements, we are able to predict the effective surface tension acting during splashing. These results suggest that droplet splashing characteristics are primarily defined by the stretching of the equilibrated droplet free surface.

Drop splashing after impact onto immiscible pools of different viscosities.

Droplet impact onto liquid pools is a canonical scenario relevant to numerous natural phenomena and industrial processes. However, despite their ubiquity, multi-fluid systems with the drop and pool consisting of different liquids are far less well understood. Our hypothesis is that the post-impact dynamics greatly depends on the pool-to-droplet viscosity ratioµp/µd, which we explore over a range of six orders of magnitude using a combination of experiments and theoretical approaches (mathematical modelling and direct numerical simulation). Our findings indicate that in this scenario the splashing threshold and the composition of the ejecta sheet are controlled by the viscosity ratio. We uncover that increasing the pool viscosity decreases the splashing threshold for high viscosity pools (µp/µd≳35) when the splash comes from the droplet. By contrast, for low viscosity pools, the splash sheet comes from the pool and increasing the pool viscosity increases the splashing threshold. Surprisingly, there are conditions for which no splashing is observed under the conditions attainable in our laboratory. Furthermore, considering the interface velocity together with asymptotic arguments underlying the generation of the ejecta has allowed us to understand meaningful variations in the pressure during impact and rationalise the observed changes in the splashing threshold.

Droplet splashing on curved substrates.

Droplets impacting dry solid substrates often splash above a certain threshold impact velocity. We hypothesise that substrate curvature alters splashing thresholds due to a modification to the lift force acting on the lamella at the point of breakup. We have undertaken high-speed imaging experiments of millimetric droplets impacting convex and concave surfaces to establish splashing thresholds and dynamics across a wide range of substrate geometries and impact conditions. Our findings indicate that the tendency of droplets to splash is proportional to the reciprocal of the substrate's radius of curvature, independent of whether the substrate is convex or concave, with it being harder for droplets to splash on small spheres. Moreover, we consistently parameterise the axisymmetric splashing threshold across all curved substrate geometries via a modification to the well-known splashing ratio. Finally, the splashing dynamics resulting from initial asymmetry between the impacting droplet and curved substrate are also elucidated.

A novel capsule-based smell test fabricated via coaxial dripping.

In this paper, we demonstrate that aromatic oil capsules, produced by dripping droplets, can offer a simple, yet effective, testing tool to aid in the diagnosis of various diseases, in which the loss of smell is a key symptom. These include chronic neurological conditions such as Parkinson's and Alzheimer's diseases, and acute respiratory infections such as that caused by COVID-19. The capsules were fabricated by concentrically dripping oil/alginate droplets, from a coaxial nozzle, into an oppositely charged ionic liquid. This fabrication technique enables full control over the capsule size, the shell thickness and the volume of the encapsulated oil. After formation, liquid capsules were left to dry and form a solid crust surrounding the oil. The prototype test consists of placing a standardized number of capsules between adhesive strips that users crush and pull apart to release the smell. In addition to the fabrication method, a simple mathematical model was developed to predict the volume of encapsulated oil within the capsule in terms of the flow rate ratio and the nozzle size. Tensile tests show that capsule strength is inversely proportional to its size owing to an increase in the shell thickness. By increasing the alginate concentration, the load required to rupture the capsule increases, to the point where capsules are too stiff to be broken by a fingertip grip. Results from a preliminary screening test, within a group of patients with Parkinson's disease, found that smells were detectable using a 'forced choice' paradigm.

The Effect of Surface Roughness on the Contact Line and Splashing Dynamics of Impacting Droplets.

Whether a droplet splashes upon impact onto a solid is known to depend not only on the fluid properties and its speed, but also on the substrate characteristics. Past research has shown that splashing is heavily influenced by the substrate roughness. Indeed, in this manuscript, we demonstrate that splashing is ruled by the surface roughness, the splashing ratio, and the dynamic contact angle. Experiments consist of water and ethanol droplets impacting onto solid substrates with varying degrees of roughness. High speed imaging is used to extract the dynamic contact angle as a function of the spreading speed for these impacting droplets. During the spreading phase, the dynamic contact angle achieves an asymptotic maximum value, which depends on the substrate roughness and the liquid properties. We found that this maximum dynamic contact angle, together with the liquid properties, the ratio of the peak to peak roughness and the surface feature mean width, determines the splashing to no-splashing threshold. In addition, these parameters consistently differentiate the splashing behaviour of impacts onto smooth hydrophilic, hydrophobic and superhydrophobic surfaces.

Shape of a recoiling liquid filament.

We study the capillary retraction of a Newtonian semi-infinite liquid filament through analytical methods. We derive a long-time asymptotic-state expansion for the filament profile using a one-dimensional free-surface slender cylindrical flow model based on the three-dimensional axisymmetric Navier-Stokes equations. The analysis identifies three distinct length and time scale regions in the retraction domain: a steady filament section, a growing spherical blob, and an intermediate matching zone. We show that liquid filaments naturally develop travelling capillary waves along their surface and a neck behind the blob. We analytically prove that the wavelength of the capillary waves is approximately 3.63 times the filament's radius at the inviscid limit. Additionally, the waves' asymptotic wavelength, decay length, and the minimum neck size are analysed in terms of the Ohnesorge number. Finally, our findings are compared with previous results from the literature and numerical simulations in Basilisk obtaining a good agreement. This analysis provides a full picture of the recoiling process going beyond the classic result of the velocity of retraction found by Taylor and Culick.

Role of the Dynamic Contact Angle on Splashing.

In this Letter, we study the splashing behavior of droplets upon impact onto a variety of substrates with different wetting properties, ranging from hydrophilic to superhydrophobic surfaces. In particular, we study the effects of the dynamic contact angle on splashing. The experimental approach uses high-speed imaging and image analysis to recover the apparent contact angle as a function of the spreading speed. Our results show that neither the Capillary number nor the so-called splashing parameter are appropriate to characterize the splashing behavior under these circumstances. However, we show that the maximum dynamic advancing contact angle and the splashing ratio ß adequately characterize the splashing behavior.

Controlled cavity collapse: scaling laws of drop formation.

The formation of transient cavities at liquid interfaces occurs in an immense variety of natural processes, among which the bursting of surface bubbles and the impact of a drop on a liquid pool are salient. The collapse of a surface liquid cavity is a well documented natural process that leads to the ejection of a thin and fast jet. Droplets generated through this process can be one order of magnitude smaller than the cavity's aperture, and they are consequently of interest in drop on demand inkjet applications. In this work, the controlled formation and collapse of a liquid cavity is analyzed, and the conditions for minimizing the resulting size and number of ejected drops are determined. The experimental and numerical models are simple and consist of a liquid reservoir, a nozzle plate with the discharge orifice, and a moving piston actuated by single half-sine-shaped pull-mode pulses. The size of the jetted droplet is described by a physical model resulting in a scaling law that is numerically and experimentally validated.

Droplet impact dynamics on textiles.

The development of textiles that repel droplets following droplet impact at a high velocity is a common requirement in a number of applications, ranging from waterproof clothing to inkjet printing, yet the underpinning physical mechanisms are not entirely understood. The impact of a droplet on the surface of a textile produces two simultaneous yet separate flows, occurring above and below the surface, and which are associated with the spreading and penetration dynamics. In this paper, we study the temporal evolution of the lateral spreading diameter of a droplet impacting both hydrophobic and hydrophilic textiles. We show that the impact on textiles at short timescales involves no deformation of the droplet shape if the textile's porosity is sufficiently low. We show that the early-stage impact penetration is solely driven by inertia and no lamella is visible. We also show that for hydrophilic textiles, depending on the impact conditions, a droplet can be captured by the textile or penetrate it. We show by balancing the dynamic impact and capillary pressures that the penetration behaviour is governed by a threshold pore size, the liquid characteristics and the droplet diameter. Our conclusions highlight that the ability of a textile to repel water is controlled by the mesh size. Our experiments and analysis were carried out on coated hydrophobic and non-coated hydrophilic textiles with four corresponding mesh sizes, and are in agreement with the previous findings on hydrophobic metallic (copper) meshes.

It's Harder to Splash on Soft Solids.

Droplets splash when they impact dry, flat substrates above a critical velocity that depends on parameters such as droplet size, viscosity, and air pressure. By imaging ethanol drops impacting silicone gels of different stiffnesses, we show that substrate stiffness also affects the splashing threshold. Splashing is reduced or even eliminated: droplets on the softest substrates need over 70% more kinetic energy to splash than they do on rigid substrates. We show that this is due to energy losses caused by deformations of soft substrates during the first few microseconds of impact. We find that solids with Young's moduli ≲100 kPa reduce splashing, in agreement with simple scaling arguments. Thus, materials like soft gels and elastomers can be used as simple coatings for effective splash prevention. Soft substrates also serve as a useful system for testing splash-formation theories and sheet-ejection mechanisms, as they allow the characteristics of ejection sheets to be controlled independently of the bulk impact dynamics of droplets.