Initial spreading of low-viscosity drops on partially wetting surfaces

Ring-shaped colloidal patterns on saline water films

HYPOTHESIS

Electrostatically stabilised colloidal particles destabilise when brought into contact with cations causing the particles to aggregate in clusters. When a drop with stabilised colloidal partices is deposited on a liquid film containing cations the delicate balance between the fluid-mechanical and physicochemical properties of the system governs the spreading dynamics and formation of colloidal particle clusters.

EXPERIMENTS

High-speed imaging and digital holographic microscopy were used to characterise the spreading process.

FINDINGS

We reveal that a spreading colloidal drop evolves into a ring-shaped pattern after it is deposited on a thin saline water film. Clustered colloidal particles aggregate into larger trapezoidally-shaped 'supraclusters'. Using a simple model we show that the trapezoidal shape of the supraclusters is determined by the transition from inertial spreading dynamics to Marangoni flow. These results may be of interest to applications such as wet-on-wet inkjet printing, where particle destabilisation and hydrodynamic flow coexist.

Rapid Spreading of Yield-Stress Liquids

When a liquid drop makes initial contact with any surface, an unbalanced surface tension force drives the contact line, causing spreading. For Newtonian liquids, either liquid inertia or viscosity dictates these early regimes of spreading, albeit with different power-law behaviors of the evolution of the dynamic spreading radius. In this work, we investigate the early regimes of spreading for yield-stress liquids. We conducted spreading experiments with hydrogels and blood with varying degrees of yield stress. We observe that for yield-stress liquids, the early regime of spreading is primarily dictated by their high shear rate viscosity. For yield-stress liquids with low values of high shear rate viscosity, the spreading dynamics mimics that of Newtonian liquids like water, i.e., an inertia-capillary regime exhibited by a power-law evolution of spreading radius with exponent 1/2. With increasing high shear rate viscosity, we observe that a deceptively similar, although slower, power-law spreading regime is obeyed. The observed regime is in fact a viscous-capillary where viscous dissipation dominates over inertia. The present findings can provide valuable insights into how to efficiently control moving contact lines of biomaterial inks, which often exhibit yield-stress behavior and operate at high print speeds, to achieve desired print resolution.

Unsteady wetting of soft solids

HYPOTHESIS

Spreading of liquids on soft solids often occurs intermittently, i.e., the liquid's wetting front switches between sticking and slipping. Studies of this so-called stick-slip wetting on soft solids mostly are confined within quasi-static or forced spreading conditions. In these situations, because the sticking duration is set much larger than the viscoelastic relaxation time of the solid, a ridge is persistently and fully developed at the wetting front as the soft solid yields to the liquid's surface tension. The sticking duration and spreading velocity, therefore, were shown to have little impact to the contact angle change required for stick-to-slip transitions. For unsteady wetting of soft solids, a commonly encountered but largely unexplored situation, we hypothesize that the stick-to-slip transition is controlled not only by a combination of sticking duration and the spreading velocity, but also by an increasing depinning threshold caused by the growing ridge at the wetting front.

EXPERIMENT

We performed unsteady wetting experiment on soft solids by letting water droplets spread freely on soft solid surfaces of various stiffness. We capture both the stick-slip spreading behavior and growing wetting ridges using synchronous high-speed imaging and high-speed interferometry. Recorded data of liquid spreading and solid deforming at the wetting front were analyzed to shed light on the relation between stick-slip characteristics and the growing wetting ridge.

FINDINGS

We find that intermittent wetting on a soft solid surface results from a competition between three key factors: liquid inertia, capillary force change during sticking, and growing pinning force caused by the solid's viscoelastic response. We theoretically formulate their quantitative contributions to predict how stick-to-slip transitions occur, i.e., how the contact angle change and sticking duration depend on the liquid's spreading velocity and the solid's viscoelastic characteristics. This provides a mechanistic understanding and methods to control unsteady wetting phenomena in diverse applications, from tissue engineering and fabrication of flexible electronics to biomedicine.

Soft wetting: Substrate softness- and time-dependent droplet/bubble adhesion

HYPOTHESIS

The droplet/bubble adhesion characteristics depend on the length of the droplet/bubble three-phase contact line. Since the deformation caused by the liquid-gas interfacial tension on the soft substrate, referred as to the wetting ridge, retards contact line spreading and retraction, we conjecture that the droplet/bubble adhesion characteristics depend also on the substrate softness.

EXPERIMENTS

Soft substrates with various shear moduli are prepared and characterized by the spreading and receding dynamics of water droplets and underwater bubbles. Snap-in and normal adhesion forces of droplets/bubbles on such soft substrates are directly measured along with the visualized droplet/bubble shape profiles.

FINDINGS

The droplet/bubble snap-in force, which corresponds to the short-time spreading dynamics, decreases with a decrease in the substrate shear modulus because of the retarded contact line spreading. The droplet maximal adhesion force on a soft substrate can be counterintuitively either smaller or larger than its counterpart on the rigid substrate depending on different dwelling times, i.e., the droplet/bubble-substrate contact time before droplet/bubble-substrate separation. The former is attributed to the retarded contact line spreading, whereas the latter is attributed to the retarded contact line retraction. The substrate softness- and dwelling time-dependent droplet/bubble adhesion reported in this study will benefit various applications related to soft substrates.

Measurement Methods for Droplet Adhesion Characteristics and Micrometer-Scale Quantification of Contact Angle on Superhydrophobic Surfaces: Challenges and Opportunities

Inspired by nature, superhydrophobic surfaces have been widely studied. Usually the wettability of a superhydrophobic surface is quantified by the macroscopic contact angle. However, this method has various limitations, especially for precision micro devices with superhydrophobic surfaces, such as biomimetic artificial compound eyes and biomimetic water strider robots. These precision micro devices with superhydrophobic surfaces proposed a higher demand for the quantification of contact angles, requiring contact angle quantification technology to have micrometer-scale measurement capabilities. In this review, it is proposed to achieve micrometer-scale quantification of superhydrophobic surface contact angles through droplet adhesion characteristics (adhesion force and contact radius). Existing contact angle quantification techniques and droplet characteristics' measurement methods were described in detail. The advancement of micrometer-scale quantification technology for the contact angle of superhydrophobic surfaces will enhance our understanding of superhydrophobic surfaces.

Rolling and Sliding Modes of Nanodroplet Spreading: Molecular Simulations and a Continuum Approach

Molecular simulations discover a new mode of dynamic wetting that manifests itself in the very earliest stages of spreading, after a droplet contacts a solid. The observed mode is a "rolling" type of motion, characterized by a contact angle lower than the classically assumed value of 180°, and precedes the conventional "sliding" mode of spreading. This motivates the development of a novel continuum framework that captures all modes of motion, allows the dominant physical mechanisms to be understood, and permits the study of larger droplets.

Predicting the Dynamics and Steady-State Shape of Cylindrical Newtonian Filaments on Solid Substrates

The spreading of liquid filaments on solid surfaces is of paramount importance to a wide range of applications including ink-jet printing, coating, and direct ink writing (DIW). However, there is a considerable lack of experimental, numerical, and theoretical studies on the spreading of filaments on solid substrates. In this work, we studied the dynamics of spreading of Newtonian filaments via experiment, numerical simulations, and theoretical analysis. More specifically, we used a novel experimental setup to validate a 2D moving mesh computational fluid dynamics (CFD) model. The CFD model is used to determine the effect of processing and fluid parameters on the dynamics of filament spreading. We experimentally showed that for a Newtonian filament, the same spreading dynamics and final shape are obtained when the initial radius is constant, independent of the magnitude in printing parameters. In other words, the only important parameter on the spreading of filaments is the initial filament radius. Using a numerical model, we showed that the initial filament radius manifests itself in two important dimensionless parameters, Bond number, Bo, and viscous timescale, τμ. Furthermore, the results clearly show that the dynamics of spreading are governed by the static advancing contact angle, θs. These three parameters determine a master spreading curve that can be used to predict the spreading of cylindrical filaments on flat substrates. Finally, we developed a theoretical model that was parameterized using experimental data to correlate the steady-state shape of filaments with Bo and θs. These results are particularly applicable for predicting and controlling the dynamics of filaments in DIW and other extrusion-based processes.

A generalized scaling theory for spontaneous spreading of Newtonian fluids on solid substrates

HYPOTHESIS

There exists a generalized solution for the spontaneous spreading dynamics of droplets taking into account the influence of interfacial tension and gravity.

EXPERIMENTS

This work presents a generalized scaling theory for the problem of spontaneous dynamic spreading of Newtonian fluids on a flat substrate using experimental analysis and numerical simulations. More specifically, we first validate and modify a dynamic contact angle model to accurately describe the dependency of contact angle on the contact line velocity, which is generalized by the capillary number. The dynamic contact model is implemented into a two-phase moving mesh computational fluid dynamics (CFD) model, which is validated using experimental results.

FINDINGS

We show that the spreading process is governed by three important parameters: the Bo number, viscous timescale τ_viscous, and static advancing contact angle, θ_s. More specifically, there exists a master spreading curve for a specific Bo and θ_s by scaling the spreading time with the τ_viscous. Moreover, we developed a correlation for prediction of the equilibrium shape of the droplets as a function of both Bo and θ_s. The results of this study can be used in a wide range of applications to predict both dynamic and equilibrium shape of droplets, such as in droplet-based additive manufacturing.

Spreading dynamics of microdroplets on nanostructured surfaces

HYPOTHESIS

Droplet spreading governs various daily phenomena and industrial processes. Insights about microdroplet spreading are limited due to experimental difficulties arising from microdroplet manipulation and substrate wettability control. For droplet sizes approaching the capillary length scale, the gravitational force plays an important role in spreading. In contrast, capillary and viscous forces dominate as the droplet size reduces to smaller length scales. We hypothesize that the dynamic spreading behavior of microdroplets whose radius is far lower than the capillary length differs substantially from established and well understood dynamics.

EXPERIMENTS

To systematically investigate the spreading dynamics of microdroplets, we develop contact-initiated wetting techniques combined with structuring-independent wettability control to achieve microdroplet (<500 μm) spreading on arbitrary surfaces while eliminating parasitic pinning effects (pining force ∼ 0) and initial impact momentum effects (Weber number ∼ 0).

FINDINGS

Our experiments reveal that the capillary-driven initial spreading of microdroplets is shorter, with significantly reduced oscillation dampening, when compared to millimeter-scale droplets. Furthermore, spreading along with capillary wave propagation results in coupling between the spreading velocity and dynamic contact angle at the contact line. These findings, along with our proposed microdroplet manipulation platform, may find application in microscale heat transfer, advanced manufacturing, and aerosol transmission studies.

Dynamic wetting of various liquids: Theoretical models, experiments, simulations and applications

Dynamic wetting is a ubiquitous phenomenon and frequently observed in our daily life, as exemplified by the famous lotus effect. It is also an interfacial process of upmost importance involving many cutting-edge applications and has hence received significantly increasing academic and industrial attention for several decades. However, we are still far away to completely understand and predict wetting dynamics for a given system due to the complexity of this dynamic process. The physics of moving contact lines is mainly ascribed to the full coupling with the solid surface on which the liquids contact, the atmosphere surrounding the liquids, and the physico-chemical characteristics of the liquids involved (small-molecule liquids, metal liquids, polymer liquids, and simulated liquids). Therefore, to deepen the understanding and efficiently harness wetting dynamics, we propose to review the major advances in the available literature. After an introduction providing a concise and general background on dynamic wetting, the main theories are presented and critically compared. Next, the dynamic wetting of various liquids ranging from small-molecule liquids to simulated liquids are systematically summarized, in which the new physical concepts (such as surface segregation, contact line fluctuations, etc.) are particularly highlighted. Subsequently, the related emerging applications are briefly presented in this review. Finally, some tentative suggestions and challenges are proposed with the aim to guide future developments.

Drawing liquid bridges from a thin viscous film

When a particle, such as dust, contacts a thin liquid film covering a surface it is trapped by the liquid. This effect is caused by the formation of a meniscus, resulting in a capillary force that makes the particle adhere to the surface. While capillary adhesion is well-characterised in static situations, the dynamic formation of the liquid bridge after the initial contact is highly intricate. Here, we experimentally study the evolution of a liquid bridge after a glass sphere is gently brought into contact with a thin viscous film. It is found that the contact creates a ripple on the thin film, which influences the growth of the meniscus. Initially, the ripple and the meniscus are coupled and exhibit similar dynamics. This initial regime is well accounted for by a scaling law derived from lubrication theory. At a later stage, the ripple is "detached" from the liquid bridge, leading to a second regime of bridge dynamics. As a result, capillary forces are time-dependent, highlighting the importance of dynamics on adhesion.

Multiscale Approach to Studying Biomolecular Interactions in Cellulose-Casein Adhesion

Casein finds application as an eco-friendly adhesive for paper, wood, glass, etc. Casein being a protein can undergo conformational and microstructural changes during various processing steps involved in interfacial bonding. This study aims at understanding the multiscale contributions of these changes in casein to its adhesion to cellulose pressboards. Investigations spanning from molecular structure to macroscopic adhesion characteristics have been used in this work. The lap shear strength of casein bonded cellulose pressboards is found to increase with the increase in casein concentration. It was observed from Fourier transform infrared spectroscopy (FTIR) investigations along with microscopy and rheological studies that casein dispersions result in more α-helical conformations during the preconcentration process of casein dispersions. This results in increased hydrophobicity of the casein particles/aggregates, which in turn affects the wetting characteristics and the adhesion behavior. Casein compositions lacking α-helices were found to enhance the bonding strength of casein with cellulose. The present study shows that the adhesion between casein and microporous cellulose substrate has contributions at the multiscale originating from the polar-polar interactions of casein and cellulose molecules, conformational changes in the protein structure of casein during drying, microstructure of casein particles in the dispersion, and the microporous nature of the cellulose boards. These interactions at multiple scales can be tuned to suit different adhesive applications using casein.

Arrested Dynamics of Droplet Spreading on Ice

We investigate the arrested spreading of room temperature droplets impacting flat ice. The use of an icy substrate eliminates the nucleation energy barrier, such that a freeze front can initiate as soon as the droplet's temperature cools down to 0 °C. We employ scaling analysis to rationalize distinct regimes of arrested hydrodynamics. For gently deposited droplets, capillary-inertial spreading is halted at the onset of contact line freezing, yielding a 1/7 scaling law for the arrested diameter. At low impact velocities (We≲100), inertial effects result in a 1/2 scaling law. At higher impact velocities (We>100), inertio-viscous spreading can spill over the frozen base of the droplet until its velocity matches that of a kinetic freeze front caused by local undercooling, resulting in a 1/5 scaling law.

Contact Line Catch Up by Growing Ice Crystals

The effect of freezing on contact line motion is a scientific challenge in the understanding of the solidification of capillary flows. In this Letter, we experimentally investigate the spreading and freezing of a water droplet on a cold substrate. We demonstrate that solidification stops the spreading because the ice crystals catch up with the advancing contact line. Indeed, we observe the formation and growth of ice crystals along the substrate during the drop spreading, and show that their velocity equals the contact line velocity when the drop stops. Modeling the growth of the crystals, we predict the shape of the crystal front and show that the substrate thermal properties play a major role on the frozen drop radius.

Is contact-line mobility a material parameter?

Dynamic wetting phenomena are typically described by a constitutive law relating the dynamic contact angle θ to contact-line velocity UCL. The so-called Davis–Hocking model is noteworthy for its simplicity and relates θ to UCL through a contact-line mobility parameter M, which has historically been used as a fitting parameter for the particular solid–liquid–gas system. The recent experimental discovery of Xia & Steen (2018) has led to the first direct measurement of M for inertial-capillary motions. This opens up exciting possibilities for anticipating rapid wetting and dewetting behaviors, as M is believed to be a material parameter that can be measured in one context and successfully applied in another. Here, we investigate the extent to which M is a material parameter through a combined experimental and numerical study of binary sessile drop coalescence. Experiments are performed using water droplets on multiple surfaces with varying wetting properties (static contact angle and hysteresis) and compared with numerical simulations that employ the Davis–Hocking condition with the mobility M a fixed parameter, as measured by the cyclically dynamic contact angle goniometer, i.e. no fitting parameter. Side-view coalescence dynamics and time traces of the projected swept areas are used as metrics to compare experiments with numerical simulation. Our results show that the Davis–Hocking model with measured mobility parameter captures the essential coalescence dynamics and outperforms the widely used Kistler dynamic contact angle model in many cases. These observations provide insights in that the mobility is indeed a material parameter.

Toward Unveiling the Anomalies Associated with the Spontaneous Spreading of Droplets

The liquid droplet spreads over a solid surface to minimize the surface energy when brought in direct contact with the surface. The spreading process is rapid in the early stages, tends to slow down during its progress, and has resulted in peculiarity due to the experimental difficulties in the accurate determination of the contact line radius. In the present numerical study, we found that drop spreading begins with a viscosity-dominated Stokes regime, where contact radius scales as r ∼ t for a wide range of drop liquid viscosities. Subsequent to the Stokes regime, the inertial regime is observed where contact radius scales as r ∼ t^0.5 for low- to medium-viscous droplets, whereas for very high viscous drops, the spreading dynamics is completely dominated by the viscous regime. It is also found that the equilibrium wetting condition does not affect the power-law scaling for the contact radius of the drop. The amplitude of capillary waves induced across the interface of the drop is observed to be sufficiently high to cause necking and ejection of satellite drops from the main drop during its spreading for low-viscous liquids from complete wetting to partial wetting conditions. A regime plot between the Ohnesorge number and advancing contact angle of the substrate is presented to demarcate the regions of damped waves without pinch-off and drop spreading with satellite drops.

Spreading of soap bubbles on dry and wet surfaces

The spreading of soap bubbles after forming contact with a substrate is experimentally studied. We find for dry glass substrate that the rim of the spreading soap bubble follows the well known scaling law for inertia dominated spreading \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r \sim t^{1/2}$$\end{document}r∼t1/2 [Eggers, J., Lister, J., and Stone, H., J. Fluid Mech. 401, 293–310 (1999)]. Varying the viscosity of the soap solutions and the coating of the glass does not affect this spreading behavior qualitatively. Yet, on a wetted surface, the rim obtains a constant radial velocity. Here, the rim splits into two and this new rim trails the main rim. Interestingly, the central film enclosed by the two rims develops radially oriented wrinkles.

Bioinspired Topological Surface for Directional Oil Lubrication

Directional droplet transport widely exists in biological surfaces that greatly inspire the development of a great deal of engineered devices allowing for directional liquid transport in diverse energy and water applications. Despite extensive advances in this area, it remains a challenge to guide the directional spreading of lubricating oils by virtue of the bioinspired design of surface topography in the lubricity field. In this paper, we develop a bioinspired topological surface textured with simple V-shaped posts elegantly distributed in the parallel channels, which allows for an efficient and unidirectional transport of various lubricating oils. We also clarify the propagation of a precursor film and the coalescence effect between the original droplet and the precursor film in the preferential direction, as well as the pinning effect in the reverse direction, which integrate seamlessly to create a long-range directional oil transportation. The directional oil transportation promises a potential application of directional lubrication, creating a functional surface consisting of two zones with different lubrication properties as evidenced by different friction coefficients.

A Numerical Study of Micro-Droplet Spreading Behaviors on Wettability-Confined Tracks Using a Three-Dimensional Phase-Field Lattice Boltzmann Model

Wettability-confined tracks have been extensively used in open-surface microfluidic devices for their high capacity of transporting droplet pumplessly. Inspired by the experimental work of Sen et al. [ Langmuir 2018 , 34 , 1899 - 1907 ], in the present study, a three-dimensional phase-field lattice Boltzmann model is developed and used to investigate the spreading behaviors of microdroplet on a series of wettability-confined tracks. The experimental findings are successfully reproduced through our simulation, where three distinct stages of droplet spreading on the horizontal wettability-confined diverging track are fairly exhibited, that is, the initial stage with droplet front spreading quickly, the intermediate stage with both droplet front and bulge moving forward at a constant speed, and the final stage with droplet front decelerating gradually. Moreover, a parametric study of track divergence angle is further performed, and the influential mechanism of track divergence angle on droplet spreading is further revealed. It is demonstrated that track divergence is responsible for the Laplace pressure gradient and capillary force inside the droplet, which drives the droplet bulge to move forward on the diverging track. With an increase in divergence angle, the capillary force increases linearly, which increases the droplet spreading speed at the initial and intermediate stages, while the peak capillary force comes earlier, and consequently the final decelerating stage comes earlier. On the basis of the parametric study and droplet volume conservation rule, a power law relation between track divergence angle and droplet spreading is proposed, which helps to identify the start of final decelerating stage. Finally, the droplet spreading over various inclined tracks is explored, which can be achieved only when the capillary force at the beginning is larger than the droplet gravity component along the inclined track surface.

Coupled flow and deformation fields due to a line load on a poroelastic half space: effect of surface stress and surface bending

In the past decade, many experiments have indicated that the surfaces of soft elastic solids can resist deformation by surface stresses. A common soft elastic solid is a hydrogel which consists of a polymer network swollen in water. Although experiments suggest that solvent flow in gels can be affected by surface stress, there is no theoretical analysis on this subject. Here we study the solvent flow near a line load acting on a linear poroelastic half space. The surface of this half space resists deformation by a constant, isotropic surface stress. It can also resist deformation by surface bending. The time-dependent displacement, stress and flow fields are determined using transform methods. Our solution indicates that the stress field underneath the line load is completely regularized by surface bending-it is bounded and continuous. For small surface bending stiffness, the line force is balanced by surface stresses; these forces form what is commonly known as 'Neumann's triangle'. We show that surface stress reduces local pore pressure and inhibits solvent flow. We use our line load solution to simulate the relaxation of the peak which is formed by applying and then removing a line force on the poroelastic half space.

Revealing How Topography of Surface Microstructures Alters Capillary Spreading

Wetting phenomena, i.e. the spreading of a liquid over a dry solid surface, are important for understanding how plants and insects imbibe water and moisture and for miniaturization in chemistry and biotechnology, among other examples. They pose fundamental challenges and possibilities, especially in dynamic situations. The surface chemistry and micro-scale roughness may determine the macroscopic spreading flow. The question here is how dynamic wetting depends on the topography of the substrate, i.e. the actual geometry of the roughness elements. To this end, we have formulated a toy model that accounts for the roughness shape, which is tested against a series of spreading experiments made on asymmetric sawtooth surface structures. The spreading speed in different directions relative to the surface pattern is found to be well described by the toy model. The toy model also shows the mechanism by which the shape of the roughness together with the line friction determines the observed slowing down of the spreading.

Wetting dynamics in two-liquid systems: Effect of the surrounding phase viscosity

This paper reports the experimental results of a water droplet spreading on a glass substrate submerged in an oil phase. The radius of the wetted area grows exponentially over time forming two distinct regimes. The early time dynamics of wetting is characterized with the time exponent of 1, referred to as the viscous regime, which is ultimately transitioned to the Tanner's regime with the time exponent of 0.1. It is revealed that an increase in the ambient phase viscosity over three decades considerably slows down the rate of three-phase contact line movement. A scaling law is developed where the three-phase contact line velocity is a function of both spreading radius and mean viscosity, close to the geometric mean of the droplet and ambient fluids' viscosities. Using the proposed scaling and mean viscosity, all plots of spreading radius for different viscosity ratios collapse to a master curve. Furthermore, several cases with multiple rupture and spreading points, i.e., wetting in a nonideal system, are considered. The growth of an equivalent wetting radius in a multiple point spreading system is predicted by the developed scaling law.

Lattice Boltzmann simulation of droplet dynamics on granular surfaces with variable wettability

Soil-composing particles undergo wettability changes, impacting hydraulic and mechanical processes such as erosion and landslides. Such processes evolve at very small scales, typically at the particle level. Here we capture the evolution of liquid interfaces in a single particle and several particles with the lattice Boltzmann (LB) method. The paper presents a three-dimensional LB study on the droplet dynamics on a layer of uniformly packed spherical particles with varying size and intrinsic contact angle (CA) aimed at mimicking conditions comparable to those of real soils. The numerical droplet is initialized close to the granular surface and deposited by gravity. Three spreading and infiltration behaviors were identified: a droplet with a stable apparent CA, a droplet with a metastable apparent CA before infiltration, and immediate infiltration. The results showed that the formation of a droplet with a stable or metastable spherical-cap shape depends on the particle size and the intrinsic CA. Furthermore, the initial wetted zone expansion was found to be governed by inertial effects with its behavior characterized by a power law. Finally, the apparent CA, which is closely related to the intrinsic CA, was found to be influenced by the particle size due to a significant portion of the droplet being embedded into the granular surface for the larger particles and reducing the apparent CA. This paper provides a basis for future research targeting the behavior of droplet interaction with granular surfaces with variable intrinsic CAs (from wettable to superhydrophobic) such as soils and other granular materials for industrial applications. The numerical approach implemented can also be extended to model other dynamic processes for a droplet, such as evaporation, high-velocity impacting, and lateral sliding.

Drop spreading and gelation of thermoresponsive polymers

Spreading and solidification of liquid droplets are elementary processes of relevance for additive manufacturing. Here we investigate the effect of heat transfer on spreading of a thermoresponsive solution (Pluronic F127) that undergoes a sol-gel transition above a critical temperature Tm. By controlling the concentration of Pluronic F127 we systematically vary Tm, while also imposing a broad range of temperatures of the solid and the liquid. We subsequently monitor the spreading dynamics over several orders of magnitude in time and determine when solidification stops the spreading. It is found that the main parameter is the difference between the substrate temperature and Tm, pointing to a local mechanism for arrest near the contact line. Unexpectedly, the spreading is also found to stop below the gelation temperature, which we attribute to a local enhancement in polymer concentration due to evaporation near the contact line.

Dynamic Spreading of Droplets on Lyophilic Micropillar-Arrayed Surfaces

The wetting kinetics of droplets on lyophilic pillar-arrayed substrates is the driving mechanism of several natural phenomena (e.g., insect capturing by Nepenthes) and many industrial technologies (e.g., gas-liquid separation). For a lyophilic pillar-arrayed surface, a fringe film is formed ahead of the contact line, resulting in distinct wetting kinetics, which needs further investigation. In this study, Si(100) substrates with square micropillars were used to investigate the early spreading of droplets on lyophilic pillar-arrayed surfaces through the droplet-spreading method. A fringe film was observed ahead of the contact line for micropillar-arrayed surfaces. The spreading radius was enhanced by micropillars and mainly caused by liquid penetration into the pillar forest, resulting in alteration of the dissipation mechanism. The early spreading of droplets on lyophilic micropillar-arrayed surface was affected only by the solid fraction and independent of the pillar height. A semitheoretical model without adjustable parameters was established on the basis of the global energetic equation, considering the local dissipation, viscous dissipation, and the dissipation in the precursor film. The prediction of the model agrees with the experimental results. Our semitheoretical model may aid in predicting the wetting kinetics on lyophilic pillar-arrayed substrates and assist the design of pillar-arrayed surfaces in practical applications.

Scaling Laws in Directional Spreading of Droplets on Wettability-Confined Diverging Tracks

Spontaneous pumpless transport of droplets on wettability-confined tracks is important for various applications, such as rapid transport and mixing of fluid droplets, enhanced dropwise condensation, biomedical devices, and so forth. Recent studies have shown that on an open surface, a superhydrophilic track of diverging width, laid on a superhydrophobic background, facilitates the transport of water from the narrower end to the wider end at unprecedented rates (up to 40 cm/s) without external actuation. The spreading behavior on such surfaces, however, has only been characterized for water. Keeping in mind that such designs play a key role for a diverse range of applications, such as handling organic liquids and in point-of-care devices, the importance of characterizing the spreading behavior of viscous liquids on such surfaces cannot be overemphasized. In the present work, the spreading behavior on the aforementioned wettability-patterned diverging tracks was observed for fluids of different viscosities. Two dimensionless variables were identified, and a comprehensive relationship was obtained. Three distinct temporal regimes of droplet spreading were established: I), a Washburn-type slow spreading, II) a much faster Laplace pressure-driven spreading, and III), a sluggish density-augmented Tanner-type film spreading. The results offer design guidance for tracks that can pumplessly manage fluids of various viscosities and surface tensions.

Nonisothermal Spreading Dynamics of Self-Rewetting Droplets

We experimentally studied the spreading dynamics of binary alcohol mixtures (and pure liquids for reference) deposited on a heated substrate in a partially wetting situation under nonisothermal conditions. We show that the spreading mechanism of an evaporating droplet exhibits a power-law growth with early-stage exponents that depend strongly and nonmonotonically on the substrate temperature. Moreover, we investigated the temporal and spatial thermal dynamics in the droplet using infrared thermography, revealing the existence of unique thermal patterns due to thermal and/or solutal instabilities, which lead to surface tension gradients, namely the Marangoni effect. Our key findings are that the temperature of the substrate drastically affects the early-stage inertial-capillary spreading regime owing to the nonmonotonic surface tension-temperature dependence of the self-rewetting liquids. At later stages of wetting, the spreading dynamics enters the viscous-capillary dominated regime, with the characteristic low kinetics mirroring the behavior of pure liquids.

Universality of oscillating boiling in Leidenfrost transition

The Leidenfrost transition leads a boiling system to the boiling crisis, a state in which the liquid loses contact with the heated surface due to excessive vapor generation. Here, using experiments of liquid droplets boiling on a heated surface, we report a phenomenon, termed oscillating boiling, at the Leidenfrost transition. We show that oscillating boiling results from the competition between two effects: separation of liquid from the heated surface due to localized boiling and rewetting. We argue theoretically that the Leidenfrost transition can be predicted based on its link with the oscillating boiling phenomenon and verify the prediction experimentally for various liquids.

Water Droplet Spreading and Wicking on Nanostructured Surfaces

Phase-change heat transfer on nanostructured surfaces is an efficient cooling method for high heat flux devices due to its superior wettability. Liquid droplet spreading and wicking effect then dominate the heat transfer. Therefore, this study investigates the flow behavior after a droplet touches a nanostructured surface focusing on the ZnO nanowire surface with three different nanowire sizes and two array types (regular and irregular). The spreading diameter and the wicking diameter are measured against time. The results show that the average spreading and wicking velocities on a regular nanostructured surface are both smaller than those on an irregular nanostructured surface and that the nanowire size affects the liquid spreading and capillary wicking.

Direct visualization of particle attachment to a pendant drop

An experimental investigation is carried out into the attachment of a single particle to a liquid drop. High-speed videography is used to directly visualize the so-called 'snap-in' effect which occurs rapidly over sub-millisecond timescales. Using high-magnification, the evolution of the contact line around the particle is tracked and dynamic features such as the contact angle, wetted radius and force are extracted from these images to help build a fundamental understanding of the process. By examining the wetted length in terms of an arc angle, ϕ, it is shown that the early wetting stage is an inertial-dominated process and best described by a power law relation, i.e. ϕ ∼ (t/τ)^α, where τ is an inertial timescale. For the subsequent lift-off stage, the initial particle displacement is matched with that predicted using a simple balance between particle weight and capillary force with reasonable agreement. The lift-off force is shown to be on the order of 1-100 μN, whilst the force of impacting droplets is known to be on the order of 10-1000 mN. This explains the ease in which liquid marbles are formed during impact experiments.

Electrostatic cloaking of surface structure for dynamic wetting

Dynamic wetting problems are fundamental to understanding the interaction between liquids and solids. Even in a superficially simple experimental situation, such as a droplet spreading over a dry surface, the result may depend not only on the liquid properties but also strongly on the substrate-surface properties; even for macroscopically smooth surfaces, the microscopic geometrical roughness can be important. In addition, because surfaces may often be naturally charged or electric fields are used to manipulate fluids, electric effects are crucial components that influence wetting phenomena. We investigate the interplay between electric forces and surface structures in dynamic wetting. Although surface microstructures can significantly hinder spreading, we find that electrostatics can "cloak" the microstructures, that is, deactivate the hindering. We identify the physics in terms of reduction in contact-line friction, which makes the dynamic wetting inertial force dominant and insensitive to the substrate properties.

Interaction between a water drop and holey graphene: retarded imbibition and generation of novel water–graphene wetting states

Water nanodrop imbibition in holey graphene is studied unraveling novel fiber-like wetting state that enhances water–accessible graphene surface area.

Drop spreading on a superhydrophobic surface: pinned contact line and bending liquid surface

On a superhydrophobic surface, a drop spreads by the bending of the air–liquid interface with the three-phase contact line remaining pinned.

Understanding the Early Regime of Drop Spreading

We present experimental data to characterize the spreading of a liquid drop on a substrate kept submerged in another liquid medium. They reveal that drop spreading always begins in a regime dominated by drop viscosity where the spreading radius scales as r ∼ t with a nonuniversal prefactor. This initial viscous regime either lasts in its entirety or switches to an intermediate inertial regime where the spreading radius grows with time following the well-established inertial scaling of r ∼ t(1/2). This latter case depends on the characteristic viscous length scale of the problem. In either case, the final stage of spreading, close to equilibrium, follows Tanner's law. Further experiments performed on the same substrate kept in ambient air reveal a similar trend, albeit with limited spatiotemporal resolution, showing the universal nature of the spreading behavior. It is also found that, for early times of spreading, the process is similar to coalescence of two freely suspended liquid drops, making the presence of the substrate and consequently the three-phase contact line insignificant.

Universal evolution of a viscous-capillary spreading drop

The rate of spreading or retraction of a drop on a flat substrate is determined through a balance of surface tension and hydrodynamic flow. While asymptotic regimes are known, no general rate equation has hitherto been available. Here, we revisit this classic problem, in a regime governed by capillary and viscous forces, by performing an exhaustive numerical study of drop evolution as a function of the contact angle with the substrate. Our study reveals a universal evolution of the drop radius parameterised only by the substrate wettability. Two limits of this evolution recover the familiar exponential and algebraic regimes. Our results show quantitative comparison with the evolution derived from lubrication theory, indicating that dissipation at the contact line is the key determinant in drop evolution. Our work, both numerical and theoretical, provides a foundation for studying the full temporal dynamics of droplet evolution under the influence of external fields and thermal fluctuations, which are of importance in nanofluidics.

Wetting dynamics of a water nanodrop on graphene

Spreading of water nanodrop on supported and unsupported graphene reveals inertia-dominated behavior.

Lattice Boltzmann investigation of droplet inertial spreading on various porous surfaces

The spreading of liquid drops on solid surfaces is a wide-spread phenomenon of both fundamental and industrial interest. In many applications, surfaces are porous and spreading patterns are very complex with respect to the case on smooth surfaces. Focusing on the inertial spreading just before the Tanner-like viscous regime, this work investigates the spreading of a low-viscosity droplet on a porous surface using lattice Boltzmann numerical simulations. The case of a flat surface is first considered, and it reveals a dependence on the solid equilibrium contact angle θ(s)(eq), which is in good agreement with published experimental data. We conducted numerical experiments with various surfaces perforated by a regular pattern of holes of infinite length. The results show that the global spreading dynamics is independent of the porosity morphology. Through the assumption that, for wetting, the pores can be regarded as surface patches with a contact angle of θ(pore)(eq)=180°, we deduce an effective equilibrium contact angle θ(eff)(eq) on the porous surface from the Cassie-Baxter law. A spreading model is then proposed to describe both a prefactor and an exponent that are similar to a flat surface whose equilibrium contact angle is θ(eff)(eq). This model compares satisfactorily with a large number of numerical experiments under varying conditions.

Spreading of a droplet over a nonisothermal substrate: multiple scaling regimes

We envisage the spreading behavior of a two-dimensional droplet under a thin-film-based paradigm, under a perfect wetting condition, while the droplet is placed over a nonisothermal substrate. Starting from the onset of thin-film behavior (or equivalently beyond the inertia-dominated initial stage), we identify the existence of mutually contrasting multiple scaling regimes defining the spreading behavior at different time scales. This is attributable to the time-stage-wise upsurge of capillarity or thermocapillarity over the other. In particular, the spreading behavior is characterized by the foot-width (w) evolution with time (t) in a power-law fashion w ∼ t(α), with α being the spreading exponent, defining the rate of spreading. Following pertinent thin-film and subsequent similarity analysis, we identify different asymptotes of α over disparate temporal scales, leading to the characterization of different scaling regimes over the entire spreading event starting from the inception of thin-film behavior. Reported literature data are found to correspond well to the present interpretations and estimations.