Impact Dynamics of Non-Newtonian Droplets on Superhydrophobic Surfaces

Droplet impact behavior on a solid surface is critical for many industrial applications such as spray coating, food production, printing, and agriculture. For all of these applications, a common challenge is to modify and control the impact regime and contact time of the droplets. This challenge becomes more critical for non-Newtonian liquids with complex rheology. In this research, we explored the impact dynamics of non-Newtonian liquids (by adding different concentrations of Xanthan into water) on superhydrophobic surfaces. Our experimental results show that by increasing the Xanthan concentration in water, the shapes of the bouncing droplet are dramatically altered, e.g., its shape at the separation moment is changed from a conventional vertical jetting into a "mushroom"-like one. As a result, the contact time of the non-Newtonian droplet could be reduced by up to ∼50%. We compare the impact scenarios of Xanthan liquids with those of glycerol solutions having a similar apparent viscosity, and results show that the differences in the elongation viscosity induce different impact dynamics of the droplets. Finally, we show that by increasing the Weber number for all of the liquids, the contact time is reduced, and the maximum spreading radius is increased.

Apparent contact angle of drops on liquid infused surfaces: geometric interpretation

We theoretically investigate the apparent contact angle of drops on liquid infused surfaces as a function of the relative size of the wetting ridge and the deposited drop. We provide an intuitive geometrical interpretation whereby the variation in the apparent contact angle is due to the rotation of the Neumann triangle at the lubricant-drop-gas contact line. We also derive linear and quadratic corrections to the apparent contact angle as power series expansion in terms of pressure differences between the lubricant, drop and gas phases. These expressions are much simpler and more compact compared to those previously derived by Semprebon et al. [Soft Matter, 2017, 13, 101-110].

Modeling ternary fluids in contact with elastic membranes

We present a thermodynamically consistent model of a ternary fluid interacting with elastic membranes. Following a free-energy modeling approach for the fluid phases, we derive the governing equations for the dynamics of the ternary fluid flow and membranes. We also provide the numerical framework for simulating such fluid-structure interaction problems. It is based on the lattice Boltzmann method for the ternary fluid (Eulerian description) and a finite difference representation of the membrane (Lagrangian description). The ternary fluid and membrane solvers are coupled through the immersed boundary method. For validation purposes, we consider the relaxation dynamics of a two-dimensional elastic capsule placed at a fluid-fluid interface. The capsule shapes, resulting from the balance of surface tension and elastic forces, are compared with equilibrium numerical solutions obtained by surface evolver. Furthermore, the Galilean invariance of the proposed model is proven. The proposed approach is versatile, allowing for the simulation of a wide range of geometries. To demonstrate this, we address the problem of a capillary bridge formed between two deformable capsules.

Capillary Bridges on Liquid-Infused Surfaces

We numerically study two-component capillary bridges formed when a liquid droplet is placed in between two liquid-infused surfaces (LIS). In contrast to commonly studied one-component capillary bridges on noninfused solid surfaces, two-component liquid bridges can exhibit a range of different morphologies where the liquid droplet is directly in contact with two, one, or none of the LIS substrates. In addition, the capillary bridges may lose stability when compressed due to the envelopment of the droplet by the lubricant. We also characterize the capillary force, maximum separation, and effective spring force and find that they are influenced by the shape and size of the lubricant ridge. Importantly, these can be tuned to increase the effective capillary adhesion strength by manipulating the lubricant pressure, Neumann angle, and wetting contact angles. As such, LIS are not only "slippery" parallel to the surface, but they are also "sticky" perpendicular to the surface.

Wetting boundaries for a ternary high-density-ratio lattice Boltzmann method

We extend a recently proposed ternary free-energy lattice Boltzmann model with high density contrast [Phys. Rev. Lett. 120, 234501 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.234501] by incorporating wetting boundaries at solid walls. The approaches are based on forcing and geometric schemes, with implementations optimized for ternary (and, more generally, higher-order multicomponent) models. Advantages and disadvantages of each method are addressed by performing both static and dynamic tests, including the capillary filling dynamics of a liquid displacing the gas phase and the self-propelled motion of a train of drops. Furthermore, we measure dynamic angles and show that the slip length critically depends on the equilibrium value of the contact angles and whether it belongs to liquid-liquid or liquid-gas interfaces. These results validate the model capabilities of simulating complex ternary fluid dynamic problems near solid boundaries, for example, drop impact solid substrates covered by a lubricant layer.

Morphological Transitions of Water Channels Induced by Vertical Vibrations

We report the results of comprehensive experiments and numerical calculations of interfacial morphologies of water confined to the hydrophilic top face of rectangular posts subjected to vertical vibrations. In response to mechanical driving, an initially flat liquid channel is collected into a liquid bulge that forms in the center of the rectangular post if the acceleration exceeds a certain threshold. The bulge morphology persists after the driving is switched off, in agreement with the morphological bistability of static interfacial shapes on posts with large length-to-width ratios. In a narrow frequency band, the channel does not decay into a bulge at any acceleration amplitude, but displays irregular capillary waves and sloshing instead. On short posts, however, a liquid bulge can be dynamically sustained through vertical vibrations but quickly decays into a homogeneous channel after the external driving is stopped. To explain the dynamic bulging of the liquid interface, we propose an effective lifting force pulling on the drop's slowly moving center of mass in the presence of fast oscillation modes.

Shape Evolution of Droplets Growing on Linear Microgrooves

Anisotropic spreading of liquids and elongated droplet shapes are often encountered on surfaces decorated with a periodic micropattern of linear surface topographies. Numerical calculations and wetting experiments show that the shape evolution of droplets that are slowly growing on a surface with parallel grooves can be grouped into two distinct morphological regimes. In the first regime, the liquid of the growing droplet spreads only into the direction parallel to the grooves. In the second regime, the three-phase contact line advances also perpendicular to the grooves, whereas the growing droplets approach a scale-invariant shape. Here, we demonstrate that shapes of droplets in contact with a large number of linear grooves are identical to the shapes of droplets confined to a plane chemical stripe, where this mapping of shapes is solely based on the knowledge of the cross section of the linear grooves and the material contact angle. The spectrum of interfacial shapes on the chemical stripe can be exploited to predict the particular growth mode and the asymptotic value of the base eccentricity in the limit of droplets covering a large number of grooves. The proposed model shows an excellent agreement with experimentally observed base eccentricities for droplets on grooves of various cross sections. The universality of the model is underlined by the accurate match with available literature data for droplet eccentricities on parallel chemical stripes.

Drop Dynamics on Liquid-Infused Surfaces: The Role of the Lubricant Ridge

We employ a free-energy lattice-Boltzmann method to study the dynamics of a ternary fluid system consisting of a liquid drop driven by a body force across a regularly textured substrate, infused by a lubricating liquid. We focus on the case of partial wetting lubricants and observe a rich interplay between contact line pinning and viscous dissipation at the lubricant ridge, which become dominant at large and small apparent angles, respectively. Our numerical investigations further demonstrate that the relative importance of viscous dissipation at the lubricant ridge depends on the drop to lubricant viscosity ratio, as well as on the shape of the wetting ridge.

Ternary Free-Energy Entropic Lattice Boltzmann Model with a High Density Ratio

A thermodynamically consistent free energy model for fluid flows comprised of one gas and two liquid components is presented and implemented using the entropic lattice Boltzmann scheme. The model allows a high density ratio, up to the order of O(10^{3}), between the liquid and gas phases, and a broad range of surface tension ratios, covering partial wetting states where Neumann triangles are formed, and full wetting states where complete encapsulation of one of the fluid components is observed. We further demonstrate that we can capture the bouncing, adhesive, and insertive regimes for the binary collisions between immiscible droplets suspended in air. Our approach opens up a vast range of multiphase flow applications involving one gas and several liquid components.

Apparent contact angle and contact angle hysteresis on liquid infused surfaces

We theoretically investigate the apparent contact angle and contact angle hysteresis of a droplet placed on a liquid infused surface. We show that the apparent contact angle is not uniquely defined by material parameters, but also has a dependence on the relative size between the droplet and its surrounding wetting ridge formed by the infusing liquid. We derive a closed form expression for the contact angle in the limit of vanishing wetting ridge, and compute the correction for small but finite ridge, which corresponds to an effective line tension term. We also predict contact angle hysteresis on liquid infused surfaces generated by the pinning of the contact lines by the surface corrugations. Our analytical expressions for both the apparent contact angle and contact angle hysteresis can be interpreted as 'weighted sums' between the contact angles of the infusing liquid relative to the droplet and surrounding gas phases, where the weighting coefficients are given by ratios of the fluid surface tensions.

Deviation of sliding drops at a chemical step

The motion of partially wetting liquid drops in contact with a solid surface is strongly affected by contact angle hysteresis and interfacial pinning. However, the majority of models proposed for drops sliding over chemical surface patterns consistently neglect the difference between advancing and receding contact angles. In this article, we present a joint experimental and numerical study of the interaction of gravity-driven drops with a chemical step formed at the junction between a hydrophilic and a hydrophobic region. It demonstrates the strong impact of a contact angle hysteresis contrast on the motion of drops at a linear chemical step. Surprisingly, the smallest driving force required to drag the drop across the step onto the lower hydrophobic surface is not observed at a right angle of incidence. Our model reveals that the non-monotonous response of this passive drop 'filter' is solely due to the higher advancing contact angle on the lower surface, and creates an instance where drop motion is affected by dissipation at the contact line rather than by surface energy.

Liquid morphologies and capillary forces between three spherical beads

Equilibrium shapes of coalesced pendular bridges in a static assembly of spherical beads are computed by numerical minimization of the interfacial energy. Our present study focuses on generic bead configurations involving three beads, one of which is in contact to the two others while there is a gap of variable size between the latter. In agreement with previous experimental studies, we find interfacial "trimer" morphologies consisting of three coalesced pendular bridges, and "dimers" of two coalesced bridges. In a certain range of the gap opening we observe a bistability between the dimer and trimer morphology during changes of the liquid volume. The magnitude of the corresponding capillary forces in presence of a trimer or dimer depends, besides the gap opening, only on the volume or Laplace pressure of the liquid. For a given Laplace pressure, and for the same gap opening, the capillary forces induced by a trimer are only slightly larger than the corresponding forces in the presence of three pendular bridges. This observation is consistent with a plateau of capillary cohesion in terms of the saturation of a wetting liquid in the funicular regime, as reported in the experimental work [Scheel et al., Nat. Mater. 7, 189 (2008)1476-112210.1038/nmat2117].

Filling transitions on rough surfaces: Inadequacy of Gaussian surface models

We present numerical studies of wetting on various topographic substrates, including random topographies. We find good agreement with recent predictions based on an analytical interface-displacement-type theory, except that we find critical end points within the physical parameter range. As predicted, Gaussian random surfaces are found to behave qualitatively different from non-Gaussian topographies. This shows that Gaussian random processes as models for rough surfaces must be used with great care, if at all, in the context of wetting phenomena.

Ternary free-energy lattice Boltzmann model with tunable surface tensions and contact angles

We present a ternary free-energy lattice Boltzmann model. The distinguishing feature of our model is that we are able to analytically derive and independently vary all fluid-fluid surface tensions and the solid surface contact angles. We carry out a number of benchmark tests: (i) double emulsions and liquid lenses to validate the surface tensions, (ii) ternary fluids in contact with a square well to compare the contact angles against analytical predictions, and (iii) ternary phase separation to verify that the multicomponent fluid dynamics is accurately captured. Additionally we also describe how the model presented here can be extended to include an arbitrary number of fluid components.

Stability Limits of Capillary Bridges: How Contact Angle Hysteresis Affects Morphology Transitions of Liquid Microstructures

The equilibrium shape of a drop in contact with solid surfaces can undergo continuous or discontinuous transitions upon changes in either drop volume or surface energies. In many instances, such transitions involve the motion of the three-phase contact line and are thus sensitive to contact angle hysteresis. Using a combination of electrowetting-based experiments and numerical calculations, we demonstrate for a generic sphere-plate confinement geometry how contact angle hysteresis affects the mechanical stability of competing axisymmetric and nonaxisymmetric drop conformations and qualitatively changes the character of transitions between them.

Role of contact-angle hysteresis for fluid transport in wet granular matter

The stability of sand castles is determined by the structure of wet granulates. Experimental data on the size distribution of fluid pockets are ambiguous with regard to their origin. We discovered that contact-angle hysteresis plays a fundamental role in the equilibrium distribution of bridge volumes, and not geometrical disorder as commonly conjectured. This has substantial consequences on the mechanical properties of wet granular beds, including a history-dependent rheology and lowered strength. Our findings are obtained using a model in which the Laplace pressures, bridge volumes, and contact angles are dynamical variables associated with the contact points. While accounting for contact line pinning, we track the temporal evolution of each bridge. We observe a crossover to a power-law decay of the variance of capillary pressures at late times and a saturation of the variance of bridge volumes to a finite value connected to contact line pinning. Large-scale simulations of liquid transport in the bridge network reveal that the equilibration dynamics at early times is well described by a mean-field model. The spread of final bridge volumes can be directly related to the magnitude of contact-angle hysteresis.

Pinning and wicking in regular pillar arrays

Pinning and wicking of a liquid meniscus in a square array of pillars is investigated in numerical energy minimizations and compared to wetting experiments. Our combined study shows that criteria for spontaneous film formation, based on thermodynamic considerations as well as on simple geometric modelling of the meniscus shape, are insufficient to predict the onset of wicking. High aspect ratio pillars with a square cross-section may display a re-entrant pinning regime as the density of the pillars is increased, a behaviour that is captured by neither of the aforementioned models. Numerically computed energy landscapes for the advancing meniscus allow us to explain the re-entrant behaviour in terms of energy barriers between topologically different meniscus shapes. Our numerical results are validated by wicking experiments where for the material contact angle θ0 = 47° the re-entrant behaviour is present for square pillars and absent for pillars with circular cross section.

On the onset of motion of sliding drops

In this article we numerically investigate the onset of motion of liquid drops in contact with a plane and homogeneous substrate with contact angle hysteresis. The drops are driven by a body force F = ρgV, where ρ is the density of the liquid, g is the acceleration of gravity, and V is the volume of the drop. We compare two protocols to vary the bond number Bo = λ(v)/λ(c) by changes of either the drop size λ(v) = V(1/3) or the capillary length λ(c) = (γ/ρg)(1/2) where γ is the interfacial tension, revealing that the transition between pinned and steady moving states can be either continuous or discontinuous. In a certain range both pinned and moving states can be found for a given bond number Bo, depending on the history of the control parameters g and V. Our calculations are extended to arbitrary combinations of static advancing and receding contact angles and provide a comprehensive picture of the depinning transition induced by a quasi-static variation of the control parameters. Finally, we demonstrate that the particular form of the contact line mobility in our model has an impact on the interfacial shape of steady moving drops.

Morphological transitions of droplets wetting rectangular domains

We report the results of comprehensive experiments and numerical calculations of interfacial morphologies of water confined to the hydrophilic top face of rectangular posts of width W = 500 μm and lengths between L = 5W and 30W. A continuous evolution of the interfacial shape from a homogeneous liquid filament to a bulged filament and back is observed during changes in the liquid volume. Above a certain threshold length of L* = 16.0W, the transition between the two morphologies is discontinuous and a bistability of interfacial shapes is observed in a certain interval of the reduced liquid volume V/W(3).

Buoyant droplets on functional fibers

In the absence of gravity, the wetting of droplets on fibers is characterized by the competition between an axisymmetric barrel morphology engulfing the fiber and a symmetry-broken clamshell morphology with the droplet sitting on the side of the fiber. In the generic case of nonzero buoyancy the cylindrical symmetry of the barrel morphology is broken, yet barrels and clamshells can still be distinguished based on their different interfacial topologies being multiply and simply connected, respectively. Next to contact angle and droplet size the capillary length appears as a third parameter controlling the droplet morphology. For droplets of variable size, contact angle and buoyancy are independently varied in experiments by use of electrowetting and density mismatch. This approach--together with the complementary numerical calculations--provides new insights into the gradual shifts of the stability limits in the presence of an external volume force. Overall, the parameter space for stable clamshells is found to expand with increasing gravitational forces, gradually shrinking the regimes of stable barrels and bistability. In addition, a new stability limit is introduced for the clamshell morphology related to a partial detachment of the wetting liquid from the fiber, appearing toward higher droplet volumes.

Suspension of water droplets on individual pillars

We report results of extensive experimental and numerical studies on the suspension of water drops deposited on cylindrical pillars having circular and square cross sections and different wettabilities. In the case of circular pillars, the drop contact line is pinned to the whole edge contour until the drop collapses due to the action of gravity. In contrast, on square pillars, the drops are suspended on the four corners and spilling along the vertical walls is observed. We have also studied the ability of the two geometries to sustain drops and found that if we compare pillars with the same characteristic size, the square is more efficient in pinning large volumes, while if we normalize the volumes to pillar areas, the opposite is true.

Anisotropy of water droplets on single rectangular posts

We report results of extensive experimental and numerical studies of the anisotropy of water drops deposited on single rectangular posts of mesoscopic size sculpted on different materials. Drops of different volume deposited on the top face of the posts assume an elongated shape along the post direction. Systematic investigations show that while the angle measured along the direction parallel to the post does not change, the one measured across them increases monotonically with the drop volume. The difference in these two angles is found to be proportional to the contact line eccentricity even for very elongated drops, regardless of the post size and material. Results obtained with the lattice Boltzmann method are consistent with these observations and indicate useful trends on the evolution of the drop shape with the system main parameters. We argue that drops deposited on single posts having a very sharp profile represent an ideal model system to investigate anisotropic wetting.