On the maximum spreading diameter of impacting droplets on well-prepared solid surfaces

This paper presents a systematic study of liquid droplet impact on three polymer surfaces: poly(methyl methacrylate), poly(methyl methacrylate/n-butyl methacrylate), and poly(n-butyl methacrylate). Changing from one surface to the next represents an incremental variation in solid surface tensions of 5-6 mJ/m2. These surfaces were prepared through careful experimental procedures that were used for the determination of solid surface tensions from contact angles. Our data for the maximum spreading diameter of water and formamide impacting on these surfaces were compared with those predicted from literature models. Of the models selected, we modified the model of Pasandideh-Fard et al. [Phys. Fluids 1996, 8, 650] and the results yielded a least error of only 5.09 +/- 5.05% in the determination of the maximum spreading diameter. The improved model was also compared with literature data, and good agreement was found. Of course, any such comparisons would rely on accurate experimental impact dynamics data on carefully prepared surfaces.     

Viscous-gravity spreading of time-varying liquid drop volumes on solid surfaces

Viscous-gravity spreading of liquid drops of time-dependent volume over a solid surface is considered. A self-similar solution for the drop configuration is obtained, in the case the liquid drop volume varies as a power-law function of time, along with the spreading laws in both cases of cylindrical and axisymmetric geometries. Results compare favorably with published experimental results and previous theoretical work. The limitations of the model are discussed, along with a comparison with viscous gravity spreading of oil on water. The validity of using approximate spreading laws is considered, and an approximate method is suggested to provide the dynamics of spreading in the general case where the drop volume does not necessarily vary as a power-law function of time.     

Molecular dynamics study of the influence of surfactant structure on surfactant-facilitated spreading of droplets on solid surfaces

The spreading of a partially wetting aqueous drop in air on a hydrophobic surface can be facilitated by the adsorption of surfactants from the drop phase onto the air/aqueous and aqueous/hydrophobic solid interfaces of the drop. At the contact line at which these interfaces meet, conventional surfactants with a linear alkyl hydrophobic chain attached to a polar group adsorb onto the surfaces, forming monolayers which remain distinct as they merge at the contact juncture. The adsorption causes a decrease in the interfacial tensions and reduction in the contact angle but the angle remains above zero so the drop is still nonwetting. Trisiloxane surfactants with a T-shaped geometry in which the hydrophobic group is composed of a trisiloxane oligomer with a polar group attached at the center of the chain can give rise to a zero contact angle at the contact line and complete wetting (superspreading). Experimental evidence suggests the adsorption of the T-shaped molecule, in addition to significantly decreasing the tensions of the interfaces (relative to the conventional surfactants), promotes the formation of a precursor film consisting of a surfactant bilayer at the contact line which facilitates the spreading. The aim of this study is to use molecular dynamics to examine if the T-shaped structure can promote spreading by the formation of a bilayer and to contrast this case with that of the linear chain surfactant where complex assembly does not occur. The simulation models the solvent as a monatomic liquid, the substrate as a particle lattice, and the surfactants as united atom structures, with all interactions given by Lennard-Jones potentials. We start with a base case in which the solvent partially wets a substrate comprised of a lattice of particles. We demonstrate that adsorbed T-shaped surfactant monolayers can, when the interaction between the solvent and the hydrophile particles is strong enough, assemble into a bilayer, allowing the drop to extend to a thin planar film. In the case of the flexible linear chain surfactant, there is no interaction between the monolayers on the two interfaces in the case of a strong hydrophile-solvent interaction and less coordination for a weaker interaction. In either case, the monolayers remain distinct, as the surfactant only marginally improves wetting.     

Surfactant-assisted spreading of a liquid drop on a smooth solid surface

Axisymmetric spreading of a liquid drop covered with an insoluble surfactant monolayer on a smooth solid substrate is numerically investigated. As the drop spreads, the adsorbed surfactant molecules are constantly redistributed along the air-liquid interface by convection and diffusion, leading to nonuniformities in surface tension along the interface. The resulting Marangoni stresses affect the spreading rate by altering the surface flow and the drop shape. In addition, surfactant accumulation in the vicinity of the moving contact line affects the spreading rate by altering the balance of line forces. Two different models for the constitutive relation at the moving contact line are used, in conjunction with a surface equation of state based on the Frumkin adsorption framework, to probe the surfactant influence. The coupled evolution equations for the drop shape and monolayer concentration profile are integrated using a pseudospectral method to determine the rate of surfactant-assisted spreading over a wide range of the dimensionless parameters governing the spreading process. The insoluble monolayer enhances spreading through two mechanisms; a reduction in the equilibrium contact angle, and an increase in the magnitude of the radial pressure gradient within the drop due to the formation of positive surface curvature near the moving contact line. Both mechanisms are driven by the accumulation of surfactant at the contact line due to surface convection. Although the Marangoni stresses induced at the air-liquid interface reduce the rate of spreading during the initial stages of spreading, their retarding effect is overwhelmed by the favorable effects of the aforementioned mechanisms to lead to an overall enhancement in the rate of spreading in most cases. The spreading rate is found to be higher for bulkier surfactants with stronger repulsive interactions. With the exception of monolayers with strong cohesive interactions which tend to retard the spreading process, the overall effect of an insoluble monolayer is to increase the rate of drop spreading. Simulation results for small Bond numbers indicate the existence of a power-law region for the time-dependence of the basal radius of the drop, consistent with experimental measurements.     

Spreading of droplets on lubricant-patterned substrates

Droplet spreading behaviors on lubricant-patterned substrates are investigated by using molecular dynamics simulations to explore application potentials in magnetic storage drive systems. Microscopic spreading processes are studied by both potential fields of lubricant-patterned substrates and single molecule movements in lubricant droplets. The potential fields indicate that the wall molecules patterned on the substrates attract the mobile ones in the lubricant droplets. Due to the attraction force, the mobile molecules experience difficulties in diffusing freely along the substrates. The single molecule movements in lubricant droplets demonstrate that during the diffusion process, the mobile molecules encounter, adsorb, encompass, and disengage the wall ones. The spreading behaviors are significantly impacted by the bonded ratio. The potential fields indicate that as the bonded ratio increases, the attractive regions of wall molecules merge to overlap, which indicate combined interactions formed by the adjacent wall molecules.     

Studies of the wetting kinetics of liquid drops on solid surfaces

The viscosity _L and the surface tension _L of the liquid as well as the equilibrium contact angle _e are essential parameters governing the wetting kinetics of liquids on solids. By means of a contact angle apparatus with video image digitization, the dynamic contact angle and the radiusr of the contact area of sessile drops on solid surfaces have simultaneously been determined in dependence on time after drop application between about 3·10^–2 s and long times.The measurements were performed with series of liquids: polydimethylsiloxanes with different molecular masses and solutions of polyisobutylene in decalin and polyacrylic acid in water, covering a wide range of concentrations. The liquids in each series have a constant surface tension, but viscosities ranging over about four orders of magnitude, allowing the influence of _L and _L to be studied independently. Solids such as glass, polyethylene and polytetrafluoroethylene were chosen so that the cases of complete wetting (spreading) and partial wetting ( _e) could be studied.The curves of cos andr/R ₀ vs. time for the different liquids of a series can be superimposed to a master curve by plotting them against _L·t _L·R ₀, whereR ₀ is the radius of the original drop. All these master curves coincide at small wetting times, with exception of the data for the polysiloxanes. That means that the early stage of the wetting process is determined only by the properties of the wetting liquid. The influence of the solid surface, characterized by the equilibrium contact angle _e becomes significant only at the end of the wetting process.Dedicated to Professor Dr. H. Willersinn on the occasion of his 65^th birthday     

Wicking and spreading of water droplets on nanotubes

Recently, there has been intensive research on the use of nanotechnology to improve the wettability of solid surfaces. It is well-known that nanostructures can improve the wettability of a surface, and this is a very important safety consideration in regard to the occurrence of boiling crises during two-phase heat transfer, especially in the operation of nuclear power plant systems. Accordingly, there is considerable interest in wetting phenomena on nanostructures in the field of nuclear heat transfer. Much of the latest research on liquid absorption on a surface with nanostructures indicates that liquid spreading is generated by capillary wicking. However, there has been comparatively little research on how capillary forces affect liquid spreading on a surface with nanotubes. In this paper, we present a visualization of liquid spreading on a zircaloy surface with nanotubes, and establish a simple quantitative method for measuring the amount of water absorbed by the nanotubes. We successfully describe liquid spreading on a two-dimensional surface via one-dimensional analysis. As a result, we are able to postulate a relationship between liquid spreading and capillary wicking in the nanotubes.     

Interfacial criteria for stabilization of liquid foams by solid particles

The stability criteria of liquid foams, stabilized by solid particles have been derived, based on the interfacial separating pressure, acting between two neighboring bubbles (foam cells). Different structures of solid particles in the cell walls have been considered, all being able to stabilize liquid foams with an increasing probability, according to the following row: structure LP1 (loosely packed single layer of particles) → structure CP1 (closely packed single layer of particles) → structure LP2C (loosely packed double layer of clustered particles) → structure LP2+C (loosely packed ‘double+’ layer of clustered particles) → structure CP2 (closely packed double layer of particles) → structure CP2+ (closely packed ‘double+’ layer of particles). It has been shown that the contact angle should be higher than a certain value Θ_o, in order to ensure stability of bubble–particles agglomerates. On the other hand, different structures of particles can stabilize the foam, if the contact angle is below the certain value (90° for the CP1 and LP1 structures, 129° for the CP2, LP2C and LP2+C structures and 180° for the CP2+ structure). The optimum value of the contact angle, being able to stabilize the foam is a difficult function of different parameters, but has been found in the interval between 50 and 90°. It has been shown that the possibility to stabilize liquid foams is connected with the value of the dimensionless quantity PR_s/σ (P: the pressure, destabilizing the foam; R_s: the radius of the stabilizing particles; σ: the surface tension of the liquid). When PR_s/σ>40, foam stabilization is absolutely impossible. When PR_s/σ<40, foam stabilization becomes possible, but it has high probability only at PR_s/σ<4. From this condition the maximum size of the particles, being able to stabilize liquid foams can be found. Trial calculations showed that particles smaller than 3 and 30 μm in diameter are requested for stabilizing water based, and liquid aluminum based foams, respectively.     

Mean-field theory of liquid droplets on roughened solid surfaces: application to superhydrophobicity

We present calculations of the density distributions and contact angles of liquid droplets on roughened solid surfaces for a lattice gas model solved in a mean-field approximation. For the case of a smooth surface, this approach yields contact angles that are well described by Young's equation. We consider rough surfaces created by placing an ordered array of pillars on a surface, modeling so-called superhydrophobic surfaces, and we have made calculations for a range of pillar heights. The apparent contact angle follows two regimes as the pillar height increases. In the first regime, the liquid penetrates the interpillar volume, and the contact angle increases with pillar height before reaching a constant value. This behavior is similar to that described by the Wenzel equation for contact angles on rough surfaces, although the contact angles are underestimated. In the second regime, the liquid does not penetrate the interpillar volume substantially, and the contact angle is independent of the pillar height. This situation is similar to that envisaged in the Cassie-Baxter equation for contact angles on heterogeneous surfaces, but the contact angles are overestimated by this equation. For larger pillar heights, two states of the droplet can be observed, one Wenzel-like and the other Cassie-like.     

Line tension effects for liquid droplets on circular surface domains

We study the morphologies of single liquid droplets wetting a substrate in the presence of the line tension of the three-phase contact line. On a homogeneous substrate, the line tension leads to a discontinuous unbinding of the droplet if its volume is decreased below a critical value. For a droplet wetting a structured surface with a circular domain, a line tension contrast gives rise to discontinuous depinning transitions of the contact line from the domain boundary as the droplet volume is varied. We calculate the corresponding free energy bifurcation diagram analytically for axisymmetric droplet shapes. Numerical minimization of the droplet free energy shows that line tension contrasts can stabilize nonaxisymmetric droplet shapes, thus modifying the bifurcation diagram. These latter shapes should be accessible to experiments and can be used to reveal the presence of a line tension contrast.     

Polymer patterns in evaporating droplets on dissolving substrates

Self-organized polymer patterns resulting from the evaporation of an organic solvent drop on a soluble layer of polymer are investigated. The patterns can be modulated by changing the rate of evaporation and also the rate of substrate dissolution controlled by its solubility. Both of these affect the contact zone motion and its instabilities, leading to spatially variable rates of substrate etching and redeposition that result from a complex interplay of several factors such as Rayleigh-Benard cells, thermocapillary flow, solutal Marangoni flow, flow due to differential evaporation, osmotic-pressure-induced flow, and contact-line pinning-depinning events. The most complex novel pattern, observed at relatively low rates of evaporation, medium solubility, and without macroscopic contact-line stick-slip, consists of a regularly undulating ring made up of a bundle of parallel spaghetti-like threads or striations and radially oriented fingerlike ridges. Increased rate of evaporation obliterates the polymer threads, producing more densely packed fingers and widely separated multiple rings due to a frequent macroscopic pinning-depinning of the contact line. Near-equilibrium conditions such as slow evaporation or increased solubility of the substrate engender a wider and less undulating single ring.     

Immiscible surfactant droplets on thin liquid films: spreading dynamics, subphase expulsion and oscillatory instabilities

After deposition of immiscible, surface-active liquids on thin liquid films of higher surface tension, Marangoni stresses thin the liquid film around the surfactant droplet and induce a radially outward flow. We observed an oscillatory instability, caused by temporary trapping and subsequent release of subphase liquid from underneath the surfactant droplet. Height profiles of the thin liquid films were monitored using optical interferometry and fluorescence microscopy, both in the vicinity of the deposited surfactant droplet and at larger distances. Numerical calculations based on the lubrication approximation are compared to the experimental results. Good agreement between the experimental and calculated far-field dynamics and values of the spreading exponents was found.     

Kinetics of fluid spreading on viscoelastic substrates

The spontaneous spreading of non‐film‐forming fluids on the surfaces of aqueous solutions of poly(2‐acrylamido‐2‐methyl‐propanesulfonic acid) and its chemically crosslinked gels was studied. The experiments were performed in the same concentration range for the solutions and gels, far above the overlap concentration of the polymer solutions. The leading edge (R) of the spreading liquid showed a power‐law behavior with time t: R = K(t + c)^α, where α is the spreading exponent and K is the spreading prefactor. α and K were significantly different for the polymer solutions and gels. Here c was a constant that depended on the initial conditions of the spreading liquids. Depending on the polymer concentration, α of the polymer solutions varied between the upper (3/4) and lower (1/10) theoretical limits for viscose liquids and solids, respectively. This indicates that no universal scaling law exists for the spreading process on viscoelastic surfaces. On the polymer gels, which were elastic substrates, universal values of α could be observed and could be expressed as R ∝ (t + c)^0.45 and R ∝ (t + c)^0.3 for miscible and nonmiscible spreading liquids, respectively; they showed no dependence on the polymer concentration or network mesh size. This shows that on an elastic gel surface, spreading is more or less similar to that on a solid surface. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 562–572, 2005     

Fast evaporation of spreading droplets of colloidal suspensions

When a coffee droplet dries on a countertop, a dark ring of coffee solute is left behind, a phenomenon often referred to as the coffee-ring effect. A closely related yet less-well-explored phenomenon is the formation of a layer of particles, or skin, at the surface of the droplet during drying. In this work, we explore the behavior of a mathematical model that can qualitatively describe both phenomena. We consider a thin axisymmetric droplet of a colloidal suspension on a horizontal substrate undergoing spreading and evaporation. In contrast to prior work, precursor films (rather than pinned contact lines) are present at the droplet edge, and evaporation is assumed to be limited by how quickly molecules can transfer out of the liquid phase (rather than by how quickly they can diffuse through the gas phase). The lubrication approximation is applied to simplify the mass and momentum conservation equations, and the colloidal particles are allowed to influence the droplet rheology through their effect on the viscosity. By describing the transport of the colloidal particles with the full convection-diffusion equation, we are able to capture depthwise gradients in particle concentration and thus describe skin formation, a feature neglected in prior models of droplet evaporation. The highly coupled model equations are solved for a range of problem parameters using a finite-difference scheme based on a moving overset grid. The presence of evaporation and a large particle Peclet number leads to the accumulation of particles at the liquid-air interface. Whereas capillarity creates a flow that drives particles to the droplet edge to produce a coffee ring, Marangoni flows can compete with this and promote skin formation. Increases in viscosity due to particle concentration slow down droplet dynamics and can lead to a reduction in the spreading rate.     

Orientational prewetting of planar solid substrates by a model liquid crystal

We present grand canonical ensemble Monte Carlo simulations of prewetting transitions in a model liquid crystal at structureless solid substrates. Molecules of the liquid crystal interact via anisometric Lennard-Jones potentials and can be anchored planar or homeotropically at the substrates. Fluid-substrate attraction is modeled by a Yukawa potential of variable range. By monitoring the grand-potential density and the nematic order parameter as functions of the chemical potential μ, several discontinuous prewetting, wetting, and isotropic-nematic phase transitions are observed. These transitions depend on both the range of the fluid-substrate attraction and the specific anchoring at the substrate. Our results show that at substrates characterized by degenerate anchoring prewetting occurs at lower μ compared with cases in which the anchoring is monostable. This indicates that prewetting transitions are driven by orientational entropy because degenerate anchoring allows for more orientationally distinct configurations of molecules compared with monostable anchoring. In addition, by analyzing local density and various local order parameters, a detailed picture of the structure of various phases emerges from our simulations.     

Spreading and sorption of droplets on layered porous substrates

In this paper spreading and sorption of a droplet on an anisotropic, layered porous substrate are investigated numerically. Flow in the saturated part of the porous material is governed by Darcy's law, assuming a sharp wetting front separating the saturated regions from the dry regions. Numerical results are presented for spreading and sorption of droplets in their dependence on the material and process parameters for axisymmetric configurations. Limiting cases of sorption into infinitely thick and very thin porous layers are considered. For an analytical sorption model for thin substrates fed by an infinite reservoir a correction term taking into account the flow resistance in the inlet region is derived and the consistence of the modified model with numerical and experimental results is shown. For two-layer substrates, numerical results on the influence of the layer permeabilities on the sorption kinetics are presented.     

Impact of picoliter droplets on superhydrophobic surfaces with ultralow spreading ratios

The impact of picoliter-sized water droplets on superhydrophobic CF(4) plasma fluorinated polybutadiene surfaces is investigated with high-speed imaging. Variation of the surface topography by plasmachemical modification enables the dynamics of wetting to be precisely controlled. Final spreading ratios as low as 0.63 can be achieved. A comparison of the maximum spreading ratio and droplet oscillation frequencies to models described in the literature shows that both are found to be much lower than theoretically predicted.     

Wetting of liquid droplets on living cells

We report here the formation of adhesive conjugates between living cells and properly tailored colloidal liquid droplets bearing a cationic surfactant. We show that the droplets could wet cell surface with a well-defined contact angle, allowing direct determination of the energy of adhesion. We also describe the effect of cationic surfactant concentration on adhesion efficiency. This provides new tools to probe living cell surface properties and find practical laws for cell adhesion on well-defined surfaces.