Wetting of structured hydrophobic surfaces by water droplets

Super-hydrophobic surfaces may arise due to an interplay between the intrinsic, relatively high, contact angle of the more or less hydrophobic solid surface employed and the geometric features of the solid surface. In the present work, this relationship was investigated for a range of different surface geometries, making use of surface free energy minimization. As a rule, the free energy minima (and maxima) occur when the Laplace and Young conditions are simultaneously fulfilled. Special effort has been devoted to investigating the free energy barriers present between the Cassie-Baxter (heterogeneous wetting) and Wenzel (homogeneous wetting) modes. The predictions made on the basis of the model calculations compare favorably with experimental results presented in the literature.     

Wetting behavior of water droplets on hydrophobic microtextures of comparable size

The wetting behavior of water droplets on periodically structured hydrophobic surfaces was investigated. The effect of structure geometry, roughness, and relative pore fraction on the contact angles was investigated experimentally for droplets of size comparable to the size of the structures. It was found that surface geometry may induce a transition from groove-filling and Wenzel-like behavior to nonfilling of surface grooves and consequential Cassie-Baxter behavior. Numerical calculations of the free energy of these systems suggest that the equilibrium behavior is in line with the experimental observations. The observations may serve as guidelines for the design of surfaces with the desired wetting behavior.     

Robust liquid crystal droplets

The preparation and properties of cyanobiphenyl liquid crystal droplets encapsulated by the polymerizable lecithin 1,2-bis(10,12-tricosadiynoyl)-sn-glyero-3-phosphocholine (DC_8,9PC) are described. Under a wide variety of preparation conditions the droplets obtain a diameter of approximately 10 mum. These droplets are stable for periods of over one year at room temperature. Furthermore, they are stable upon temperature cycling between the nematic and isotropic phases and between the smectic A to nematic to isotropic phase transitions.     

Robust liquid crystal droplets

The preparation and properties of cyanobiphenyl liquid crystal droplets encapsulated by the polymerizable lecithin 1,2-bis(10,12-tricosadiynoyl)-sn-glyero-3-phosphocholine (DC_8,9PC) are described. Under a wide variety of preparation conditions the droplets obtain a diameter of approximately 10 mum. These droplets are stable for periods of over one year at room temperature. Furthermore, they are stable upon temperature cycling between the nematic and isotropic phases and between the smectic A to nematic to isotropic phase transitions.     

Crystallization of condensation droplets on a liquid surface

Highly ordered microporous two-dimensional membranes have been obtained from polymer solutions (Widawski et al. (1994) Nature 369: 397–399). Recently, a mechanism for the formation of such membranes was proposed, involving water vapour condensation (induced by the rapid evaporation of the volatile solvent) onto the surface of solutions and the formation of floating water droplets. Unfortunately, the droplets growth process was not observed, and consequently only qualitative information was reported. In the present paper, results of light-scattering experiments with this system are reported. The formation of water droplets growing at the surface of the solution has been observed and the evolution with time of the mean droplet radius has been found to be described by a power law with an exponent of 1/3, proving that no coalescence processes occur. This particular behaviour is attributed to the precipitation of the polymer at the water/solution interface and to the formation of a mechanically resistant polymer layer encapsulating each droplet. In this way, water droplets behave like solid particles, allowing compact sheets to be formed. The presence of important surface currents is believed to promote the formation of “polycrystal” and “monocrystal” patterns. Received: 4 January 1999 Accepted in revised form: 15 February 1999     

Wetting and dynamics of structured liquid films

The stability of a sufficiently thin, supported, homopolymer film against the development of local thickness fluctuations which can become amplified, eventually leading to structural destabilization of the film, is typically determined by long and short‐range intermolecular forces. In A‐B diblock copolymers, the connectivity between the blocks, the preferential attraction of one block to an external interface, combined with an incompatibility between the A‐B segments, the situation is very different. Two cases, largely dictated by χN, wher χ is the Flory‐Huggins interaction parameter and N is the degree of polymerization, can arise in thin copolyme films. When χN is large, thin films exhibit comparatively stable topographical structures, where the dimensions of the topographies normal to the substrate reflect a natural length‐scale associated with phase separation in the material. In the other situation, where χN is sufficiently small, the copolymer bulk structure is homogeneous. An ordered structure can be induced into the otherwise compositionally homogeneous structure in the vicinity of a substrate. Here, depending on film thickness, a series of transient and stable topographies can develop. Wetting, early stage structural destabilization dynamics leading to the formation of droplets, and late stage coarsening of the droplets are discussed. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2219–2235, 2003     

Spreading of viscous droplets on a non viscous liquid

Some polymer melts (of high viscosity ) can wet completely the surface of a non miscible, simple liquid. We discuss here the laws of spreading for a macroscopic droplet of this type, when the internal friction of the droplet dominates. We predict a droplet radius increasing liket ^1/4 wheret is the spreading time, or equivalently a droplet curvature decreasing liket ^–1. The droplet should be surrounded by a precursor film, which is not discussed in the present note.     

Sliding behavior of liquid droplets on tilted Langmuir-Blodgett surfaces

The sliding behavior of liquid droplets on inclined Langmuir-Blodgett surfaces was investigated. The critical sliding angle defined as the tilt angle of the surface at which the drop slides down as well as the advancing and receding contact angles was measured for five different liquids on five surfaces. In addition, the contact line geometry was analyzed at critical sliding angle. The experimental relationship between the surface tension forces resulting from contact angle hysteresis and the weight of the drop was compared to theoretical predictions. Even though the shape of the drop bases was found as skewed ellipses, a model assuming parallel-sided elongated drops is shown to describe reasonably the experimental values. This result probably indicates the main influence of the capillary forces at the rear and front edges of the drop with respect to that exerted on the lateral sides.     

Flow behaviours of liquid crystal droplets on polyimide alignment layers

The flow behaviours of liquid crystal droplets on polyimide alignment layers and during assembling between two substrates have been directly observed. The droplet shape became elliptical with time on the rubbed polyimide layer, where the major axis of the elliptical droplet was parallel to the rubbing direction. Rubbing enhanced the wettability between the liquid crystal and the polyimide layer. During the assembling process, the liquid crystal droplets elliptically splayed out between two substrates assembled antiparallel. The liquid crystal molecules preferentially flowed parallel to the rubbing direction in a two-step flow mode; the droplet diameter slowly increased at the first step, and then it rapidly increased at the second step. The two-step flow of the droplet proved to be due to the thickness of the droplet dependent on the rubbing strength.     

Equilibrium contact angles of liquid droplets on ideal rough solids

This work proposes a theoretical model for predicting the apparent equilibrium contact angle of a liquid on an ideal rough surface that is homogeneous and has a negligible body force, line tension, or contact angle hysteresis between solid and liquid. The model is derived from the conservation equations and the free-energy minimization theory for the changes of state of liquid droplets. The work of adhesion is expressed as the contact angles in the wetting process of the liquid droplets. Equilibrium contact angles of liquid droplets for rough surfaces are expressed as functions of the area ratios for the solid, liquid, and surrounding gas and the roughness ratio and wetting ratio of the liquid on the solid for the partially and fully wet states. It is found that the ideal critical angle for accentuating the contact angles by the surface roughness is 48°. The present model is compared with existing experimental data and the classical Wenzel and Cassie-Baxter models and agrees with most of the experimental data for various surfaces and liquids better than does the Wenzel model and accounts for trends that the Wenzel model cannot explain.     

The evaporation/condensation transition of liquid droplets

The condensation of a supersaturated vapor enclosed in a finite system is considered. A phenomenological analysis reveals that the vapor is found to be stable at densities well above coexistence. The system size at which the supersaturated vapor condenses into a droplet is found to be governed by a typical length scale which depends on the coexistence densities, temperature and surface tension. When fluctuations are neglected, the chemical potential is seen to show a discontinuity at an effective spinodal point, where the inhomogeneous state becomes more stable than the homogeneous state. If fluctuations are taken into account, the transition is rounded, but the slope of the chemical potential versus density isotherm develops a discontinuity in the thermodynamic limit. In order to test the theoretical predictions, we perform a simulation study of droplet condensation for a Lennard-Jones fluid and obtain loops in the chemical potential versus density and pressure. By computing probability distributions for the cluster size, chemical potential, and internal energy, we confirm that the effective spinodal point may be identified with the occurrence of a first order phase transition, resulting in the condensation of a droplet. An accurate equation of state is employed in order to estimate the droplet size and the coexisting vapor density and good quantitative agreement with the simulation data is obtained. The results highlight the need of an accurate equation of state data for the Laplace equation to have predictive power.     

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 encapsulated and stabilised blue-phase liquid crystal droplets

Polymer-encapsulated–polymer-stabilised blue-phase liquid crystals (LCs) are investigated. Encapsulated droplets are formed in a polyvinyl alcohol solution by emulsification, and blue-phase (BP) LCs in the droplets are stabilised via the polymerisation of reactive monomers to extend the BP temperature range. Polymer stabilised droplets are found to cause the expansion of the BP temperature range from 53°C to below 0°C. The effects of composition on droplet formation and the electro-optical behaviour and morphological properties of these droplets are reported.     

Controlling and characterizing the coagulation of liquid aerosol droplets

We demonstrate that optical tweezers can be used to control and characterize the coagulation and mixing state of aerosols. Liquid aerosol droplets of 2-14 mum in diameter are optically trapped and characterized by spontaneous and stimulated Raman scatterings, which together provide a unique signature of droplet size and composition. From the conventional bright field image, the size of the trapped droplet can be estimated and compared with that determined from stimulated Raman scattering, and the motion of the particle within the trapping plane can be recorded. A maximum of four droplets can be manipulated in tandem by forming multiple optical traps through rapid beam steering. The coagulation of two droplets can be studied directly by controlling two droplets. The limiting conditions under which optical forces and capillary forces dominate the aerosol coagulation event are explored by varying the relative optical trap strengths and characterizing the coagulation of different droplet sizes. Finally, we demonstrate that the coagulation of different aerosol components can be compared and the mixing state of the final coagulated droplet can be investigated. In particular, we compare the outcome of the coagulation of an aqueous sodium chloride aerosol droplet with a second aqueous droplet, with an ethanol droplet or with a decane droplet.     

Influence of K24 on the structure of nematic liquid crystal droplets

A phenomenological free energy is used to describe the stable ordering of nematic liquid crystals confined to supramicron spherical cavities. In particular the effects of the saddle splay elastic constant, K₂₄, on the equilibrium structures and phase diagram of droplets with homeotropic surface anchoring are discussed. Some structures are illustrated by the corresponding simulated polarization microscope textures. Possibilities for an experimental determination of the saddle-splay elastic constant and surface anchoring strength by studying the radial-axial structural transition in such droplets are analysed. It is shown that the K₂₄ term in the elastic free energy stabilizes a deformed droplet structure even in the limit of the zero anchoring strength.     

Structure of liquid crystal droplets with chiral propeller texture

We experimentally studied a nematic liquid crystal whose molecules form twisted head-to-head H-bonded dimers. We observed that when the material transformed from the isotropic to nematic phase, it formed droplets with chiral propeller textures. We carried out a computer simulation to investigate the liquid crystal director configuration inside the droplets and to study the effects of elastic constants and chirality on the droplet texture. Results of our study show it is likely that the material in the droplets had nonzero chirality due to spontaneous chiral phase separation.     

Isothermal noncoalescence of liquid droplets at the air-liquid interface

The mechanism of the generation and sustainability of noncoalescent droplets (NCDs) was investigated at the liquid-air interface of the same liquids in the context of inkjet printing. The Weber number (We) was used to correlate and predict the generation of NCDs in a falling-drop experiment. This study found that NCDs can be generated for We higher than 130. We values of this magnitude are relevant to inkjet printing. The formation of NCD can reduce the print quality because the NCD droplets roll away uncontrollably from the print target, thus reducing print resolution. This study also used a simple experiment to demonstrate the physical origin of the NCD, which is the existence of a gaseous cushion between the liquid drop and the liquid-air interface that supports the drop. The gaseous cushion has a thickness greater than the van der Waals attraction range (around 10 nm).     

Electrical actuation of dielectric droplets by negative liquid dielectrophoresis

This paper presents an electrical actuation scheme of dielectric droplet by negative liquid dielectrophoresis. A general model of lumped parameter electromechanics for evaluating the electromechanical force acting on the droplets is established. The model reveals the influence of actuation voltage, device geometry, and dielectric parameter on the actuation force for both conductive and dielectric medium. Using this model, we compare the actuation forces for four liquid combinations in the parallel-plate geometry and predict the low voltage actuation of dielectric droplets by negative dielectrophoresis. Parallel experimental results demonstrate such electric actuation of dielectric droplets, including droplet transport, splitting, merging, and dispending. All these dielectric droplet manipulations are achieved at voltages < 100 V_rms. The frequency dependence of droplet actuation velocity in aqueous solution is discussed and the existence of surfactant molecules is believed to play an important role by realigning with the AC electric field. Finally, we present coplanar manipulation of oil and water droplets and formation of oil-in-water emulsion droplet by applying the same low voltage.     

Interfacial effects in the spreading kinetics of liquid droplets on solid substrates

Several theories deal with the spreading kinetics of liquids on solid substrate, most of which relate the rate of spreading to the surface tension and the viscosity of the liquid. Measurements of the spreading of a number of liquids exhibiting a wide range of surface tension and viscosity on dry soda-lime glass have been carried out to validate the proposed models. The measurements used a small droplet of constant volume to minimize gravitational effects. The contact radius was acquired as a function of time by an image analysis system. It was noted that power law theories describe the spreading rate for silicone oil on glass. However, significant departures were noted in the case of other liquids. Mechanistic considerations of our data suggest that equal volume droplets of similar surface tension and of diverse viscosity spread to the same area but at different rates. On the other hand, the spreading rate of glycerine, which exhibits incomplete spreading on glass, and that of silicone oil, with comparable viscosity behave similarly. These observations seemingly support the view that surface tension acts to retain the spherical shape of the droplet, whereas the difference between the solid-liquid and solid-vapor interfacial energies acts to enlarge the contact area. In the meantime, viscous dissipation acts to retard the spreading rate, past a constant rate regime.     

Displacement of liquid droplets on a surface by a shearing air flow

The motion of droplets on surfaces is crucial to the performance of a wide range of processes; this study examines the initiation of droplet motion through a shearing mechanism generated here by a controlled air flow. Systematic experiments are carried out for a range of fluids and well defined surfaces. A model is postulated that balances surface tension forces at the contact line and the drag force due to the air motion. Experiments reveal that the critical velocity at which droplet motion is initiated depends on the contact angle and the droplet size. Visualizations highlight three modes of motion: (I) the droplet retains a footprint similar to that at the point of motion; (II) a tail exists at the rear of the droplet; (III) a trail remains behind the droplet (that can shed smaller droplets). The predictions of droplet initiation velocity are good for type I motion, in accordance with the assumptions inherent within the model. This model confirms the dominant physics associated with the initiation of droplet motion and provides a useful predictive expression.