Droplet on a liquid substrate: Wetting,dewetting, dynamics,instabilities

Droplets on a liquid substrate (‘liquid lenses’) play an important role in various branches of engineering, including microfluidics, chemical engineering, environment protection, etc. In the present paper, we discuss basic phenomena characteristic for liquid lenses. We recall classical results on the shape of an equilibrium droplet and the kinds of droplet wetting. We overview briefly the main theoretical approaches used for the analysis of droplet dynamics, discuss the phenomena accompanying a droplet impact, physical effects used for droplet manipulations, and the factors that determine the interaction between droplets. We describe the main types of droplet instabilities leading to oscillations, self-propulsion, and disintegration of droplets. Some promising directions of further research are listed.     

The role of capillary and surface forces in the crossover behavior of solid nanoparticles at liquid interfaces

We investigate the interaction between a nanoparticle and an oil-water interface with particular emphasis on the particle crossing through the interface. The formation of a three-phase contact line is investigated in two cases, namely in the presence and in the absence of surface forces. We carefully examine the interplay between capillary and surface forces in such systems. Two instabilities of the interface (snap-in/snap-out) as the particle is moved through the interface are identified and quantitatively described. While the snap-in instability was observed in some AFM studies, the precise interface position and configuration relative to the particle at the instability depends on the nature of the surface forces present in the system. After the snap-in, the particle is adsorbed and must overcome an energy barrier due to the interface deformation in order to cross-over to the other liquid. We make quantitative predictions on the interface configuration at the instabilities and the free energy barrier height. The roles of particle size and different interaction parameters characterizing the system in determining the magnitude of the energy barrier for crossing and in the formation of a three-phase contact line are discussed. Ultimately, this study will enable us to make quantitative predictions on capillary effects in nanoparticle-microemulsions mixtures and other colloidal systems. For particles in the micrometer range and larger the capillary forces dominate over the surface forces and dictate how the snap-in occurs. However, the situation becomes different for particle sizes smaller than about 100 nm. The presence of surface forces modifies the interface configuration and the free energy jump at the snap-in instability.     

Evolution of fractal-like surface structures in layers of polyacrylonitrile solutions by interfacial dynamic processes

Solvent evaporation causes concentration and temperature gradients at the free surface of a coating polymer solution. Thereby surface-tension-driven flows can result in a surface instability with regular structures within the layer. Different types of surface structures can occur at spots with thickness differences. One can find fractal-like structures especially in the edge zone of a layer. The evolution of such fractal-like structures at the surfaces of coating solutions of polyacrylonitrile (PAN) in dimethylformamide (DMF) during layer hardening is examined. Condensation of water on the surface of the fluid layer exerts a strong influence on the formation of these structures. Solutions of PAN in DMF are important for the production of ultrafiltration membranes. Such membranes are produced by precipitation in a water bath after a short open time.     

On the role of surface charges for homogeneous freezing of supercooled water microdroplets

Charge induced changes in homogeneous freezing rates of water have been proposed to constitute a possible link between the global atmospheric electric circuit and cloud microphysics and thus climate. We report here on high precision measurements of the homogeneous nucleation rate of charged, electro-dynamically levitated single water droplets as a function of their surface charge. No evidence has been found that the homogeneous volume specific ice nucleation rate of supercooled microdroplets is influenced by surface charges in the range between +/-200 elementary charges per μm(2). It has also been suggested that filamentation in highly electrified liquids can induce freezing at temperatures well above the homogeneous freezing limit. We report here the observation of Coulomb instabilities of highly charged droplets that are accompanied with the formation and ejection of fine filaments from the liquid supercooled droplets. Down to temperatures of 240 K, which is close to the homogeneous freezing limit of uncharged water, no filamentation induced freezing has been detected. At even lower temperatures, the droplets froze before the instability was reached. These findings rule out that filamentation exerts an important influence on ice formation in supercooled water. Combining these findings, we conclude that the surface charges (even at their maximum possible density) have no significant effect on the homogeneous ice nucleation rate of supercooled cloud droplets.     

Dewetting of liquid filaments in wedge-shaped grooves

The dewetting of liquid filaments in linear grooves of a triangular cross section is studied experimentally and theoretically. Homogeneous filaments of glassy polystyrene (PS) are prepared in triangular grooves in a nonequilibrium state. At elevated temperatures, the molten PS restores its material contact angle with the substrate. Liquid filaments with a convex liquid-vapor interface decay into isolated droplets with a characteristic spacing depending on the wedge geometry, wettability, and filament width. This instability is driven by the interplay of local filament width and Laplace pressure and constitutes a wide class of 1D instabilities that also include the Rayleigh-Plateau instability as a special case. Our results show an accurately exponential buildup of the instability, suggesting that fluctuations have a minor influence in our system.     

Competing liquid phase instabilities during pulsed laser induced self-assembly of copper rings into ordered nanoparticle arrays on SiO2

Nanoscale copper rings of different radii, thicknesses, and widths were synthesized on silicon dioxide thin films and were subsequently liquefied via a nanosecond pulse laser treatment. During the nanoscale liquid lifetimes, the rings experience competing retraction dynamics and thin film and/or Rayleigh-Plateau types of instabilities, which lead to arrays of ordered nanodroplets. Surprisingly, the results are significantly different from those of similar experiments carried out on a Si surface. We use hydrodynamic simulations to elucidate how the different liquid/solid interactions control the different instability mechanisms in the present problem.     

Highly productive droplet formation by anisotropic elongation of a thread flow in a microchannel

We developed a microfluidic device to form monodisperse droplets with high productivity by anisotropic elongation of a thread flow, defined as a threadlike flow of a dispersed liquid phase in a flow of an immiscible, continuous liquid phase. The thread flow was anisotropically elongated in the depth direction in a straight microchannel with a step, where the microchannel depth changed. Consequently, the elongated thread flow was given capillary instability (Rayleigh-Plateau instability) and was continuously transformed into monodisperse droplets at the downstream area of the step in the microchannel. We examined the effects of the flow rates of the dispersed phase and the continuous phase on the droplet formation behavior, including the droplet diameter and droplet formation frequency. The droplet diameter increased as the fraction of the dispersed-phase flow rate relative to the total flow rate increased and was independent of the total flow rate. The droplet formation frequency proportionally increased with the total flow rate at a constant dispersed-phase flow rate fraction. These results are explained in terms of a mechanism similar to that of droplet formation from a cylindrical liquid thread flow by Rayleigh-Plateau instability. The microfluidic device described was capable of forming monodisperse droplets with a 160-microm average diameter and 3-microm standard deviation at a droplet formation frequency of 350 droplets per second from a single thread flow. The highest total flow rate achieved was 6 mL/h using the present device composed of a straight microchannel with a step. We also demonstrated parallel droplet formation by anisotropic elongation of multiple thread flows; the process was applied to form W/O and O/W droplets. The highly productive droplet formation process presented in this study is expected to be useful for future industrial applications.     

Instabilities of nematic liquid crystal films

We discuss instabilities exhibited by free surface nematic liquid crystal (NLC) films of nanoscale thickness deposited on solid substrates, with a focus on surface instabilities that lead to dewetting. Such instabilities have been discussed extensively; however, there is still no consensus regarding the interpretation of experimental results, appropriate modeling approaches, or instability mechanisms. Instabilities of thin NLC free surface films are related to a wider class of problems involving dewetting of non-Newtonian fluids. For nanoscale films, the substrate–film interaction, often modeled by a suitable disjoining pressure, becomes relevant. For NLCs, one can extend the formulation to include the elastic energy of the NLC film, leading to an ‘effective’ disjoining pressure, playing an important role in instability development. Focusing on thin film modeling within the framework of the long-wave asymptotic model, we discuss various instability mechanisms and outline problems where new research is needed.     

Evaporation of sessile droplets of dilute aqueous solutions containing sodium n-alkylates from polymer surfaces: influences of alkyl length and concentration of solute

The evaporation of sessile droplets placed on polymer surfaces was studied by microscopic observation of the changes in shape of aqueous solution droplets in which the alkyl lengths and the initial concentrations of sodium n-alkylates were varied. Although the initial contact angles of the droplets were not significantly different, the evaporation process varied significantly with the alkyl length of the sodium n-alkylate employed. For the sodium dodecanoate (C 12), showing the highest surface activity, the concentration was found to have a significant effect on the evaporation process of the droplets. In the evaporation of water droplets, variations in the three distinct stages were caused by the different concentration of solutes distributed near or at the air/water interface. It is revealed that the concentration of droplet solute near the air/water interface requires not only solvent evaporation but also some affinity of the solute for the interface. The initial C 12 concentration-dependence of the evaporation of C 12 solution droplets is discussed with particular emphasis on the sudden spreading or sudden contraction of the contact area near the end of evaporation. It is suggested that the cluster formation by C 12 molecules at the air/liquid interface during the evaporation causes Marangoni instability in an evaporating droplet, and the clusters are expected to move dynamically, depending on the droplet concentration of C 12, from the droplet center to the contact line and vice versa, showing Marangoni flow along the air/water interface.     

Hydrodynamic Instabilities Driven by Acid-base Neutralization Reaction in Immiscible System

The hydrodynamic instabilities driven by an acid-base neutralization reaction, in contact along a plane interface, placed in a Hele-Shaw cell under the gravitational field are reported.The system consists of the heavier aqueous tetramethyle-ammonium hydroxide below the lighter layer of organic phase with propionic acid as reacting specie. The effect of chemical composition on hydrodynamic instabilities during interfacial mass transfer accompanied by a neutralization reaction is investigated. Depending on the initial concentration of the reacting species, Marangoni convection in the form of roll cells or trains of waves is observed. Mach-Zehnder interferometer is used to measure the change in base concentration at the time of instability formation. The results show that the instabilities resulted from the convection flow are more efficient to the mechanism of mass transfer and can drastically alter pattern formation in the system.     

界面上蜂窝状多孔薄膜的构建、性质和应用

综述了以Breath Figure(呼吸图案)法制备聚合物及纳米颗粒蜂窝状多孔结构的研究现状.当潮湿的气流吹到聚合物或纳米颗粒的有机溶液表面时,溶剂蒸发导致水微滴在液体表面冷凝重排成六角阵列结构.溶剂和水微滴蒸发完毕后,聚合物或纳米颗粒在基底上形成具有六角阵列的蜂窝状多孔结构.该技术是自组装领域的一大进展,在生物技术、组织工程、微图像技术、高端分离技术、光催化及医药等领域有望获得重要应用.本文系统阐述了规整蜂窝状孔结构材料的构建方法、构建材料、形成机理以及影响因素(包括湿度、浓度、气流方向和速度、溶剂、基底曲率等),评述了蜂窝状多孔薄膜的性质和应用,并对其在化学和材料科学领域的应用前景作了展望.     

The chaos-to-order transition in critical modes of shearing for polymer and nanocomposite melts

Two unusual experimental phenomena that were found for polymer melts or solutions containing the dispersed phases of Na-montmorillonite or detonation synthesis nanodiamond have been studied. These phenomena consist in the reduction of viscosity upon addition of specified amount of particles and in the formation of regular morphology by these particles in strong flows looking as a system of concentric rings. In other words, under certain conditions, there is transition to stratified shear stream and the viscosity of such a regular heterogeneous system canbe lower than that for the polymer matrix itself. Hence, both phenomena are mutually related; and the main problem here is the analysis of driving forces leading to the regular texture formation taking place in intense flows for unfilled viscoelastic polymers as well. As a preliminary explanation, the conception of the special kind of the elastic instability is discussed. This instability appears either in the regular helix-like structure formation or in the irregular elastic turbulence. The particles of the filler play a role of tracers that revealed the relief of texture.     

Multiple emulsion stability: pressure balance and interfacial film strength

The objective of this study was to investigate the significance of inner and outer phase pressure, as well as interfacial film strength on W/O/W multiple emulsion stability using microscopy and long-term stability tests. It was observed that immediately upon applying a coverslip to samples the multiple droplets deformed and there was coalescence of the inner aqueous droplets. Under certain conditions (such as lipophilic surfactant concentration and internal phase osmotic pressure) the destabilized multiple emulsions formed unique metastable structures that had a "dimpled" appearance. The formation of these metastable structures correlated with the real-time instability of the W/O/W multiple emulsions investigated. Multiple emulsion stability also correlated with the interfacial film strength (measured by interfacial elasticity) of the hydrophobic surfactant at the mineral oil/external continuous aqueous phase interface. The formation of the metastable dimpled structures and the long-term stability of the multiple emulsions were dependent on the osmotic pressure of the inner droplets and the Laplace curvature pressure as described by the Walstra Equation (P. Walstra, "Encyclopedia of Emulsion Technology" (P. Becher, Ed.), Vol. 4. Dekker, New York, 1996). It appears that the effect of coverslip pressure on multiple emulsions may be useful as an accelerated stability testing method or for initial formulation screening.     

Self-organised microdots formed by dewetting in a highly volatile liquid

Dewetting induced self-organisation was used to prepare an ordered microstructure from a highly volatile liquid. Dewetting of an evaporating iron oxide precursor solute on silicon substrate resulted in arrays of microdots with nearly hexagonal and tetragonal symmetries. Ordered structures form either by stick-slip motion or fingering instability at the receding contact line of evaporating droplets. Subsequent thermal treatment at 550 °C yields crystalline Fe(2)O(3) microdots with a diameter range of 1-4 μm. The size, density and shape of the microdots can be changed by using patterned substrates with different surface energies.     

Temperature-induced self-pinning and nanolayering of AuSi eutectic droplets

A process for self-pinning of AuSi eutectic alloy droplets to a Si substrate, induced by a controlled temperature annealing in ultrahigh vacuum, is presented. Surface pinning of AuSi 3D droplets to the Si substrate is found to be a consequence of the readjustment in the chemical composition of the droplets upon annealing, as required to maintain thermodynamic equilibrium at the solid-liquid interface. Structural and morphological changes leading to the pinning of the droplets to the substrate are analyzed. Phase separation is observed upon cooling of the droplets, leading to the formation of amorphous Si-rich channels within the core and the formation of crystalline Si nanoshells on the outside. The mechanism leading to the pinning and surface layering provides new insight into the role of alloying during growth of silicon nanowires and may be relevant to the engineering of nanoscale Si cavities.     

Mechanisms of equilibrium shape transitions of liquid droplets in electrowetting

Liquid droplets bridging the gap between two dielectric-coated horizontal electrode plates suffer breakup instabilities when a voltage applied between the electrodes exceeds a threshold. Interestingly enough, broken liquid bridges (i.e. a pair of a sessile and a pendant drop) can spontaneously rejoin if the voltage is still applied to the electrodes. Here we study the electro-hydrostatics of the liquid bridges in the joined or broken state and we illuminate the mechanisms of the shape transitions that lead to bridge rupture or droplet joining. The governing equations of the capillary electro-hydrostatics form nonlinear and free boundary problems which are solved numerically by the Galerkin/finite element method. On one hand, we found that capillary bridges become unstable at a turning point bifurcation in their solution space. The solutions past the turning point are unstable and the instability signals the bridge rupture. On the other hand, the separate droplets approach each other as the applied voltage increases. However, solutions become unstable past a critical voltage at a turning point bifurcation and the droplets join. By studying the relative position of the turning points corresponding to bridge rupture and droplet joining, respectively, we define parameter regions where stable bridges or separate droplets or oscillations between them can be realized.     

Stability and disturbance of coating films

In the studies of two-roll metering and application systems, two types of disturbances were observed. These were termed “ring type” and “irregular” disturbances. This research established that the physical reason for the appearance of the ring type instability is the competition between surface tension and centrifugal forces at the liquid-air interface. The rings are generated at the surface of the dynamic liquid meniscus, in the gap between the rolls, because of the very large centrifugal forces there. Considering conditions of a constant interfacial pressure difference (pressure jump), one can reduce the problem to one with only one free parameter, viz., the radius of the meniscus, and calculate the wavelength of the disturbances. There is no single formula which will adequately describe the dynamic meniscus. Its curvature depends on the rheological properties of the fluid and on the kinematic conditions in the process. Dimensional analysis is combined with experimental findings to yield a formula for the radius of the meniscus for fluids having a high yield stress for the case of two counter-rotating rolls.The rheological behavior of a flowing starch adhesive in the dynamical meniscus is analyzed. The theoretical and experimental studies show that systems using two counter-rotating rolls practically always produced ring-type instabilities with all types of fluids.The picture is more complex for co-rotating roll systems. When non-Newtonian adhesives are used, ring type disturbances are observed in one zone of roll speed ratios, and irregular disturbances are observed in another zone. The two zones are separated by a speed ratio zone (a “speed window”) where a more or less perfectly stable fluid layer is observed. When Newtonian oils are used, there are two such speed windows. The first one corresponds to very low metering roll speeds and a minimum of liquid transfer to the applicator roll. The second stable zone occurs at high metering roll speeds and yields a maximum of liquid transfer. The physical reason for the high transfer rate in the high speed “window” is considered and shown to be the thin air layer following the surface of the metering roll. The air pumped into the metering gap returns along the applicator roll and accelerates the film on the applicator roll in the process. Under these conditions the fluid-air interface may become unstable, leading to the “irregular” type of disturbance.     

Influence of weak anchoring on flow instabilities in nematic liquid crystals

We analyse the homogeneous instabilities in a nematic liquid crystal subjected to plane steady Couette or Poiseuille flow in the case when the director is prealigned perpendicular to the flow plane taking into account weak anchoring at the confining surfaces. The critical shear rate decreases for decreasing anchoring strength and goes to zero in the limit of torque-free boundary conditions. For Poiseuille flow two types of instability arise depending on the values of the azimuthal (W_a) and polar (W_p) surface anchoring strengths. The critical line in (W_a,W_p) space which separates the two instabilities regimes is obtained.     

Surfactant influence on rivulet droplet flow in minitubes and capillaries and its downstream evolution

During our investigations of two-phase flow in long hydrophobic minitubes and capillaries, we have observed transformation of the main rivulet into different new hydrodynamic modes with the use of different kinds of surfactants. The destabilization of rivulet flow at air velocities <80 m/s occurs primarily due to the strong branching off of sub-rivulets from the main rivulet during the downstream flow in the tube. The addition of some surfactants of not-so-high surface activity was found to increase the frequency of sub-rivulet formation and to suppress the Rayleigh and sinuous instabilities of the formed sub-rivulets. Such instabilities result in subsequent fragmentation of the sub-rivulets and in the formation of linear or sinuous arrays of sub-rivulet fragments (SRFs), which later transform into random arrays of SRFs. In the downstream flow, SRFs further transform into large sliding cornered droplets and linear droplet arrays (LDAs), a phenomenon which agrees with recent theories. At higher surface activity, suppression of the Rayleigh instability of sub-rivulets with surfactants becomes significant, which prevents sub-rivulet fragmentation, and only the rivulet and sub-rivulets can be visualized in the tube. At the highest surface activity, the bottom rivulet transforms rapidly into an annular liquid film. The surfactant influence on the behavior of the rivulets in minitubes is incomparably stronger than the classic example of the known surfactant stabilizing influence on a free jet. The evolution of a rivulet in the downstream flow inside a long minitube includes the following sequence of hydrodynamic modes/patterns: i) single rivulet; ii) rivulet and sub-rivulets; and iii) rivulet, sub-rivulets, sub-rivulet fragments, cornered droplets, linear droplet arrays, linear arrays of sub-rivulet fragments and annular film. The formation of these many different hydrodynamic patterns downstream is in drastic contrast with the known characteristics of two-phase flow, which demonstrates one mode for the entire tube length. Recent achievements in fluid mechanics regarding the stability of sliding thin films and in wetting dynamics have allowed us to interpret many of our findings. However, the most important phenomenon of the surfactant influence on sub-rivulet formation remains poorly understood. To achieve further progress in this new area, an interdisciplinary approach based on the use of methods of two-phase flow, wetting dynamics and interfacial rheology will be necessary.