Models of adsorption at a line of three-phase contact

Two model density distributions at a line of three-phase contact for which the adsorptions are readily calculated are analyzed. One of them provides a numerical illustration of a recently found surprising fact about the thermodynamics of adsorption at such contact lines. A form of the line analogue of the Gibbs adsorption equation is conjectured, and it is noted that the conjecture is in principle testable by computer simulation and by experiment.     

Cusp at the three-fluid contact line in a cylindrical pore

In a cylindrical pore of arbitrary wettability, we analyse the existence of a three-fluid contact line connecting the fluid-fluid interfaces between two bulk phases and the third phase contained in a cusp near the pore wall. This analysis is supported by the very similar, but simpler, analysis for a constriction between parallel plates. From the force balance at the contact line and the equations for the interface curvatures we derive expressions for the cusp height and for the capillary entry pressure related to piston-like displacement between the two bulk phases. The latter is independent of the existence of a cusp and its phase pressure. Based on some realistic assumptions, of which the most important is that a cusp grows continuously from the onset when its phase pressure is increased, we analyse under which conditions a cusp can exist, and, when it exists, what its behaviour is as a function of the cusp phase pressure. We find a simple criterion involving (two ratios of) the three interfacial tensions and two of the three contact angles, which determines whether the three-fluid contact line and, consequently, a cusp exists. The range of contact angles, as well as the size of the cusp increases, when the cusp phase is close to spreading. Not only cusps of the wetting phase can occur, but also of the intermediate-wetting phase. Numerical examples are presented to illustrate the range of behaviour of the cusps.     

Simulations of a weakly conducting droplet under the influence of an alternating electric field

We investigate the electrohydrodynamics of an initially spherical droplet under the influence of an external alternating electric field by conducting axisymmetric numerical simulations using a charge-conservative volume-of-fluid based finite volume flow solver. The mean amplitude of shape oscillations of a droplet subjected to an alternating electric field for leaky dielectric fluids is similar to the steady-state deformation under an equivalent root mean squared direct electric field for all possible electrical conductivity ratio and permittivity ratio of the droplet to the surrounding fluid. In contrast, our simulations for weakly conducting media show that this equivalence between alternating and direct electric fields does not hold for . Moreover, for a range of parameters, the deformation obtained using the alternating and direct electric fields is qualitatively different, that is, for low and high , the droplet becomes prolate under alternating electric field but deforms to an oblate shape in the case of the equivalent direct electric field. A parametric study is conducted by varying the time period of the applied alternating electric field, the permittivity and the electrical conductivity ratios. It is observed that while increasing has a negligible effect on the deformation dynamics of the droplet for , it enhances the deformation of the droplet when for both alternating and direct electric fields. We believe that our results may be of immense consequence in explaining the morphological evolution of droplets in a plethora of scenarios ranging from nature to biology.     

Use of IR thermography to investigate heated droplet evaporation and contact line dynamics

In this paper we present the results of an experimental study investigating interfacial properties during the evaporation of sessile water droplets on a heated substrate. This study uses infrared thermography to map the droplet interfacial temperature. The measurements evidence nonuniform temperature and gradients that evolve in time during the evaporation process. A general scaling law for the interfacial temperature is deduced from the experimental observations. A theoretical analysis is performed to predict the local evaporation rates and their evolution in time. The use of energy conservation laws enabled us to deduce a general expression for the interfacial temperature. The comparison between the theory and experiments shows good agreement and allows us to rationalize the experimental observations. The thermography analysis also enabled the detection of the three-phase contact line location and its dynamics. To our knowledge, such measurements are performed for the first time using thermography.     

Dynamic meniscus growth at a scanning probe tip in contact with a gold substrate

Environmental scanning electron microscopy was used to investigate the dynamic meniscus growth at a cantilever in contact with a substrate. The meniscus was observed to take many minutes to reach an equilibrium state. The observed growth rate is similar to initial patterning rates observed from dip-pen nanolithography and suggest that the meniscus growth may be the rate-limiting step in initial pattering rates.     

Geometric view of the thermodynamics of adsorption at a line of three-phase contact

We consider three fluid phases meeting at a line of common contact and study the linear excesses per unit length of the contact line (the linear adsorptions Lambda(i)) of the fluid's components. In any plane perpendicular to the contact line, the locus of choices for the otherwise arbitrary location of that line that makes one of the linear adsorptions, say Lambda(2), vanish, is a rectangular hyperbola. Two of the adsorptions Lambda(2) and Lambda(3) then both vanish when the contact line is chosen to pass through any of the intersections of the two corresponding hyperbolas Lambda(2)=0 and Lambda(3)=0. There may be two or four such real intersections. It is found most surprisingly, and confirmed in a numerical example, that Lambda(1(2,3)), the adsorption of component 1 in a frame of reference in which the adsorptions Lambda(2) and Lambda(3) are both 0, depends on which intersection of the hyperbolas Lambda(2)=0 and Lambda(3)=0 is chosen for the location of the contact line. This implies that what had long been taken to be the line analog of the Gibbs adsorption equation is incomplete; there must be additional, previously unanticipated terms in the relation, consistent with the invariance of the line tension to choice of location of the contact line. It is then not Lambda(1(2,3)) by itself but a related expression containing it that must be invariant, and this invariance is also confirmed in the numerical example. The presence of the additional terms in the adsorption equation is further confirmed and their origin clarified in a mean-field density-functional model. The supplemental terms vanish at a wetting transition, where one of the contact angles goes to 0.     

Truncated versus extended microfilms at a vapor-liquid contact line on a heated substrate

The microstructure of a contact line formed by a liquid and its pure vapor on a perfectly wetted superheated smooth substrate, with the disjoining pressure most often in the form of a positive inverse cubic law (nonpolar case), is routinely considered to end up in a microfilm extended over adjacent "dry" parts of the solid surface. Invoking the spreading coefficient as an additional independent parameter within this framework, we argue however that a regime with a truncated microfilm is chosen instead if the spreading coefficient is decreased below a positive (still perfect wetting) critical value dependent upon the superheat, in which case the extended-microfilm thickness is surpassed by that of the "pancake" introduced by de Gennes and co-workers. Conversely, for a given positive spreading coefficient, there is a critical superheat above which the microfilm gets truncated, whereas for a negative one (partial wetting) the truncated regime should be preferred at any superheat. A parametric study of the apparent contact angle (a nonlinear eigenvalue of the steady microstructure problem) versus the spreading coefficient is carried out. When the latter is negative, Young's law is asymptotically recovered. Microfilm fronts on a bare surface are shown to be advancing or receding in accordance with the selected regime. A slightly more general class of disjoining pressures is also touched upon. The analysis is based in part upon thermodynamic considerations and in part upon a standard one-sided model of an evaporating liquid layer in the lubrication approximation.     

Modeling of the moving deformed triple contact line: influence of the fluid inertia

For partial wetting, motion of the triple liquid-gas-solid contact line is influenced by heterogeneities of the solid surface. This influence can be strong in the case of inertial (e.g., oscillation) flows where the line can be pinned or move intermittently. A model that takes into account both surface defects and fluid inertia is proposed. The viscous dissipation in the bulk of the fluid is assumed to be negligible as compared to the dissipation in the vicinity of the contact line. The equations of motion and the boundary condition at the contact line are derived from Hamilton's principle. The rapid capillary rise along a vertical inhomogeneous wall is treated as an example.     

Probing with a laser sheet the contact angle distribution along a contact line

An optical method for probing contact angle distribution along contact lines of any shape using a laser sheet is proposed. This method is applied to a dry patch formed inside a film flowing along an inclined plane, both liquid and solid being transparent. Falling normally to the plane, a laser sheet cuts the contact line and is moved along this line. Distortions of the sheet trace observed on a screen put below the plane allow us to extract the contact angle distribution and the local line inclination along the line. Our results show that the contact angle around a dry patch is nearly constant and equal to the static advancing angle, at least when the evolution of its shape is followed for increasing flow rates. This supports a model of dry patch shape recently proposed by Podgorski and co-workers. Preliminary results obtained for decreasing flow are also qualitatively observed.     

Potential-induced switching of electrical contact by controlling droplet shapes at hydrophilic/hydrophobic interfaces

Asymmetrical deformation of an aqueous electrolyte droplet bridging two bipyridinium-modified Au-electrodes is achieved upon the application of voltages resulting in the selective reduction and oxidation of the bipyridinium units on the two electrodes. The different contact angles at the right and left sides of the droplet originate from the electrochemically controlled changes of the wetting properties of the modified electrodes. The reversible and repeatable formation of an electrolytic contact between a side Pt-wire electrode and the respective bottom Au-electrode is controlled by the voltage applied between the two bottom Au-electrodes.     

Moving contact lines of a colloidal suspension in the presence of drying

This article presents the first experimental study of an advancing contact line for a colloidal suspension. A competition between the hydrodynamic flow due to the drop velocity and the drying is exhibited: drying accounts for particle agglomeration that pins the contact line whereas the liquid flow dilutes the agglomerated particles and allows the contact line to advance continuously. The dilution dominates at low concentration and high velocity, but at high concentration and low velocity, the contact line can be pinned by the particle agglomeration, which leads to a stick-slip motion of the contact line. The calculation of the critical speed splitting both regimes gives an order of magnitude comparable to that of experiments. Moreover, a model of agglomeration gives an estimation of both the size of the wrinkles formed during stick-slip and the force exerted by the wrinkle on the contact line.     

Spreading of an inkjet droplet on a solid surface with a controlled contact angle at low Weber and Reynolds numbers

Even though the inkjet technology has been recognized as one of the most promising technologies for electronic and bio industries, the full understanding of the dynamics of an inkjet droplet at its operating conditions is still lacking. In this study, the normal impact of water droplets on solid substrates was investigated experimentally. The size of water droplets studied here was 46 microm and was much smaller than the most of the previous studies on drop impact. The Weber number (We) and Reynolds number (Re) were 0.05-2 and 10-100, respectively, and the Ohnesorge number was fixed at 0.017. The wettability of the solid substrate was varied by adsorbing a self-assembled monolayer of octadecyltrichlorosilane followed by the exposure to UV-ozone plasma. The impact scenarios for low We impacts were found to be qualitatively different from the high to moderate We impacts. Neither the development of a thin film and lamella under the traveling sphere nor the entrapment of small bubbles was observed. The dynamics of droplet impact at the conditions studied here is found to proceed under the combined influences of inertia, surface tension, and viscosity without being dominated by one specific mechanism. The maximum spreading factor (beta), the ratio of the diameter of the wetted surface and the drop diameter before impact, was correlated well with the relationship ln beta=0.090 ln We/(fs-cos theta)+0.151 for three decades of We/(fs-cos theta), where theta is the equilibrium contact angle, and fs is the ratio between the surface areas contacting the air and the solid substrate. The result implies that the final shape of the droplet is determined by the surface phenomenon rather than fluid mechanical effects.     

Study of the morphology of the three-phase contact line and its evolution by morphological examination after droplet evaporation of aqueous polymer solutions

The local morphology and its evolution of an air-liquid-solid three-phase contact line was studied on the homogeneous surfaces of homopolymer of polystyrene (PS) and poly(methyl methacrylate) (PMMA) and the nanostructured surface of diblock copolymer of PS- b-PMMA by the approach of the morphological study of the residual solid after droplet evaporation of water-soluble polymers such as poly(vinylpyrrolidone) (PVP) and poly(acrylic acid). The observation by atomic force microscopy discovered the stripelike "button-and-ribbon" structure of the precipitated polymer solute along the moving direction of the contact line. On the surface of PS- b-PMMA, the morphology of PVP has a close correlation with the nanostructure of PS- b-PMMA. The results exhibit the local morphology of the contact line and its evolution, revealing its pinning and depinning processes on the nanometer scale.     

Self-propelled motion of a fluid droplet under chemical reaction

We study self-propelled dynamics of a droplet due to a Marangoni effect and chemical reactions in a binary fluid with a dilute third component of chemical product which affects the interfacial energy of a droplet. The equation for the migration velocity of the center of mass of a droplet is derived in the limit of an infinitesimally thin interface. We found that there is a bifurcation from a motionless state to a propagating state of droplet by changing the strength of the Marangoni effect.     

Analysis of the relationship between liquid droplet size and contact angle

The purpose of this paper is to present a consistent theoretical concept that can explain the various physical phenomena associated with the effect of droplet size on contact angle for droplets on solid surfaces, and with the geometry of the liquid/gas/solid contact line in general. Two droplet geometries have been considered: uniformly elongated droplets and axisymmetric droplets. It has been shown that the contact angle for elongated droplets is size-independent and, thus, satisfies the Young equation for constant material and interfacial properties. On the other hand, whereas the contact angle for axisymmetric droplets is size-dependent and does not satisfy the original Young equation, it is shown that this contact angle can still be predicted for any combination of droplet and substrate materials, and a given mass of the droplet. The theoretical work has been combined with the development of numerical schemes of solving the Laplace-Young equation for various droplet geometries. The proposed approach has been applied to different material/substrate combinations and validated against several sets of experimental data. As a result, a method has been developed for predicting the contact angle of both long and axisymmetric sessile droplets of arbitrary sizes for given liquid/solid/gas properties.     

Post-self-repair process of neuron cells under the influence of neutral and cationic nanoparticles

Alkylated nanoparticles induce malignant lysosome damages and unrepairable genome injuries which cannot be caused by aminated nanoparticles. Therefore, cells exposed to alkylated nanoparticles initiate post-self-repair effect by down regulating Fbw7 and accumulating cyclin E to maintain the replication of injured DNA.     

Post-self-repair process of neuron cells under the influence of neutral and cationic nanoparticles

The prevalence of functionalized nanoparticles in biological and clinical fields attracts intensive toxicology investigations. Minimizing the nanoparticles’ biohazard remains a challenge due to the insufficient understanding on the nanoparticle-induced cell death mechanism. In the presented study, we observed the lysosome and genome injuries and so caused cell cycle changes and regulations of retinal ganglion neuron cell 5 (RGC-5) induced by aminated and alkylated nanoparticles. Alkylated nanoparticles induced malignant lysosome and genome damages followed by severe post-self-repair responses. RGC-5 treated with alkylated nanoparticles presented dramatic S phase prolongation resulted from cyclin E accumulation mediated by Fbw7 downregulation, which assisted DNA replication after failed self-repair of the malignantly damaged DNA caused by alkylated nanoparticles. Differently, aminated nanoparticles in RGC-5 induced moderate lysosome and genome injuries and these damages could be repaired in the p21-involved pathway, so that cells did not induce apparent cyclin E accumulation nor Fbw7 downregulation as post-self-repair response. These results helped us to understand the toxicity of analogous nanoparticles on retinal ganglions such as glaucoma treatment. This work provides new insights into nanoparticle functionalization and toxicity in relation to the research on the toxicology and pathology of nerve cells.     

Anomalous contact angle hysteresis of a captive bubble: advancing contact line pinning

Contact angle hysteresis of a sessile drop on a substrate consists of continuous invasion of liquid phase with the advancing angle (θ(a)) and contact line pinning of liquid phase retreat until the receding angle (θ(r)) is reached. Receding pinning is generally attributed to localized defects that are more wettable than the rest of the surface. However, the defect model cannot explain advancing pinning of liquid phase invasion driven by a deflating bubble and continuous retreat of liquid phase driven by the inflating bubble. A simple thermodynamic model based on adhesion hysteresis is proposed to explain anomalous contact angle hysteresis of a captive bubble quantitatively. The adhesion model involves two solid–liquid interfacial tensions (γ(sl) > γ(sl)′). Young’s equation with γ(sl) gives the advancing angle θ(a) while that with γ(sl)′ due to surface rearrangement yields the receding angle θ(r). Our analytical analysis indicates that contact line pinning represents frustration in surface free energy, and the equilibrium shape corresponds to a nondifferential minimum instead of a local minimum. On the basis of our thermodynamic model, Surface Evolver simulations are performed to reproduce both advancing and receding behavior associated with a captive bubble on the acrylic glass.     

Modeling contact angle hysteresis of a liquid droplet sitting on a cosine wave-like pattern surface

A liquid droplet sitting on a hydrophobic surface with a cosine wave-like square-array pattern in the Wenzel state is simulated by using the Surface Evolver to determine the contact angle. For a fixed drop volume, multiple metastable states are obtained at two different surface roughnesses. Unusual and non-circular shape of the three-phase contact line of a liquid droplet sitting on the model surface is observed due to corrugation and distortion of the contact line by structure of the roughness. The contact angle varies along the contact line for each metastable state. The maximum and minimum contact angles among the multiple metastable states at a fixed viewing angle correspond to the advancing and the receding contact angles, respectively. It is interesting to observe that the advancing/receding contact angles (and contact angle hysteresis) are a function of viewing angle. In addition, the receding (or advancing) contact angles at different viewing angles are determined at different metastable states. The contact angle of minimum energy among the multiple metastable states is defined as the most stable (equilibrium) contact angle. The Wenzel model is not able to describe the contact angle along the three-phase contact line. The contact angle hysteresis at different drop volumes is determined. The number of the metastable states increases with increasing drop volume. Drop volume effect on the contact angles is also discussed.