Spontaneous pattern formation by dip coating of colloidal suspensions on homogeneous surfaces

We study the slow withdrawal of a partially wet vertical plate at velocity U from a suspension of well-wet particles. Periodic horizontal striped assemblies form spontaneously at the three-phase contact line on energetically uniform surfaces. Stripe width and spacing depend on the withdrawal velocity U relative to a transition velocity Ut. Thick stripes separated by large spaces form for UUt, thin stripes separated by small spaces form. The stripe spacing is reduced by an order of magnitude and varies weakly with U until a maximum velocity is reached at which the stripes fail to form. A partially wet surface can entrain a meniscus. For UUt, we infer that a film of thickness h is entrained above the meniscus. When h is smaller than the particle diameter D, particles aggregate where the entrained film thickens to match up to the wetting meniscus. When an entrained particle becomes exposed to air by evaporation, it becomes the new pinning site from which the next film is entrained. The film thickness h increases with U; at some velocity, h becomes comparable to D. Particles flow into the film and deposit there in a disordered manner. A diagram summarizing particle deposition is developed as a function of D, U, and h.     

On the Landau-Levich transition

We discuss here the nature of the Landau-Levich transition, that is, the dynamical transition that occurs when drawing a solid out of a bath of a liquid that partially wets this solid. Above a threshold velocity, a film is entrained by the solid. We measure the macroscopic contact angle between the liquid and the solid by different methods, and conclude that this angle might be discontinuous at the transition. We also present a model to understand this fact and the shape of the meniscus as drawing the solid.     

Liquid Entrainment from the Meniscus of a Liquid Wedge by a Moving Horizontal Plate

A hydrodynamic model is proposed for smear formation during the drawing of a film from the meniscus of a limited-volume liquid wedge. It was assumed that the regime of the flow is capillary and the characteristic time of the film formation is small compared to the characteristic time of the change in the meniscus curvature. At small time intervals, the film thickness was determined according to the Landau–Levich–Derjaguin method. At large time intervals, the curvature of the meniscus is described by a linear differential equation for the dynamics of the liquid wedge volume. Under these conditions, the film thickness changes along the plate according to a linear law with the tangent coefficient depending on the capillary number according to a power law, and the profile of the longitudinal section of the smear is close to a right triangle.     

Free-standing films of twist grain boundary TGBA and UTGBC* liquid crystals studied by fluorescence confocal polarizing microscopy

The director structures, meniscus profile, and defects in free-standing films of the twist grain boundary TGB_A and UTGB_C* liquid crystals were studied. The films were characterized by a combination of polarizing microscopy and fluorescence confocal polarizing microscopy. Five principal regions of meniscus were distinguished. When film thickness in the meniscus is much smaller then the TGB pitch, there is no difference between the free-standing films of TGB and ordinary smectic A liquid crystals. When the film thickness is larger than the TGB pitch, filamentary texture is observed. The 3D director pattern of the filaments are similar to the ground state director fields of TGB_A and UTGB_C* liquid crystals. In the intermediate thickness region of the meniscus, when the film thickness and TGB pitch are commensurate, a unique radial pattern is observed. Based on the fluorescence confocal polarizing microscopy studies of the director field, we propose a model for the 3D director structure in this part of the meniscus.     

Free-standing films of twist grain boundary TGBA and UTGBC* liquid crystals studied by fluorescence confocal polarizing microscopy

The director structures, meniscus profile, and defects in free-standing films of the twist grain boundary TGB_A and UTGB_C* liquid crystals were studied. The films were characterized by a combination of polarizing microscopy and fluorescence confocal polarizing microscopy. Five principal regions of meniscus were distinguished. When film thickness in the meniscus is much smaller then the TGB pitch, there is no difference between the free-standing films of TGB and ordinary smectic A liquid crystals. When the film thickness is larger than the TGB pitch, filamentary texture is observed. The 3D director pattern of the filaments are similar to the ground state director fields of TGB_A and UTGB_C* liquid crystals. In the intermediate thickness region of the meniscus, when the film thickness and TGB pitch are commensurate, a unique radial pattern is observed. Based on the fluorescence confocal polarizing microscopy studies of the director field, we propose a model for the 3D director structure in this part of the meniscus.     

Disjoining pressure measurements using a microfabricated groove for a molecularly thin polymer liquid film on a solid surface

A method for measuring disjoining pressure of a molecularly thin liquid film on a solid surface by using a microfabricated groove has been developed. The shape of the meniscus of a thin film in the microgroove was measured with an atomic force microscope, and the disjoining pressure was obtained from the capillary pressure obtained from the measured curvature of the meniscus. Our method is applicable to a film with a thickness greater than the diameter of gyration in the polymer molecule. Moreover, the method can detect the changes in the disjoining pressure caused by ultraviolet light irradiation, and it is effective in investigating the intermolecular interaction between a thin film and a solid surface.     

Interfacial phenomena and dynamic contact angle modulation in microcapillary flows subjected to electroosmotic actuation

The dynamic evolution of an incompressible liquid meniscus inside a microcapillary is investigated, under the combined influences of viscous, capillary, intermolecular, pondermotive, and electroosmotic effects. In the limit of small capillary numbers, an advancing meniscus shape is shown to merge smoothly with the precursor film, using matched asymptotic analysis. A scaling relationship is also established for the dynamic contact angle as a nondimensional function of the capillary number and the applied electrical voltage. The analysis is further generalized by invoking a kinetic slip model for overcoming the constraints of meniscus tip singularity. The kinetic slip model is subsequently utilized to analyze the interfacial dynamics from the perspective of the results obtained from the matched asymptotic analysis. A generalization is achieved in this regard, which may provide a sound basis for controlling the topographical features of a dynamically evolving meniscus in a microcapillary subjected to electrokinetic effects. These results are also in excellent agreement with the experimental findings over a wide range of capillary number values.     

Dynamic response of geometrically constrained vapor bubbles

We consider a two-dimensional model of a vapor bubble between two horizontal parallel boundaries held at different temperatures. When the temperatures are constant, a steady state can be achieved such that evaporation near the contact lines at the hot bottom plate is balanced by condensation in colder areas of the interface near the top. The dynamic response of the bubble is probed by treating the case of time-dependent wall temperatures. For periodic modulations of the wall temperature the bubble oscillates about the steady state. In order to describe such time-dependent behavior we consider the limit of small capillary number, in which the effects of heat and mass transfer are significant only near the contact lines at the bottom plate and in a small region near the top. When the bottom temperature is modulated and the top temperature is held fixed, the amplitude of forced oscillations is constant for low-frequency modulations and then rapidly decays in the high-frequency regime. When the top temperature is modulated with fixed bottom temperature, the dynamic-response curve is flat in the low-frequency regime as well, but it also flattens out when the frequency is increased. This shape of the response curve is shown to be the result of the nonmonotonic behavior of the thickness of the liquid film between the bubble interface and the top plate: when the temperature is decreased, the film thickness increases rapidly, but then slowly decays to a value which is smaller than the initial thickness. The dynamic response is also studied as a function of the forcing amplitude.     

Switching direction of laterally ordered monolayers induced by transfer instability

Langmuir-Blodgett monolayers may show nanoscopic periodic patterns parallel and/or perpendicular to the transfer direction. The experimental findings are interpreted by a nonequilibrium model based on the stability of surfactant concentration and film thickness coupled fluctuations near the meniscus of a surfactant-covered receding thin film. In the high and low transfer speed limits, periodic fluctuations of the fluid subphase thickness, respectively perpendicular and parallel to the transfer, are selected. A qualitative phase diagram shows how transfer speed and film density manage the pattern shape.     

Wetting: Inverse Dynamic Problem and Equations for Microscopic Parameters

Movement of a liquid meniscus in a low-diameter capillary while it is being filled or emptied is considered. The liquid is nonvolatile. Assuming low Reynolds number and low capillary number, the liquid-gas interface shape is studied. Angles of inclination of this boundary to the solid near the contact line are small. Consideration is given to the inverse problem in wetting dynamics: to establish an analytic expression for the universal constant that influences the dynamics of a three-phase contact line. Inverse relations for microscopic parameters in terms of macroscopic measured values obtained in experiments with a meniscus moving through a capillary are derived. The inverse relations are substantiated independently. To do so, numerical experiments for a van der Waals liquid have been carried out, using the de Gennes model of partial wetting. General formulas for microparameters agree well with numerical experiments. The article provides the similarity criterion which influences the wetting in the case of a van der Waals liquid meniscus. The inverse dynamic problem for both an advancing and a receding meniscus is solved. A relation for the critical speed of meniscus recession is proposed. Two contact angles for a meniscus are discussed. Behavior of dynamic contact angles in the vicinity of the critical speed is studied. One of the angles is shown to vanish at less than the critical speed, and the other one, exactly at the critical speed. In the case of an advancing meniscus the equations for microparameters are valid for both partial and complete wetting. The proposed inverse expression for complete wetting allows determination of the maximum precursor film thickness and its dependence on the motion speed (also determination of the Hamaker constant in the case of a van der Waals liquid). Copyright 2000 Academic Press.     

Modified Tilting-Plate Method for Measuring Contact Angles

The additivity of the dynamic curvature of a thermocapillary depression and the static curvature of liquid meniscus is experimentally confirmed. A high sensitivity of response shape to the static curvature of liquid surface is used to improve the tilting-plate method. The results of measuring contact angles by this method are well consistent with the data obtained by the sessile drop method. The behavior of meniscus is analyzed in the tilting of a plate with various positioning of its rotation axis in relation to the liquid–gas interface. The applicability limits of the modified method are indicated.     

On the shape of a hydrostatic meniscus attached to a corrugated plate or wavy cylinder

The shape of a hydrostatic meniscus attached at a fixed contact angle to a vertical plate or circular cylinder with periodic corrugations is studied by analytical and numerical methods, and the effect of wall irregularities on the shape of the contact line and vertical component of the capillary force is discussed. An asymptotic analysis for a plate with small-amplitude sinusoidal corrugations is carried out to first order with respect to the corrugation amplitude, and a boundary-value problem is formulated and solved by a shooting method to determine the meniscus shape and elevation of the contact line. The meniscus attached to a corrugated plate with rounded corners produced by a Schwarz-Christoffel mapping function for a triangular wave is considered by numerical methods. The Laplace-Young equation determining the meniscus shape is solved in orthogonal curvilinear coordinates generated by conformal mapping using a finite-difference method. The numerical results are successfully compared with the predictions of the perturbation expansion for small amplitudes and discussed with reference to the rise of a meniscus inside a dihedral angle for large amplitudes. A companion asymptotic analysis is presented for a meniscus outside a vertical circular cylinder with small-amplitude sinusoidal corrugations. The analytical predictions are successfully compared with numerical solutions of the Laplace-Young equation for a meniscus outside an elliptical cylinder with aspect ratio near unity, regarded as a deformed circle.     

Kinetics of Gas Bubble Motion in a Capillary

Two flow regimes were discovered by measuring flow rate vof water through thin capillaries containing small gas bubble. The first regime is realized at a low pressure drop P, when the main resistance to flow is created by the wetting film. The estimate of its thickness makes it possible to determine the parameters of the isotherm of the electrostatic component of the disjoining pressure corresponding to the constant charge of the film–gas interface and potential of the quartz surface, which requires the application of a new calculation procedure. As Pincreases, an advancing meniscus forms contact angle of 50°–60° due to the film rupture when it reaches critical pressure in the thinnest part near the meniscus. In this case, the rate vis controlled by the flow in the filled part of a capillary, although some additional viscous drag is also created by the film moving in front of advancing meniscus. The longer the bubble, the greater this contribution.     

Soap film electrochemistry

In this paper we present preliminary electrochemical investigations into the transport properties of free standing ultra-thin surfactant films and the associated meniscus. We describe a new electrochemical cell composed of a 25 μm diameter gold wire placed through a stable surfactant film which served as the electrolyte. Solutions containing anionic sodium dodecyl sulphate (SDS) or non-ionic Triton-X100 surfactants, with background electrolyte NaCl and with electroactive probe ferrocyanide or ferrocene methanol, were used to create the surfactant films. The electrolyte was an ultra-thin surfactant film creating a two dimensional solution with a thickness between 300 and 1000 nm, and its meniscus at the gold wire, within which the electroactive probe was free to diffuse. Cyclic voltammetry was used to oxidise and reduce the electroactive probe within the surfactant film and meniscus. It was shown that films and the associated meniscus formed from SDS solution almost completely excluded negatively charged ferrocyanide. A finite difference simulation showed that the voltammetry was dominated by the meniscus region, the unusual spatially-varying bounded geometry of which resulted in an unusual dependence on potential scan rate of the peak to peak separation (decreasing with increasing scan rate) and anodic:cathodic peak current ratio (increasing with increasing scan rate).     

Three minimum wet thickness regions of slot die coating

An experimental study was carried out to determine the minimum wet thickness of slot die coating for low-viscosity solutions. There exist three distinct coating regions (I, II, and III), depending on the physical properties of the coating fluid, die geometry, and flow conditions. A critical Reynolds number was found, below which viscous and surface tension effects are important. In Region I, the minimum wet thickness increases with increasing capillary number and becomes independent of capillary number in Region II. Region III exists above the critical Reynolds number where fluid inertia is dominant. In this region, the minimum wet thickness decreases as Reynolds number increases. Flow visualization on the coating bead reveals that the position of the downstream meniscus of the coating bead determines the types of coating region, whereas the shape and position of the upstream meniscus determine the type of coating defects. It was also observed that the downstream meniscus was not located at the die lip corner and both the static and dynamic contact angles varied under different conditions. These findings are critical for realistic theoretical study of slot die coating.     

Fine Structure of Meniscus of a Wetting Liquid

Equilibrium of a capillary meniscus near a wetting film on a solid in a gravitational field is considered. Unlike previous studies, the present study proves that the fine meniscus structure in a gravitational field is a universal feature—it takes place in a wide variety of problems. In the general case, the capillary meniscus is at a certain distance from the wetting film and does not intersect it. The relation for the minimum distance from the arbitrary meniscus to the solid generalizes the Derjaguin formula for a flat slit. An equation that optimally approximates the meniscus with due account of the contribution of the meniscus/film transition region is derived. A refined solution to the problem of a meniscus on a vertical plate is derived within the perturbation theory. Both gravity and nonuniformity of the vertical static film above a capillary–gravitational meniscus do not affect the minimum distance (the influence is less than 0.0001). A general method for solving sophisticated problems of capillary equilibrium in gravitational field is proposed.     

Electric field enhanced spreading of partially wetting thin liquid films

Equilibrium and dynamic electrowetting behavior of ultrathin liquid films of surfactant (SDS) laden water over silicon substrate (with native oxide) is investigated. A nonobtrusive optical method, namely, image analyzing interferometry, is used to measure the meniscus profile, adsorbed film thickness, and the curvature of the capillary meniscus. Significant advancement of the contact line of the liquid meniscus, as a result of the application of electric field, is observed even at relatively lower values of applied voltages. The results clearly demonstrate the balance of intermolecular and surface forces with additional contribution from Maxwell stress at the interline. The singular nature of Maxwell stress is exploited in this analysis to model the equilibrium meniscus profile using the augmented Young-Laplace equation, leading to the in situ evaluation of the dispersion constant. The electrowetting dynamics has been explored by measuring the velocity of the advancing interline. The interplay of different forces at the interface is modeled using a control volume approach, leading to an expression for the interline velocity. The model-predicted interline velocities are successfully compared with the experimentally measured velocities. Beyond a critical voltage, contact line instability resulting in emission of droplets from the curved meniscus has been observed.     

Spreading, evaporation, and contact line dynamics of surfactant-laden microdrops

An optical technique based on the reflectivity measurements of a thin film was used to experimentally study the spreading, evaporation, contact line motion, and thin film characteristics of drops consisting of a water-surfactant (polyalkyleneoxide-modified heptamethyltrisiloxane, called superspreader) solution on a fused silica surface. On the basis of the experimental observations, we concluded that the surfactant adsorbs primarily at the solid-liquid and liquid-vapor interfaces near the contact line region. At equilibrium, the completely wetting corner meniscus was associated with a flat adsorbed film having a thickness of approximately 31 nm. The calculated Hamaker constant, A = -4.47 x 10(-)(20) J, shows that this thin film was stable under equilibrium conditions. During a subsequent evaporation/condensation phase-change process, the thin film of the surfactant solution was unstable, and it broke into microdrops having a finite contact angle. The thickness of the adsorbed film associated with the drops was lower than that of the equilibrium meniscus. The drop profiles were experimentally measured and analyzed during the phase-change process as the contact line advanced and receded. The apparent contact angle, the maximum concave curvature near the contact line region, and the convex curvature of the drop increased as the drop grew during condensation, whereas these quantities decreased during evaporation. The position of the maximum concave curvature of the drop moved toward the center of the drop during condensation, whereas it moved away from the center during evaporation. The contact line velocity was correlated to the observed experimental results and was compared with the results of the drops of a pure alcohol. The experimentally obtained thickness profiles, contact angle profiles, and curvature profiles of the drops explain how the surfactant adsorption affects the contact line motion. We found that there was an abrupt change in the velocity of the contact line when the adsorbed film of the surfactant solution was just hydrated or desiccated during the phase-change processes. This result shows the effect of vesicles and aggregates of the surfactant on the shape evolution of the drops. For these surfactant-laden water drops, we found that the apparent contact angle increased during condensation and decreased during evaporation. However, for the drop of a pure liquid (n-butanol and 2-propanol) the apparent contact angle remained constant at a constant velocity during condensation and evaporation. The contact line was pinned during the evaporation and spreading of the surfactant-laden water drops, but it was not pinned for a drop of a pure alcohol (self-similar shape evolution).     

Liquid coating of moving fiber at the nanoscale

Using large scale molecular dynamics, we study the contact line motion of a liquid meniscus crossed by a moving nanofiber. Varying the amplitude of the liquid/solid interactions, we analyze the shape of the meniscus versus time for a range of velocities. The associated contact angles are estimated by fitting the profiles using the James equation. The corresponding flux lines describing the displacement of the liquid molecules inside the meniscus have also been measured. The analysis of the dynamic contact angle is in agreement with the molecular-kinetic theory and confirms the existence of an optimal speed for wetting.     

Deformation of advancing gas-liquid interfaces in capillary tubes

Deformation of an advancing gas-liquid meniscus is considered in two cases: prewetted and dry capillary tubes. The shape, slope, and curvature of the gas-liquid interface are determined assuming small Weber and Bond numbers, i.e., in the case of negligible inertia and gravity terms. For the prewetted capillary case, the dynamic contact angle rate-dependency is found to depend on both the capillary number and the ratio of the macroscopic prewetting film thickness to the capillary radius. Results are found intermediate between rate-dependency relations available in the literature. In the case of dry capillaries, the relative magnitudes of the viscous, capillary, and disjoining pressure effects are determined. The actual location of the three-phase contact line is analyzed in relation to the spreading coefficient. Results for the dynamic contact angle rate-dependency are found to agree well with published experimental data. In both cases, prewetted and dry capillaries, results are compared with Tanner's relationship and previous theoretical investigations.