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.     

Direct measurement of the viscous force between two spherical particles trapped in a thin wetting film

Here we present the first direct measurement of the viscous drag force between two spherical particles of millimeter size trapped in a thin wetting film. Each particle is constrained by the liquid/air interface and the solid substrate. The viscous force is counterbalanced by another known force, the attractive capillary immersion force between identical particles protruding from the film surface. The results of the measurements provide evidence for an increased hydrodynamic force due to a non-Stokesian resistance to the particle motion. Our findings can be applied to the self-assembly of colloidal particles in a two-dimensional array for coating and to the friction between small species and a solid. Received: 19 March 1999 Accepted in revised form: 11 May 1999     

Patterned deposition at moving contact lines

When a simple or complex liquid recedes from a smooth solid substrate it often leaves a homogeneous or structured deposit behind. In the case of a receding non-volatile pure liquid the deposit might be a liquid film or an arrangement of droplets depending on the receding speed of the meniscus and the wetting properties of the system. For complex liquids with volatile components as, e.g., polymer solutions and particle or surfactant suspensions, the deposit might be a homogeneous or structured layer of solute — with structures ranging from line patterns that can be orthogonal or parallel to the receding contact line via hexagonal or square arrangements of drops to complicated hierarchical structures. We review a number of recent experiments and modelling approaches with a particular focus on mesoscopic hydrodynamic long-wave models. The conclusion highlights open question and speculates about future developments.     

Effect of growth conditions on the structure of two-dimensional latex crystals: modeling

Essential experimental features of the nucleation and growth of a 2D colloidal crystal on a solid substrate are modeled. The crystal, composed of sub-micron-sized latex spheres, is grown by the evaporation of water from the particle suspension in a circular cell. The calculation of the meniscus profile in the cell allows the prediction of the particle volume fraction in the suspension surrounding the crystal as a function of time. This quantity enters into a convective-diffusion model for the crystal growth which calculates the crystal radius as a function of time. Comparison with experimental data for 2D latex particle crystals shows predominant convective growth over a wide range of evaporation rates set by varying the humidity of the air. Microscopic parameters of the particle assembly can also be estimated such as the particle velocity, diffusivity, characteristic time constants, Peclet number, etc. The nucleation is simulated by simultaneously solving the equations of motion for the ensemble of particles trapped in a thin liquid film using the discrete-element method. These equations account for the forces which are physically important in the system: contact particle–particle friction, increased viscous resistance during the particle motion in a wetting film, long-range capillary attraction between two particles screened by the rest of particles. The final result of the simulation is a particle cluster of hexagonal packing, whose structure resembles very much the monolayer nucleus of latex particles observed experimentally. The models proposed by us could also be implemented for the aggregation of species in a variety of practical processes such as coating, texturing, crystal growth from a melt or liquid solution, or a biological array. Received: 10 May 1999 Accepted in revised form: 6 July 1999     

Detachment force of particles from air-liquid interfaces of films and bubbles

The detachment force required to pull a microparticle from an air-liquid interface is measured using atomic force microscopy (AFM) and the colloidal probe technique. Water, solutions of sodium dodecyl sulfate (SDS), and silicone oils are tested in order to study the effects of surface tension and viscosity. Two different liquid geometries are considered: the air-liquid interface of a bubble and a liquid film on a solid substrate. It was shown that detaching particles from liquid films is fundamentally different than from bubbles or drops due to the restricted flow of the liquid phase. Additional force is required to detach a particle from a film, and the maximum force during detachment is not necessarily at the position where the particle breaks away from the interface (as seen in bubble or drop systems). This is due to the dynamics of meniscus formation and viscous effects, which must be considered if the liquid is constrained in a film. The magnitude of these effects is related to the liquid viscosity, film thickness, and detachment speed.     

Crystallization mechanisms in convective particle assembly

Colloidal particles are continuously assembled into crystalline particle coatings using convective fluid flows. Assembly takes place inside a meniscus on a wetting reservoir. The shape of the meniscus defines the profile of the convective flow and the motion of the particles. We use optical interference microscopy, particle image velocimetry, and particle tracking to analyze the particles' trajectory from the liquid reservoir to the film growth front and inside the deposited film as a function of temperature. Our results indicate a transition from assembly at a static film growth front at high deposition temperatures to assembly in a precursor film with high particle mobility at low deposition temperatures. A simple model that compares the convective drag on the particles to the thermal agitation explains this behavior. Convective assembly mechanisms exhibit a pronounced temperature dependency and require a temperature that provides sufficient evaporation. Capillary mechanisms are nearly temperature independent and govern assembly at lower temperatures. The model fits the experimental data with temperature and particle size as variable parameters and allows prediction of the transition temperatures. While the two mechanisms are markedly different, dried particle films from both assembly regimes exhibit hexagonal particle packings. We show that films assembled by convective mechanisms exhibit greater regularity than those assembled by capillary mechanisms.     

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.     

Adhesion of suspension particles on the wall surface of the container

Summary Particles of the pharmaceutical suspension often adhere on the container wall and cause several serious troubles. This adhesion proceeds by two steps; (1) particle trapping and (2) particle adhering. Particle trapping occurs only when the suspension spreads on the wall surface to make the even, thin liquid film of the medium, which traps the particles by pressure due to the surface tension of the medium acting upon the water line of the particle surface. The thinner film and the greater surface tension of the medium give the stronger trapping effect. The number of trapped particles is directly proportional to the concentration of the suspension and to square root of the particle diameter. The overall observed trappable nature of the particle was expressed by trappability constant.Some of the trapped particles develop to adhesion; the adhesion amount was proportional to the number of the particle in the unit volume of the suspension (concentration of the suspension) and related with particle diameter, wetting interval, wetting frequency, temperature, and flow rate of the suspension. p_H of the medium did not give any effect on the adhesion. The important rôle of a thin liquid film for the adhesion, was also investigated and discussed in connection with three types of the wetting.

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Zusammenfassung Partikel von Arzneimittelsuspensionen bleiben sehr oft an den Behälterwänden hängen und verursachen bei der Handhabung der Suspensionen viele Schwierigkeiten. Die Ursachen für dieses Verhalten werden ausführlich erläutert.

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With 15 figures in 22 details and 3 tables     

Some mechanisms of immiscible fluid displacement in small networks

We report experimental observations on immiscible displacement in two small networks using three different pairs of fluids, air-oil, air-water, and oil-water, to vary the wettability. The experiments were run for a wide range of capillary number, from 10⁻⁷ to 10⁻³. Various mechanisms are observed. These are film spreading and drainage, Haines' jump, free slip and stick-slip meniscus motion, contact angle hysteresis, snap-off, coalescence, and blocking of film and bubble. For the air-oil case, oil is perfectly wetting in the network. In imbibition, the displacement occurs first via thin film spreading, followed by snap-off of menisci, and then by piston-like displacement at low flow rates. As the flow rate increases, piston-like displacement dominates because film spreading is comparatively slow. Snap-off of menisci in the throats is a necessary condition for air trapping. In drainage, meniscus snap-off and coalescence are observed in one network. For both imbibition and drainage, during each snap-off or piston-like displacement event, all menisci move freely along the channels to adjust their curvatures, due to the lubrication of the wetting film. For the other two fluid pairs at low flow rates, this curvature readjustment through free slipping of meniscus is not observed, presumably due to the absence of wetting film during the displacement. At high flow rate, oscillation of menisci due to volumetric competition is observed. Neither wetting film spreading nor throat snap-off is observed. Stick and slip motion of meniscus is observed, probably due to the roughness and/or heterogeneous wettability of the solid surface. For the oil-water system the wettability seems to be time dependent. Coalescence between two menisci can occur in the throat, in the pore, or at the pore-throat boundary during displacement. Trapping of the displaced phase is due to its being bypassed or snapped off in the throat.     

Theory of slope-dependent disjoining pressure with application to Lennard-Jones liquid films

A liquid film of thickness h<100 nm is subject to additional intermolecular forces, which are collectively called disjoining pressure Pi. Since Pi dominates at small film thicknesses, it determines the stability and wettability of thin films. Current theory derived for uniform films gives Pi=Pi(h). This solution has been applied recently to non-uniform films and becomes unbounded near a contact line as h-->0. Consequently, many different effects have been considered to eliminate or circumvent this singularity. We present a mean-field theory of Pi that depends on the slope h(x) as well as the height h of the film. When this theory is implemented for Lennard-Jones liquid films, the new Pi=Pi(h,h(x)) is bounded near a contact line as h-->0. Thus, the singularity in Pi(h) is artificial because it results from extending a theory beyond its range of validity. We also show that the new Pi can capture all three regimes of drop behavior (complete wetting, partial wetting, and pseudo-partial wetting) without altering the signs of the long and short-range interactions. We find that a drop with a precursor film is linearly stable.     

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.     

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.     

Particles at the airway interfaces of the lung

Inhaled particles may land on the surface of the lung’s airspaces. Upon making contact with the airway wall, the processes of retention and clearance begin. Particle retention depends on many factors; among these are: (1) particle size, shape, solubility, surface chemistry and elastic properties of both the particles and the lung surface. (2) The anatomical location of the deposition site. (3) The structures with which the particle interacts at the site of deposition, including the surfactant film at the air–liquid interface, the aqueous phase, free cells like macrophages, lymphocytes and granulocytes, the epithelial cells and dendritic cells that reside at the basal side of the epithelium. Particles, after their deposition are wetted and displaced towards the epithelium by the surfactant film during the retention process. In vitro experiments have demonstrated that the extent of particle immersion depends on the surface tension of the surfactant film. The lower the surface tension, the greater is the immersion of the particles into the aqueous phase. Experimental results demonstrate consistently greater immersion of smaller particles into a liquid substrate covered with a surfactant film than that for larger particles. The exact mechanism, especially the initial wetting process, is not yet understood and requires further experiments. Line tension is a possible explanation for the dependence of particle displacement on particle size.     

Nonlinear stability analysis of a two-layer thin liquid film: dewetting and autophobic behavior

The nonlinear stability analysis of a liquid film composed of two superposed thin layers of immiscible liquids resting on a solid substrate is performed. It is shown that the coupling of van der Waals interactions in the two layers can lead to an autophobic behavior in the form of spinodal decomposition of two planar liquid layers into a system of localized drops divided by almost planar wetting layers. The results of the weakly nonlinear analysis near the instability threshold are confirmed by the numerical solution of a system of two strongly nonlinear evolution equations for the liquid-liquid and liquid-gas interfaces. The kinetics of the drop coarsening at late stages is studied and is found to be close to that reported for a one-layer film. It is also shown that gravity effects can become significant even for very thin two-layer films.     

Reorganization of small Co particles on Al2O3 surfaces monitored by ferromagnetic resonance

Changes of the magnetic properties of ferromagnetic Co particles deposited on the radical31 x radical31R +/- 9 degrees reconstructed alpha-Al2O3(0001) as well as on a thin alumina film grown on a NiAl(110) substrate were investigated as a function of thermal annealing. On the thin film changes of the magnetic response were found above 500 K which correlates with changes in the particle size distribution. Annealing to 870 K leads to a permeation of the metal though the oxide film which causes significant changes in the ferromagnetic resonance response. On the alpha-Al2O3 single crystal sintering of particles requires temperatures above 600 K being about 100 K higher as compared to the thin alumina film. For large clusters intraparticle redistribution takes place already below 600 K a phenomenon not observed for the small clusters. In addition, a significant dependence of the measured g values from the substrate as well as the thermal treatment is found which can be understood in terms of the structural properties of the systems.     

Monte Carlo simulation methods for computing the wetting and drying properties of model systems

We introduce general Monte Carlo simulation methods for determining the wetting and drying properties of model systems. We employ an interface-potential-based approach in which the interfacial properties of a system are related to the surface excess free energy of a thin fluid film in contact with a surface. Two versions of this approach are explored: a "spreading" method focused on the growth of a thin liquid film from a surface in a mother vapor and a "drying" method focused on the growth of a thin vapor film from a surface in a mother liquid. The former provides a direct measure of the spreading coefficient while the latter provides an analogous drying coefficient. When coupled with an independent measure of the liquid-vapor surface tension, these coefficients enable one to compute the contact angle. We also show how one can combine information gathered from application of the spreading and drying methods at a common state point to obtain direct measures of the contact angle and liquid-vapor surface tension. The computational strategies introduced here are applied to two model systems. One includes a monatomic Lennard-Jones fluid that interacts with a structureless substrate via a long-ranged substrate potential. The second model contains a monatomic Lennard-Jones fluid that interacts with an atomistically detailed substrate via a short-ranged potential. Expanded ensemble techniques are coupled with the interface potential approach to compile the temperature- and substrate strength-dependence of various interfacial properties for these systems. Overall, we find that the approach pursued here provides an efficient and precise means to calculate the wetting and drying properties of model systems.     

Liquid templating for nanoparticle organization into complex patterns

Dewetting of thin films of charged polymer solutions produces complex patterns that can be applied to direct nanoparticle organization on solid substrates. The morphology produced by dewetting can be controlled by the solution properties, temperature, and substrate wetting. In this work, new results on this liquid-template self-assembly system are presented, with special emphasis on producing large arrays of organized nanoparticles. On a hydrophilic substrate with complete wetting, the patterns include polygonal networks and parallel-track arrays that extend over several hundreds of microns. These large structures are formed under well-controlled drying conditions and characterized by scanning electron microscopy, which is better suited for the examination of large as well as small areas than atomic force microscopy. On partial wetting substrates, new patterns are observed, including a complex set of parallel curved bands with variable particle number densities.