Wetting films on chemically heterogeneous substrates

Three-Phase Fluid Coexistence in Heterogenous Slits

We study the competition between local (bridging) and global condensation of fluid in a chemically heterogeneous capillary slit made from two parallel adjacent walls each patterned with a single stripe. Using a mesoscopic modified Kelvin equation, which determines the shape of the menisci pinned at the stripe edges in the bridge phase, we determine the conditions under which the local bridging transition precedes capillary condensation as the pressure (or chemical potential) is increased. Provided the contact angle of the stripe is less than that of the outer wall we show that triple points, where evaporated, locally condensed, and globally condensed states all coexist are possible depending on the value of the aspect ratio a=L/H, where H is the stripe width and L the wall separation. In particular, for a capillary made from completely dry walls patterned with completely wet stripes the condition for the triple point occurs when the aspect ratio takes its maximum possible value 8/π. These predictions are tested using a fully microscopic classical density functional theory and shown to be remarkably accurate even for molecularly narrow slits. The qualitative differences with local and global condensation in heterogeneous cylindrical pores are also highlighted.

Symmetry-breaking morphological transitions at chemically nanopatterned walls

We study the structure and morphological changes of fluids that are in contact with solid composites formed by alternating and microscopically wide stripes of two different materials. One type of the stripes interacts with the fluid via long-ranged Lennard-Jones-like potential and tends to be completely wet, while the other type is purely repulsive and thus tends to be completely dry. We consider closed systems with a fixed number of particles that allows for stabilization of fluid configurations breaking the lateral symmetry of the wall potential. These include liquid morphologies corresponding to a sessile drop that is formed by a sequence of bridging transitions that connect neighboring wet regions adsorbed at the attractive stripes. We study the character of the transitions depending on the wall composition, stripes width, and system size. Using a (classical) nonlocal density functional theory (DFT), we show that the transitions between different liquid morphologies are typically weakly first-order but become rounded if the wavelength of the system is lower than a certain critical value L_{c}. We also argue that in the thermodynamic limit, i.e., for macroscopically large systems, the wall becomes wet via an infinite sequence of first-order bridging transitions that are, however, getting rapidly weaker and weaker and eventually become indistinguishable from a continuous process as the size of the bridging drop increases. Finally, we construct the global phase diagram and study the density dependence of the contact angle of the bridging drops using DFT density profiles and a simple macroscopic theory.

Crossover from three- to six-fold symmetry of colloidal aggregates in circular traps

At sufficiently low temperatures and high densities, repulsive spherical particles in two-dimensions (2d) form close-packed structures with six-fold symmetry. By contrast, when the interparticle interaction has an attractive anisotropic component, the structure may exhibit the symmetry of the interaction. We consider a suspension of spherical particles interacting through an isotropic repulsive potential and a three-fold symmetric attractive interaction, confined in circular potential traps in 2d. We find that, due to the competition between the interparticle and the external potentials, the particles self-organize into structures with three- or six-fold symmetry, depending on the width of the traps. For intermediate trap widths, a core-shell structure is formed, where the core has six-fold symmetry and the shell is three-fold symmetric. When the width of the trap changes periodically in time, the symmetry of the colloidal structure also changes, but it does not necessarily follow that of the corresponding static trap.

Percolation of functionalized colloids on patterned substrates

We study the percolation properties for a system of functionalized colloids on patterned substrates via Monte Carlo simulations. The colloidal particles are modeled as hard disks with three equally-distributed attractive patches on their perimeter. We describe the patterns on the substrate as circular potential wells of radius Rp arranged in a regular square or hexagonal lattice. We find a nonmonotonic behavior of the percolation threshold (packing fraction) as a function of Rp. For attractive wells, the percolation threshold is higher than the one for clean (non-patterned) substrates if the circular wells are non-overlapping and can only be lower if the wells overlap. For repulsive wells we find the opposite behavior. In addition, at high packing fractions the formation of both structural and bond defects suppress percolation. As a result, the percolation diagram is reentrant with the non-percolated state occurring at very low and intermediate densities.

Nematic films at chemically structured surfaces

We investigate theoretically the morphology of a thin nematic film adsorbed at flat substrate patterned by stripes with alternating aligning properties, normal and tangential respectively. We construct a simple 'exactly-solvable' effective interfacial model where the liquid crystal distortions are accounted for via an effective interface potential. We find that chemically patterned substrates can strongly deform the nematic-air interface. The amplitude of this substrate-induced undulations increases with decreasing average film thickness and with increasing surface pattern pitch. We find a regime where the interfacial deformation may be described in terms of a material-independent universal scaling function. Surprisingly, the predictions of the effective interfacial model agree semi-quantitatively with the results of the numerical solution of a full model based on the Landau-de Gennes theory coupled to a square-gradient phase field free energy functional for a two phase system.

Nonadditivity of van der Waals forces on liquid surfaces

We present an approach for modeling nanoscale wetting and dewetting of textured solid surfaces that exploits recently developed, sophisticated techniques for computing exact long-range dispersive van der Waals (vdW) or (more generally) Casimir forces in arbitrary geometries. We apply these techniques to solve the variational formulation of the Young-Laplace equation and predict the equilibrium shapes of liquid-vacuum interfaces near solid gratings. We show that commonly employed methods of computing vdW interactions based on additive Hamaker or Derjaguin approximations, which neglect important electromagnetic boundary effects, can result in large discrepancies in the shapes and behaviors of liquid surfaces compared to exact methods.

Droplets pinned at chemically inhomogenous substrates: A simulation study of the two-dimensional Ising case

As a simplified model of a liquid nanostripe adsorbed on a chemically structured substrate surface, a two-dimensional Ising system with two boundaries at which surface fields act is studied. At the upper boundary, the surface field is uniformly negative, while at the lower boundary (a distance L apart), the surface field is negative only outside a range of extension b, where a positive surface stabilizes a droplet of the phase with positive magnetization for temperatures T exceeding the critical temperature T_{w} of the wetting transition of this model. We investigate the local order parameter profiles across the droplet, both in the directions parallel and perpendicular to the substrate, varying both b and T. Also, precursor effects to droplet formation as T approaches T_{w} from below are studied. In accord with theoretical predictions, for T>T_{w} the droplet is found to have the shape of a semiellipse, where the width (distance of the interface from the substrate) scale is proportional to b (b^{1/2}). So, the area of the droplet is proportional to b^{3/2}, and the temperature dependence of the corresponding prefactor, which also involves the interfacial stiffness, is studied.

Stability and break-up of thin liquid films on patterned and structured surfaces

Solid surfaces with chemical patterning or topographical structure have attracted attention due to many potential applications such as manufacture of flexible electronics, microfluidic devices, microscale cooling systems, as well as development of self-cleaning, antifogging, and antimicrobial surfaces. In many configurations involving patterned or structured surfaces, liquid films are in contact with such solid surfaces and the issue of film stability becomes important. Studies of stability in this context have been largely focused on specific applications and often not connected to each other. The purpose of the present review is to provide a unified view of the topic of stability and rupture of liquid films on patterned and structured surfaces, with particular focus on common mathematical methods, such as lubrication approximation for the liquid flow, bifurcation analysis, and Floquet theory, which can be used for a wide variety of problems. The physical mechanisms of the instability discussed include disjoining pressure, thermocapillarity, and classical hydrodynamic instability of gravity-driven flows. Motion of a contact line formed after the film rupture is also discussed, with emphasis on how the receding contact angle is expected to depend on the small-scale properties of the substrate.

Filling and wetting transitions at grooved substrates

The wetting and filling properties of a fluid adsorbed on a solid grooved substrate are studied by means of a microscopic density functional theory. The grooved substrates are modelled using a solid slab, interacting with the fluid particles via long-range dispersion forces, to which a one-dimensional array of infinitely long rectangular grooves is sculpted. By investigating the effect of the groove periodicity and the width of the grooves and the ridges, a rich variety of different wetting morphologies is found. In particular, we show that for a saturated ambient gas, the adsorbent can occur in one of four wetting states characterized by (i) empty grooves, (ii) filled grooves, (iii) a formation of mesoscopic hemispherical caps (iv) a macroscopically wet surface. The character of the transition between particular regimes, that also extend off-coexistence, sensitively depends on the model geometry. The temperature at which the system becomes completely wet is considerably higher than that for a flat wall.

Stability of thin liquid films and sessile droplets under confinement

The stability of nonvolatile thin liquid films and of sessile droplets is strongly affected by finite size effects. We analyze their stability within the framework of density functional theory using the sharp kink approximation, i.e., on the basis of an effective interface Hamiltonian. We show that finite size effects suppress spinodal dewetting of films because it is driven by a long-wavelength instability. Therefore nonvolatile films are stable if the substrate area is too small. Similarly, nonvolatile droplets connected to a wetting film become unstable if the substrate area is too large. This instability of a nonvolatile sessile droplet turns out to be equivalent to the instability of a volatile drop which can attain chemical equilibrium with its vapor.

Delta-comb potential in modeling three-phase contact line (TPCL) on periodically patterned surfaces

This work is a study of wetting of small water droplets on smooth glass surfaces with periodic patterns in the form of imprinted net with hydrophilic cells and hydrophobic bars. Microcover slides consisted of soda lime glass were used. The imprinted images of the net were with cell sizes in the range 40-200 μm, which corresponds to a quite narrow scope of hydrophilic surface fractions f(1)(30-36%) due to the relative increase in the size of the hydrophobic bars. The receding contact angles θ(R) of small water droplets, positioned on the patterned surfaces, were measured. The experiment showed significantly lower receding contact angles as compared to the theoretical expectations by the Cassie formula, which accounts for the contribution to the contact angle of the surface fraction of the imprinted hydrophobic/hydrophilic net. For this reason, we developed new theory accounting for the periodicity of the surface and the contribution of the three-phase contact line on the contact angle. This new theory considered delta-comb potential energy Δ(x,y) of the surface, effective line tension κ, and the lattice parameter a. The restriction of theory was discussed as well. It was pointed out that the theory is not valid for very small and very large lattice parameters.

Dynamics of nanodroplets on topographically structured substrates

Mesoscopic hydrodynamic equations are solved to investigate the dynamics of nanodroplets positioned near a topographic step of the supporting substrate. Our results show that the dynamics depends on the characteristic length scales of the system given by the height of the step and the size of the nanodroplets as well as on the constituting substances of both the nanodroplets and the substrate. The lateral motion of nanodroplets far from the step can be described well in terms of a power law of the distance from the step. In general the direction of motion depends on the details of the effective laterally varying intermolecular forces. But for nanodroplets positioned far from the step it is solely given by the sign of the Hamaker constant of the system. Moreover, our study reveals that the steps always act as a barrier for transporting liquid droplets from one side of the step to the other.

Liquid Spreading under Nanoscale Confinement

Dynamic atomic force microscopy in the noncontact regime is used to study the morphology of a nonvolatile liquid (squalane) as it spreads along wettable nanostripes embedded in a nonwettable surface. Results show that the liquid profile depends on the amount of lateral confinement imposed by the nanostripes, and it is truncated at the microscopic contact line in good qualitative agreement with classical mesoscale hydrodynamics. However, the width of the contact line is found to be significantly larger than expected theoretically. This behavior may originate from small chemical inhomogeneity of the patterned stripes as well as from thermal fluctuations of the contact line.

Morphology and phase behavior of ethanol nanodrops condensed on chemically patterned surfaces

Equilibrium wetting of ethanol onto chemically patterned nanostripes has been investigated using environmental atomic force microscopy (AFM) in noncontact mode. The chemical patterns are composed of COOH-terminated "wetting" regions and CH3-terminated "nonwetting" regions. A specially designed environmental AFM chamber allowed for accurate measurements of droplet height as a function of the temperature offset between the substrate and a macroscopic ethanol reservoir. At saturation, the height dependence scales with droplet width according to w1/2, in excellent agreement with the augmented Young equation (AYE) modeled with dispersive, nonretarded surface potentials. At small under- and oversaturations, the AYE model accurately fits the data if an effective DeltaT is used as a fitting parameter. There is a systematic difference between the measured DeltaT and the values extracted from the fits to the data. In addition to static measurements, we present time-resolved measurements of the droplet height which enable the study of condensation-evaporation dynamics of nanometer-scale drops.

Motion of nanodroplets near chemical heterogeneities

We investigate the dynamics of nanoscale droplets in the vicinity of chemical steps which separate parts of a substrate with different wettabilities. Due to long-ranged dispersion forces, nanodroplets positioned on one side of the step perceive the different character of the other side even at a finite distance from the step, leading to a dynamic response. The direction of the ensuing motion of such droplets depends not only on the difference between the equilibrium contact angles on these two parts but in particular on the difference between the corresponding Hamaker constants. Therefore, the motion is not necessarily directed toward the more wettable side and can also be different from that of droplets which span the step.

Cell dynamics simulation of droplet and bridge formation within striped nanocapillaries

The kinetics of droplet and bridge formation within striped nanocapillaries is studied when the wetting film grows via interface-limited growth. The phenomenological time-dependent Ginzburg-Landau (TDGL)-type model with thermal noise is used and numerically solved using the cell dynamics method. The model is two-dimensional and consists of undersaturated vapor confined within a nanocapillary made of two infinitely wide flat substrates. The surface of the substrate is chemically heterogeneous with a single stripe of lyophilic domain that exerts long-range attractive potential to the vapor molecule. The dynamics of nucleation and subsequent growth of droplet and bridge can be simulated and visualized. In particular, the evolution of the morphology from droplet or bump to bridge is clearly identified. The crucial role played by the substrate potential on the morphology of bridge of nanoscopic size is clarified. Nearly temperature-independent evolution of capillary condensation is predicted when the interface-limited growth dominates. In addition, it is shown that the dynamics of capillary condensation follows the scenario of capillary condensation proposed by Everett and Haynes three decades ago.

Fluid bridges confined between chemically nanopatterned solid substrates

We discuss equilibrium properties of classical fluids confined to nanoscopic volumes by solid substrates. The substrates themselves are endowed with wettable chemical patterns of variable symmetry. We develop a thermodynamic description suitable for these highly anisotropic systems. Based upon a combination of Monte Carlo simulations in the grand canonical ensemble and lattice density functional theory at mean-field level we analyze the structure and phase behaviour of the confined fluid. Under suitable thermodynamic conditions the fluid may condense partially in regions controlled by the wettable nanopatterns. The resulting fluid bridges are established as thermodynamic phases and exhibit unique rheological features.

Complete wetting of pits and grooves

For one-component volatile fluids governed by dispersion forces an effective interface Hamiltonian, derived from a microscopic density functional theory, is used to study complete wetting of geometrically structured substrates. Also the long range of substrate potentials is explicitly taken into account. Four types of geometrical patterns are considered: i) one-dimensional periodic arrays of rectangular or parabolic grooves and ii) two-dimensional lattices of cylindrical or parabolic pits. We present numerical evidence that at the centers of the cavity regions the thicknesses of the adsorbed films obey precisely the same geometrical covariance relation, which has been recently reported for complete cone and wedge filling. However, this covariance does not hold for the laterally averaged wetting film thicknesses. For sufficiently deep cavities with vertical walls and close to liquid-gas phase coexistence in the bulk, the film thicknesses exhibit an effective planar scaling regime, which as a function of undersaturation is characterized by a power law with the common critical exponent -1/3 as for a flat substrate, but with the amplitude depending on the geometrical features.

Motion of nanodroplets near edges and wedges

Nanodroplets residing near wedges or edges of solid substrates exhibit a disjoining pressure induced dynamics. Our nanoscale hydrodynamic calculations reveal that nonvolatile droplets are attracted or repelled from edges or wedges depending on details of the corresponding laterally varying disjoining pressure generated, e.g., by a possible surface coating.

Point tension in adsorption at a chemically inhomogeneous substrate in two dimensions

We study adsorption of liquid at a one-dimensional substrate composed of a single chemical inhomogeneity of width 2L placed on an otherwise homogeneous, planar, solid surface. The excess point free energy eta(L,T) associated with the adsorbed layer's inhomogeneity induced by the substrate's chemical structure is calculated within exact continuum transfer-matrix approach. It is shown that the way eta(L,T) varies with L depends sensitively on the temperature regime. It exhibits logarithmic divergence as a function of L in the limit L-->infinity for temperatures such that the chemical inhomogeneity is completely wetted by the liquid. In the opposite case eta(L,T) converges for large L to 2eta0, where eta0 is the corresponding point tension, and the dominant L-dependent correction to 2eta0 decays exponentially. The interaction between the liquid layer inhomogeneities at -L and L for the two temperature regimes is discussed and compared to earlier mean-field theory predictions.

Forces between chemically structured substrates mediated by critical fluids

We consider binary liquid mixtures close to their critical points confined by two parallel, geometrically flat, and chemically structured substrates. Universal order parameter profiles are calculated within mean field theory for periodic patterns of stripes with alternating preferences for the two species of the mixture and with different relative positions of the two substrates. From the order parameter profiles the effective forces between the two plates are derived. The tuning of Casimir amplitudes is discussed.

Wetting of rings on a nanopatterned surface: a lattice model study

We perform mean-field density functional theory calculations on a lattice model to study the wetting of a solid substrate decorated with a ring pattern of nanoscale dimensions. We have found three different liquid morphologies on the substrate: a ring morphology where the liquid covers the pattern, a bulge morphology where a droplet is forming on one side of the ring, and a morphology where the liquid forms a cap spanning the nonwetting disk inside the pattern. We investigate the relative stability of these morphologies as a function of the ring size, wall-fluid interaction, and temperature. The results found are in very good agreement with experiments and calculations performed on similar systems at a micrometer length scale. The bulge morphology has also been observed in Monte Carlo simulations of the lattice model. Our results show that (i) morphologies of wetting patterns previously observed on a much larger (microm) scale can also form on a nm length scale, (ii) whether or not this happens depends crucially on the size of the wettable pattern, and (iii) the wettable ring may only be partially wet by the bulge morphology of the fluid. This morphology is a result of a spontaneously broken symmetry in the system.

Influence of physical and chemical heterogeneity shape on thin film rupture

It is known that the breakup times for thin liquid films on solid surfaces can be substantially smaller if the surface is heterogeneous, either chemically or physically. In this paper we explore issues related to the effect of the shape of the physical and chemical heterogeneities on the breakup time and the thinning behavior. We consider two shapes, sinusoidal and exponential, for both physical and chemical gradients and compare the breakup times for these two different forms of gradients. Furthermore, the wavelength of the sinusoidal gradients and the length scale of the exponential gradients are varied and the effects of these on the breakup times and the film evolution are determined. For the sinusoidal gradients, we also obtain analytical results for shape evolution that are valid at short times and for small amplitude perturbation of the physical/chemical heterogeneities. The fastest growing modes are determined for spinodal breakup and also for both shapes (sinusoidal and exponential) of physical and chemical heterogeneities. The breakup times for the fastest growing modes from the linear and the nonlinear studies are compared for spinodal breakup and these results are also compared with those for both chemical and physical heterogeneities, of both sinusoidal and exponential shapes. Results show that the presence of heterogeneities, in general, accelerates the breakup of the film. In the linear regime, the growth rates are the same for the chemical and physical heterogeneities and spinodal breakup, and the effect of the heterogeneities is manifested as increased amplitude of initial perturbation. The effect of the chemical and physical heterogeneities dominate the film dynamics at early times, becoming less important at later times. The growth rates and equivalently the breakup times for the films on heterogeneous surfaces depend on the length scale over which physical/chemical gradients occur, and as the length scale approaches zero, which implies that the gradients become very steep, the effect of the heterogeneities on the breakup times becomes small.

Liquid nanostripes

Equilibrium wetting of ethanol, a volatile liquid, onto chemically patterned nanostripes has been investigated using noncontact atomic force microscopy (AFM). The chemical patterns, generated by a conducting AFM tip, are composed of COOH terminated "wetting" regions and CH3 terminated "nonwetting" regions. Controlled amounts of ethanol, from the vapor phase, condense on the COOH stripes and their shape is imaged in situ versus their width (70 < w < 300 nm). The measured profile shapes at saturation and their w(1/2) height dependence are well described by density functional theory with dispersive, nonretarded potentials.

Phase-field modeling of wetting on structured surfaces

We study the dynamics and equilibrium profile shapes of contact lines for wetting in the case of a spatially inhomogeneous solid wall with stripe defects. Using a phase-field model with conserved dynamics, we first numerically determine the contact line behavior in the case of a stripe defect of varying widths. For narrow defects, we find that the maximum distortion of the contact line and the healing length is related to the defect width, while for wide defects, it saturates to constant values. This behavior is in quantitative agreement with the experimental data. In addition, we examine the shape of the contact line between two stripe defects as a function of their separation. Using the phase-field model, we also analytically estimate the contact line configuration and find good qualitative agreement with the numerical results.

Influence of inhomogeneous substrate curvature on line tension

Line tension accompanying equilibrium liquidlike films adsorbed at cylinder-shaped substrates equipped with chemical heterogeneities is studied within an effective interfacial Hamiltonian approach. The heterogeneity has the form of a stripe of width 2L. The leading corrections to the line tension coefficient due to nonzero substrate curvature R(-1) are derived. Their character is shown to be sensitively dependent on the system's temperature regime. For temperatures low enough that both the homogeneous components of the heterogeneous substrate remain nonwetted, the leading curvature correction is found to be proportional to R(-1). For temperatures such that one of the solid surface components is wetted by the fluid, one obtains corrections to the line tension of the order of either (L/R) ln R or R(-1/2) depending on the relative values of R and the heterogeneity width 2L . For temperatures exceeding wetting temperatures of both the substrate components, the line tension is shown to decay to 0 in the limit R --> infinity according to the power law eta approximately R(-1/2).

Critical adsorption at chemically structured substrates

We consider binary liquid mixtures near their critical consolute points and exposed to geometrically flat but chemically structured substrates. The chemical contrast between the various substrate structures amounts to opposite local preferences for the two species of the binary liquid mixtures. Order parameter profiles are calculated for a chemical step, for a single chemical stripe, and for a periodic stripe pattern. The order parameter distributions exhibit frustration across the chemical steps which heals upon approaching the bulk. The corresponding spatial variation of the order parameter and its dependence on temperature are governed by universal scaling functions which we calculate within mean field theory. These scaling functions also determine the universal behavior of the excess adsorption relative to suitably chosen reference systems.

Surface patterning via evaporation of ultrathin films containing nanoparticles

The dewetting dynamics of ultrathin films containing potentially surface-active nanoparticles is considered in the presence of evaporation. Evolution equations for the film height and particle surface and bulk concentration are derived using a lubrication model coupled by a constitutive relation for the dependence of the viscosity on local particle concentration. A linear stability analysis and numerical simulations are used to determine how particle mass distribution depends on the various physical parameters such as equilibrium film separation distance, initial packing concentration, rate of evaporation, and particle surface activity. Our results show that when starting from an initially uniform distribution the particles become aligned into distinct "bands" in rectilinear geometry, or "rings" in cylindrical geometry. The functional dependence of the pattern spacing on relevant system parameters is studied and detailed herein.

Simulating the dynamic behavior of immiscible binary fluids in three-dimensional chemically patterned microchannels

Using computer simulations, we investigate the behavior of an immiscible binary AB fluid that is driven to flow through a microchannel, which is decorated with a checkerboard pattern of chemically distinct A- and B-like patches on the top and bottom walls. We isolate conditions where the coupling between the imposed flow field and thermodynamic interactions yields a rich interfacial behavior between the A and B fluids and complex velocity patterns over the checkerboard domains. In effect, the A and B fluids undergo extensive mixing in specific regions of the channel, even for low Reynolds number flow. Decreasing the height-to-width ratio of the patterned microchannel enhances the extent of mixing between these two components. On the other hand, the length of the A/B interfaces is optimized in microchannels that have a square cross section. The results provide guidelines for designing microfluidic devices that can be used to effectively intermix multicomponent fluids.

Coarsening dynamics of dewetting films

Lubrication theory for unstable thin liquid films on solid substrates is used to model the coarsening dynamics in the long-time behavior of dewetting films. The dominant physical effects that drive the fluid dynamics in dewetting films are surface tension and intermolecular interactions with the solid substrate. Instabilities in these films lead to rupture and other morphological changes that promote nonuniformity in the films. Following the initial instabilities, the films break up into near-equilibrium droplets connected by an ultrathin film. For longer times, the fluid will undergo a coarsening process in which droplets both move and exchange mass on slow time scales. The dynamics of this coarsening process will be obtained through the asymptotic reduction of the long-wave PDE governing the thin film to a set of ODEs for the evolution of the droplets. From this, a scaling law that governs the coarsening rate is derived.

Complete wetting on a linear wedge

We have measured the growth of liquid films of Ar adsorbed on well defined arrays of microscopic linear wedges sculpted on thin Si wafers and on a stainless steel disk. On these patterns, a clear cross-over from a planarlike to a geometry dependent growth behavior is observed. This crossover is found to depend on the characteristic wedge size. Near liquid-vapor bulk coexistence, the film mass is observed to diverge as a power law of the chemical potential difference from saturation with an exponent in very good agreement with the value of -2 expected for a linear wedge. This exponent is not affected by the opening angles of the wedges. All these findings are in accordance with a recent scaling theory.

Adsorption in a nonsymmetric wedge

We study adsorption in a nonsymmetric wedge consisting of two chemically different, homogeneous planes. First, we macroscopically analyze configurations of nonvolatile liquid drop placed in such a two-dimensional wedge and construct phase diagrams describing transitions between various interfacial shapes. Then adsorption is discussed within MFT based on the effective interfacial Hamiltonian. Two regimes for the system parameters--the wedge opening angle (2phi) and the critical wetting temperatures of each of the planar walls (T(W1) and T(W2), T(W2)<T(W1))--are identified. In one of them we find the critical filling transition at T(F)<T(W2) and the corresponding critical indices which are equal to those found for a symmetric wedge. In the other regime (T(W2)<T(F)<T(W1)) interfacial configurations are similar to those exhibited in the case of a planar substrate consisting of two chemically different parts. In the borderline case (T(F)=T(W2)), the interface profile above the wall with the lower wetting temperature becomes parallel to it. The line tensions corresponding to T(F)<T(W2) and T(F)=T(W2) cases are evaluated and the critical exponents - different in each case - are identified. An effective one-dimensional Hamiltonian describing fluctuations along the wedge is constructed for the T(F)<T(W2) case.

Decoration lattices of colloids adsorbed on stripe-patterned substrates

The equilibrium structure of decoration lattices composed of colloidal particles adsorbed on periodic stripe-patterned substrates is calculated as a function of the stripe width and separation and for different interparticle interactions. Due to a competition of length scales, a wealth of different stable decoration lattices occurs such as triangular, quadratic, rhombic, kitelike, and sheared honeycomb lattices, triangular slices as well as triangle superlattices. This is of relevance for constructing templates that enforce crystal growth of unusual solid structures.

Using patterned substrates to promote mixing in microchannels

Using a lattice Boltzmann model for fluid dynamics, we investigate the flow and phase behavior of a binary fluid moving over a patterned substrate within a microchannel. The binary fluid consists of two immiscible components, A and B, and this liquid is subjected to a Poiseuille flow. The substrate is decorated with a checkerboard pattern of A- and B-like patches. Through a coupling of hydrodynamics and thermodynamics, each component is driven to flow from the nonwettable domains to wettable regions. As a consequence, the A and B fluids undergo extensive mixing within the microchannels. We investigate how the degree of mixing depends on the size of the patches, the velocity of the imposed flow field, and the characteristics of the fluid. The results provide guidelines for creating localized "mixing stations" within microfluidic devices. The findings also reveal how a combination of imposed flow fields and surface patterning can be exploited to control the phase behavior of complex fluids.

Correlation of stress and structure in a simple fluid confined to a pore with furrowed walls

A Lennard-Jones (12,6) film confined between two furrowed walls was simulated by the grand canonical ensemble Monte Carlo method. The walls are constructed by gouging triangular grooves in planar substrates that are structureless on the molecular scale. The furrows are infinitely long in one transverse direction (y) and of nanoscopic width (s(x)) and depth (D). The furrows in the two walls are maintained parallel and in register. The diagonal components of the stress tensor (T(alphaalpha), alpha=x,y,z) are computed as functions of D and the separation between the substrates (s(z)) at fixed temperature, chemical potential, and s(x). The T(alphaalpha) for the film between the furrowed walls are strongly shifted from their counterparts for the film between flat (i.e., planar) walls. The shifts are rationalized in terms of the structure of the film, which becomes more ordered as the furrows deepen and the packing of film molecules becomes more restricted in the two dimensions normal to the y direction. The results demonstrate the profound impact of the coupling between molecular and nanoscopic scales on the properties of geometrically constrained fluids.