Nonlinear instabilities and pathways of rupture in thin liquid bilayers

A long-wave nonlinear analysis of dewetting of thin (<100 nm) liquid bilayers on solid substrates is presented. The short and the long time dynamics, interfacial morphologies, and the pathways of rupture and dewetting are studied to assess the roles of interfacial energies, film thicknesses, and viscosities. The twin interfaces (liquid-liquid and liquid-air) of bilayers under the influence of attractive van der Waals forces show a variety of dewetting pathways which, depending on the interfacial energies and film thicknesses, initially start with one of the two basic modes of instability--in-phase bending and out-of-phase squeezing. These short time modes of evolution and the extent of relative deformations at the interfaces are predicted from the linear stability analysis and verified by the nonlinear simulations. Simulations also show that in the later nonlinear regime, the intermolecular and viscous forces can profoundly modify the initial mode of instability and its growth rate leading to different pathways of dewetting and late stage morphologies. The complex late time patterns such as embedded droplets, inversion of top and bottom phases, and encapsulation of one fluid into the other are also engendered by tuning the intermolecular forces.     

Stability of thin stagnant film on a solid surface with a viscoelastic air-liquid interface

Linear stability analysis for a film on a solid surface with a viscoelastic air-liquid interface is presented. The interfacial dilatational and shear viscoelastic properties were described by Maxwell models. Dilatational and shear interfacial elasticity and viscosity were shown to improve film stability. When the interfacial rheological properties are extremely large or small, the maximum perturbation growth coefficient is shown to reduce to those for immobile and mobile interfaces respectively. Calculated values of maximum growth coefficient for thin film stabilized by 0.5% beta-lactoglobulin approached those of mobile films for thick (>2000 nm) and those for immobile films for thin (<100 nm) films respectively with the values lying between the two limits for intermediate film thicknesses.     

Dynamic interfacial effect of electroosmotic slip flow with a moving capillary front in hydrophobic circular microchannels

Miniaturization of chemical analysis using microfabrication is an emerging technology. The use of polymeric materials as opposed to conventional glass substrate is also a promising alternative. As most polymeric materials are hydrophobic relative to glass, we describe here the implication for the loading process of electroosmotic flow (EOF) when a three-phase (solid-liquid-vapor) contact line exists. The presence of these interfaces can result in a large Laplace pressure that resists EOF and hence hinders its flow performance. This effect depends on the phenomenological contact angle at the solid-liquid interface. In our model for EOF, we considered simultaneously the presence of an electric double layer, liquid slips via a weaker solid-liquid interaction and Laplace pressure across a liquid-vapor interface.     

Instabilities and pattern miniaturization in confined and free elastic-viscous bilayers

We present an analysis of the instabilities engendered by van der Waals forces in bilayer systems composed of a soft elastic film (<10 microm) and a thin (<100 nm) viscous liquid film. We consider two configurations of such systems: (a) Confined bilayers, where the bilayer is sandwiched between two rigid substrates, and (b) free bilayers, where the viscous film is sandwiched between a rigid substrate and the elastic film. Linear stability analysis shows that the time and length scales of the instabilities can be tuned over a very wide range by changing the film thickness and the material properties such as shear modulus, surface tension, and viscosity. In particular, very short wavelengths comparable to the film thickness can be obtained in bilayers, which is in contrast to the instability wavelengths in single viscous and elastic films. It is also shown that the instabilities at the interfaces of the free bilayers are initiated via an in-phase "bending" mode rather than out-of-phase "squeezing" mode. The amplitudes of deformations at both the elastic-air and elastic-viscous interfaces become more similar as the elastic film thickness decreases and its modulus increases. These findings may have potential applications in the self-organized patterning of soft materials.     

Dewetting of thin liquid films near soft elastomeric layers

Thin liquid film instabilities driven by van der Waals forces and in the proximity of soft elastomeric layers are considered in this work through two model problems: (i) a liquid film resting on an elastomeric layer and (ii) a liquid film bounded from one side by a rigid substrate and from the other side by an elastomeric layer. The elastomeric layers are modeled as linear viscoelastic solids, van der Waals forces are assumed to act only in the liquid, and lubrication theory and linear stability analysis are applied. For a liquid film resting on an elastomeric layer, substrate deformability has a destabilizing effect, as evidenced by an increase in the maximum growth rate and range of unstable wavenumbers. The destabilization worsens for thicker solid layers and is due to a lowering of the effective liquid-air interfacial tension. For an elastomeric layer resting on a liquid film, layer deformability has a stabilizing effect for thin layers but a destabilizing effect for thicker layers, with the former due to an enhancement and the latter due to a reduction of the effective solid-air interfacial tension. The results presented here suggest the possibility of exploiting the dewetting of thin liquid films to create topographically patterned surfaces on soft polymeric solids.     

Nanoscale actuation of electrokinetic flows on thermoreversible surfaces

We report on a novel approach for controlling nanohydrodynamic properties at the solid-liquid interfaces through the use of stimuli-responding polymer coatings. The end-tethered polymers undergo a phase separation upon external activation. The reversible change in the thickness and polarity of the grafted polymers yields in a dynamic control of the surface-generated, electrokinetic phenomena. Nonactivated, swollen polymers are thicker than the electrical double layer (EDL) and prohibit the development of an EOF even on charged surfaces. On the other hand, activated polymer chains shrink and become thinner than the EDL and allow for the EOF to build up unimpeded. We show here that, for given experimental conditions, the EOF velocity on the shrunken surface is 35 times greater than the one on the nonactivated surface. Furthermore, we reveal that coupling of such surfaces with dense arrays of thermal actuators developed in our laboratory can lead to novel micro- and nanofluidic devices.     

Linear stability of a surfactant-laden annular film in a time-periodic pressure-driven flow through a capillary

This paper analyzes the effect of surfactant on the linear stability of an annular film in a capillary undergoing a time-periodic pressure gradient force. The annular film is thin compared to the radius of the tube. An asymptotic analysis yields a coupled set of equations with time-periodic coefficients for the perturbed fluid-fluid interface and the interfacial surfactant concentration. Wei and Rumschitzki (submitted for publication) previously showed that the interaction between a surfactant and a steady base flow could induce a more severe instability than a stationary base state. The present work demonstrates that time-periodic base flows can modify the features of the steady-flow-based instability, depending on surface tension, surfactant activity, and oscillatory frequency. For an oscillatory base flow (with zero mean), the growth rate decreases monotonically as the frequency increases. In the low-frequency limit, the growth rate approaches a maximum corresponding to the growth rate of a steady base flow having the same amplitude. In the high-frequency limit, the growth rate reaches a minimum corresponding to the growth rate in the limit of a stationary base state. The underlying mechanisms are explained in detail, and extension to other time-periodic forms is further exploited.     

Instability of confined thin liquid film trilayers

The instability of a system in which three stratified thin liquid films are confined in a channel with parallel walls and the interior film is subject to van der Waals-driven breakup is examined in this work. We derive a model based on lubrication theory and consisting of a pair of nonlinear partial differential equations describing the position of the two liquid interfaces. A linear stability analysis is carried out to show that the effects of varying the boundary film thicknesses can be understood in terms of several known limits, including a supported monolayer, confined bilayer, and supported bilayer. Variation of the boundary film viscosities is shown in many cases to eliminate the supported-bilayer limit. The parameter regimes in which squeezing and bending modes dominate the initial growth are determined, and nonlinear simulations are used to show that the mode always switches to squeezing near rupture. It is also found that a multi-modal dispersion relation may be created by asymmetries in thickness ratio, but not viscosity ratio, even in the absence of asymmetric interfacial tensions. The results of this study are expected to be relevant to multiphase microfluidic systems and the lithographic printing process.     

Nematic-isotropic interfaces under shear: a molecular-dynamics simulation

We present a large-scale molecular-dynamics study of nematic-paranematic interfaces under shear. We use a model of soft repulsive ellipsoidal particles with well-known equilibrium properties, and consider interfaces which are oriented normal to the direction of the shear gradient (common stress case). The director at the interface is oriented parallel to the interface (planar). A fixed average shear rate is imposed with moving periodic boundary conditions, and the heat is dissipated with a profile-unbiased thermostat. First, we study the properties of the interface at one particular shear rate in detail. The local interfacial profiles and the capillary wave fluctuations of the interfaces are calculated and compared with those of the corresponding equilibrium interface. Under shear, the interfacial width broadens and the capillary wave amplitudes at large wavelengths increase. The strain is distributed inhomogeneously in the system (shear banding), the local shear rate in the nematic region being distinctly higher than in the paranematic region. Surprisingly, we also observe (symmetry-breaking) flow in the vorticity direction, with opposite direction in the nematic and the paranematic state. Finally, we investigate the stability of the interface for other shear rates and construct a nonequilibrium phase diagram.     

Elastic instabilities in the electroosmotic flow of non-Newtonian fluids through T-shaped microchannels

Electroosmotic flow (EOF) has been widely used to transport fluids and samples in micro- and nanofluidic channels for lab-on-a-chip applications. This essentially surface-driven plug-like flow is, however, sensitive to both the fluid and wall properties, of which any inhomogeneity may draw disturbances to the flow and even instabilities. Existing studies on EOF instabilities have been focused primarily upon Newtonian fluids though many of the chemical and biological solutions are actually non-Newtonian. We carry out a systematic experimental investigation of the fluid rheological effects on the elastic instability in the EOF of phosphate buffer-based polymer solutions through T-shaped microchannels. We find that electro-elastic instabilities can be induced in shear thinning polyacrylamide (PAA) and xanthan gum (XG) solutions if the applied direct current voltage is above a threshold value. However, no instabilities are observed in Newtonian or weakly shear thinning viscoelastic fluids including polyethylene oxide (PEO), polyvinylpyrrolidone (PVP), and hyaluronic acid (HA) solutions. We also perform a quantitative analysis of the wave parameters for the observed elasto-elastic instabilities.     

Instability, dynamics, and morphology of thin slipping films

Based on the linear stability and nonlinear simulations, we show that the surface instability, dynamics, and morphology of supported thin liquid films are profoundly altered by the presence of slippage on the substrate. A general dispersion equation for flow in slipping thin films is derived and simplified to identify three different regimes of slippage (weak, moderate, and strong) and obtain the length and time scales of instability in them. For illustration, the ubiquitous van der Waals interactions have been employed. Different regimes of slip-flow can be predicted based on a nondimensional parameter, xi, which is a function of slip length, film thickness, intermolecular potential, and interfacial tension. Two distinct transitions from weak to moderate slip and from moderate to strong slip occur at xiT1 approximately 0.01 and xiT2 approximately 500, respectively. More specifically, a decrease in film thickness causes transitions from weak to moderate to strong slip regime. Even a weak slippage causes faster breakup of a thin film, whereas slippage beyond a transition value (slip length, bT1) increases the length scale of instability and reduces the number density of holes compared to the nonslipping case. Strong slippage produces holes faster, and the holes are fewer in number and have less developed rims. The exponents for the length scale (lambdam infinity h0n; h0 is film thickness) and time scale of instability (tr infinity h0m) change nonmonotonically with slippage (for nonretarded van der Waals instability, n E (1.25, 2), m E (3, 6)). Retardation in van der Waals potential increases the exponents (n E (1.5, 2.5), m E (5, 8)). The initial stage of evolution of a slipping film, simulated based on nonlinear equations, follows the length scale and time scale of instability, close to the prediction of linear analysis. It is hoped that the present analysis will help in better interpretation of thin film experiments, in estimation of slippage, and in the determination of intermolecular forces from the length and time scales of the instability.     

Capillary zone electrophoresis with electroosmotic flow controlled by external radial electric field.

A new way of regulation of electroosmotic flow (EOF) in capillary zone electrophoresis (CZE) by external electric field has been developed. A set of three high-voltage power supplies is used to form a radial electric field across the capillary wall. One power supply is applied in the usual way as a driving force of CZE and EOF to the ends of the inner capillary compartment dipped into the electrode vessels and filled with background electrolyte. Two power supplies are connected to the ends of the outer low-conductivity coating of the capillary which is formed by the dispersion of copolymer of aniline and p-phenylenediamine in polystyrene matrix. The difference between electric potentials on the outer capillary surface and inside the capillary determines the voltage of radial electric field across the capillary wall and affects the electrokinetic potential at the solid-liquid interface inside the capillary. The effect of magnitude and polarity of external radial electric field on the flow rate of EOF, on the migration times of charged analytes and on the separation efficiency and resolution of CZE separations of synthetic oligopeptides, diglycine, triglycine and octapeptide fragments of human insulin was evaluated. Through the EOF control by external electric field the dynamic effective length of the capillary was obtained and the speed of analysis and resolution of CZE separations of peptide analytes could be optimized.     

Dewetting behavior of aqueous cationic surfactant solutions on liquid films

Previous experimental work has shown that the spreading of a drop of aqueous anionic surfactant solution on a liquid film supported by a negatively charged solid substrate may give rise to a fingering instability (Afsar-Siddiqui, A. B.; Luckham P, F.; Matar, O. K. Langmuir 2003, 19, 703-708). However, upon deposition of a cationic surfactant on a similarly charged support, the surfactant will adsorb onto the solid-liquid interface rendering it hydrophobic. Water is then expelled from the hydrophobic regions, causing film rupture and dewetting. In this paper, experimental results are presented showing how the surfactant concentration and film thickness affect the dewetting behavior of aqueous dodecyltrimethylammonium bromide solutions. At low surfactant concentrations and large film thicknesses, the film ruptures at a point from which dewetting proceeds. At higher concentrations and smaller film thicknesses, the ruptured region is annular in shape and fluid moves away from this region. At still higher concentrations and smaller film thicknesses, the deposited surfactant forms a cap at the point of deposition that neither spreads nor retracts. This variation in dewetting mode is explained by considering the relative Marangoni and bulk diffusion time scales as well as the mode of assembly of the surfactant adsorbed on the solid surface.     

Molecular dynamics study on ultrathin liquid water film sheared between platinum solid walls: liquid structure and energy and momentum transfer

Molecular dynamics simulation has been performed on a liquid film that is sheared in between solid surfaces. As a shear is given to the liquid film, a Couette-like flow is generated in the liquid and energy conversion occurs from the macroscopic flow to the thermal energy, which is discharged back to the solid walls. In such a way, momentum and thermal energy fluxes are present simultaneously. And all these thermal and fluid phenomena take place in highly nonequilibrium state where thermal energy is not distributed equally to each degree of freedom of molecular motion in the vicinities of the solid-liquid interface. In the present paper, platinum and water are employed as solid and liquid, respectively. First, the structure and orientation of water molecules in the vicinities of the solid surfaces are analyzed and how these structure and orientation are influenced by the shear is considered. Based on this result, momentum and thermal energy transfer in the vicinities of and at the solid-liquid interfaces are investigated in detail. Results are compared with those of our previous study, in which monatomic and diatomic molecules are employed as liquid.     

Effect of interfacial mobility on rupture of thin stagnant films on a solid surface due to random mechanical perturbations

Previous analysis of Narsimhan [G. Narsimhan, J. Colloid Interface Sci. 287 (2005) 624-633] for the evaluation of rupture of a nondraining thin film on a solid support due to imposed random mechanical perturbations modeled as a Gaussian white noise has been extended for partially mobile gas-liquid interfaces. The average rupture time of film is evaluated by first passage time analysis (as the mean time for the amplitude of perturbation to become equal to film thickness). The interfacial mobility is accounted for through surface viscosity as well as Marangoni effect. The mean rupture time for partially mobile gas-liquid interface, as characterized by two dimensionless groups, dimensionless surface viscosity and Marangoni number, lies between the two extreme limits for fully mobile and immobile films. The critical wavenumber for minimum rupture time is shown to be insensitive to interfacial mobility. However, the critical dimensionless surface viscosity and critical Marangoni number at which the behavior of thin film deviates from that of fully mobile film and the behavior approaches that of fully immobile film are smaller for higher Hamaker constants, smaller film thickness and smaller surface potentials.     

Determination of interfacial tension from crystallization and dissolution data: a comparison with other methods

Methods for the determination of interfacial tension between a solid and a liquid are reviewed including solubility/particle size, crystallization and dissolution kinetics. The use of solubility as a function of particle size, originally put forward by Ostwald and later corrected by Freundlich, may be unjustified for determining interfacial tension at solid-liquid interfaces. The interfacial tension values between solutions and sparingly soluble minerals such as hydroxyapatite, fluorapatite, brushite, octacalcium phosphate, calcium oxalate monohydrate, barium sulfate, calcium sulfate, calcite, and divalent metal fluorides are discussed. A comparison of these results is made with contact angle or wetting measurements. The interfacial tension values obtained from constant composition reaction kinetics are of the same order of magnitude as those determined using a contact angle method involving thin layer wicking techniques.     

Three-phase contact parameters measurements for silica-mixed cationic–anionic surfactant systems

The stability and interactions in thin wetting films between the silica surface and air bubble containing (a) straight chain C₁₀ amine and (b) cationic/anionic surfactant mixture of a straight chain C₁₀ amine with sodium C₈, C₁₀ and (straight chain) C₁₂ sulfonates, were studied using the microscopic thin wetting film method developed by Platikanov [D. Platikanov, J. Phys. Chem. 68 (1964) 3619]. Film lifetimes, three-phase contact (TPC) expansion rate, receding contact angles and surface tension were measured. The presence of the mixed cationic/anionic surfactants was found to lessen contact angles and suppresses the thin aqueous film rupture, thus inducing longer film lifetime, as compared to the pure amine system. In the case of mixed surfactants heterocoagulation could arise through the formation of positively charged interfacial complexes. Mixed solution of cationic and anionic surfactants shows synergistic lowering in surface tension. The formation of the interfacial complex at the air/solution interface was confirmed by surface tension data. It was also shown, that the chain length compatibility between the anionic and cationic surfactants system controls the strength of the interfacial complex. The observed phenomena were discussed in terms of the electrostatic heterocoagulation theory, where the interactions can be attractive or repulsive depending on the different surface activity and charge of the respective surfactants at the two interfaces.     

Nonaqueous capillary electrophoresis using a titania-coated capillary

In this work, an ordered mesoporous titania film was introduced to coat a capillary by means of the sol-gel technique. Its electroosmotic flow (EOF) property was investigated in a variety of nonaqueous media (methanol, formamide and N,N'-dimethylformamide and mixtures of methanol and acetonitrile). The titania-coated capillary exhibited a distinctive EOF behavior, the direction and magnitude of which were strongly dependent on various parameters such as the solvent composition, apparent pH (pH*) and the electrolytes. The nonaqueous capillary electrophoresis separation of several alkaloids was investigated in the positively charged titania-coated capillary. Comparison of separation between coated and uncoated capillaries under optimal nonaqueous conditions was also carried out.     

Chiral anion exchangers applied to capillary electrochromatography enantioseparation of oppositely charged chiral analytes: investigation of stationary and mobile phase parameters

Weak anion-exchange (WAX) type chiral stationary phases (CSPs) based on tert.-butyl carbamoyl quinine as chiral selector (SO) and different types of silica particles (porous and non-porous) as chromatographic support are evaluated in packed capillary electrochromatography (CEC). Their ability to resolve the enantiomers of negatively charged chiral analytes, e.g., N-derivatized amino acids, in the anion-exchange mode and their electrochromatographic characteristics are described in dependence of several mobile phase parameters (pH, buffer type and concentration, organic modifier type and concentration) and other experimental variables (electric field strength, capillary temperature). The inherent "zwitterionic" surface character of such silica-based WAX type CSPs (positively charged SO and negatively charged residual silanols) allows the reversal of the electroosmotic flow (EOF) towards the anode at pH values below the isoelectric point (pI) of the modified surface, whereas a cathodic EOF results at pH values above the pI. Since for negatively charged analytes also an electrophoretic transport increment has to be considered, which can be either in or against the EOF direction, several distinct modes of elution have been observed under different stationary phase and mobile phase conditions: (i) co-electrophoretic elution of the negatively charged solutes with the anodic EOF in the negative polarity mode, (ii) counter-electrophoretic elution with the cathodic EOF in the positive polarity mode, and (iii) electrophoretically dominated elution in the negative polarity mode with a cathodic EOF directed to the injection end of the capillary. Useful enantioseparations of chiral acids have been obtained with all three modes. Enantioselectivity values as high as under pressure-driven conditions and theoretical plate numbers up to 120000 per meter could be achieved under electrically driven conditions. A repeatability study yielded RSD values below 2% for retention times and RSD values in the range of 5-10% for theoretical plate numbers and resolution, thus clearly establishing the reliability of the investigated anion-exchange type CEC enantioseparation methods.     

非离子表面活性剂Triton X-100溶液在不同生长期小麦叶片表面的润湿行为

选择不同生长期小麦叶片,利用座滴法研究了非离子表面活性剂Triton X-100在小麦叶片表面接触角,考察浓度对接触角、粘附张力、固-液界面张力及润湿状态的影响。研究表明,在低浓度下,表面活性剂分子在气-液界面吸附量(ΓLV)和固-液界面吸附量(Γ'SL)相似,但吸附量较少形成了不饱和吸附层,接触角保持不变,其润湿状态为Cassie-Baxter状态;当浓度进一步增加,液滴突破叶片表面三维立体结构中存在的钉扎效应,取代空气层而处于Wenzel状态,接触角陡降,同时Γ'SL/ΓLV远大于1;当浓度超过临界胶束浓度(CMC)时,表面活性剂分子在气-液界面和固-液界面形成饱和吸附层,并产生毛细管效应,使溶液在小麦叶片三维立体结构中产生半渗透过程,此时接触角保持不变。