Instability and dynamics of thin viscoelastic liquid films

Instability and rupture of ultrathin freestanding viscoelastic solid films

We analyze the instability of viscoelastic solid freestanding thin films under the influence of van der Waals forces using linear stability analysis and nonlinear simulations. Linear stability analysis shows that the zero-frequency elastic modulus governs the onset of instability and stabilizes the film beyond a critical value analogous to thin supported viscoelastic solid films. However, for freestanding solid films, the critical shear modulus is found to be independent of surface tension, unlike that of thin supported viscoelastic solid films. It is further shown that freestanding viscoelastic solid films with higher moduli can be destabilized for a given film thickness and Hamaker constant compared to supported solid films. In contrast to thin viscoelastic liquid films where the growth rate is enhanced due to elastic effects but length scale is unaltered, freestanding films with solidlike viscoelasticity show a retarded growth rate and enhanced length scale. The presence of solidlike viscoelasticity has a stabilizing effect and affects all the key aspects of instability such as critical wave number, dominant wave number, and maximum growth rate. We numerically solve the set of coupled nonlinear evolution equations for film thickness and tangential displacement in order to elucidate the dynamics of film rupture. Our simulations show that, consistent with the linear stability predictions, an increase in the elastic modulus delays film rupture. The dynamics exhibits self-similarity in the vicinity of film rupture and the film thins as (t_{r}-t)^{3/4}, where t_{r} is the rupture time and t_{r}-t is the time remaining until film rupture. The scaling exponent 3/4 obtained for a thin freestanding viscoelastic solid film is significantly greater than the scaling exponent (1/3) for a thin freestanding viscous film.

Non-linear dynamics and self-similarity in the rupture of ultra-thin viscoelastic liquid coatings

The influence of viscoelasticity on the dewetting of ultrathin polymer films is unraveled by means of theory and numerical simulations in the inertialess limit. Three viscoelastic models are employed to analyse the dynamics of the film, namely the Oldroyd-B, Giesekus, and FENE-P models. We revisit the linear stability analysis first derived by [Tomar et al., Eur. Phys. J. E., 2006, 20, 185-200] for a Jeffrey's film to conclude that all three models formally share the same dispersion relation. For times close to the rupture singularity, the self-similar regime recently discovered [Moreno-Boza et al., Phys. Rev. Fluids, 2020, 5, 014002], where the dimensionless minimum film thickness scales with the dimensionless time until rupture as hmin = 0.665τ1/3, is asymptotically established independently of the rheological model. The spatial structure of the flow is characterised by a Newtonian core and a thin viscoelastic boundary layer at the free surface, where polymeric stresses become singular as τ → 0. The Deborah number and the solvent-to-total viscosity ratio affect the rupture time but not the length scale of the resulting dewetting pattern and asymptotic flow structure close to rupture, which is thus shown to be universal. Our three-dimensional simulations lead us to conclude that bulk viscoelasticity alone does not explain the experimental observations of dewetting of polymeric films near the glass transition.

Thin viscoelastic dewetting films of Jeffreys type subjected to gravity and substrate interactions

This work presents a study of the interfacial dynamics of thin viscoelastic films subjected to the gravitational force and substrate interactions induced by the disjoining pressure, in two spatial dimensions. The governing equation is derived as a long-wave approximation of the Navier-Stokes equations for incompressible viscoelastic liquids under the effect of gravity, with the Jeffreys model for viscoelastic stresses. For the particular cases of horizontal or inverted planes, the linear stability analysis is performed to investigate the influence of the physical parameters involved on the growth rate and length scales of instabilities. Numerical simulations of the nonlinear regime of the dewetting process are presented for the particular case of an inverted plane. Both gravity and the disjoining pressure are found to affect not only the length scale of instabilities, but also the final configuration of dewetting, by favoring the formation of satellite droplets, that are suppressed by the slippage with the solid substrate.

Cavity shape transformation during peeling on elastic microchannel-patterned substrates filled with a viscous liquid

Inspired by the detachment mechanics of natural adhesive pads, we studied the change in cavity shape during peel tests on a 10% cross-linked polydimethylsiloxane (PDMS) elastic microchannel filled with 1% cross-linked viscous PDMS liquid (patterned bilayer). During peeling, we explored cavity shape as a function of microchannel dimensions and correlated the dimensionless cavity shape factor (CSF) and characteristic stress decay length, K^-1. The peel test on the liquid-filled elastic microchannel shows three distinct cavity-shape regimes, elliptical, circular, and binary, based on the values of CSF and K^-1. Such cavity formation and shape regimes could be important for improving the design of pressure-sensitive adhesives.

Centrifugal instability of pulsed Taylor-Couette flow in a Maxwell fluid

Centrifugal instability of a pulsed flow in a viscoelastic fluid confined in a Taylor-Couette system is investigated. Both cylinders are subject to an out-of-phase modulation of rotation with equal modulation amplitude and modulation frequency. The fluid is assumed to obey a linear Maxwell fluid with a relaxation time and a constant viscosity. Attention is focused on the linear stability analysis and on the effect of Deborah and frequency numbers on the critical values of the Taylor and wave numbers. Using Floquet theory, we show that in the limit of low frequency, the Deborah number has no effect on the stability of the basic state which tends to the classical configuration of steady circular Couette flow. When the frequency number increases, the stability of the basic flow is enhanced and the Deborah number has a destabilizing effect which is strongly pronounced in the high-frequency limit. In this frequency limit, the critical parameters tend to constant values independently of the frequency number. These numerical results are in good agreement with the asymptotic solutions obtained in the limit of low and high frequencies. Moreover, a correlation between the rheological proprieties of the fluid in a rheometric experience, especially the loss and storage modulus, and this hydrodynamical instability behavior is presented.

Hierarchical Micro/Nano Structures by Combined Self-Organized Dewetting and Photopatterning of Photoresist Thin Films

Photoresists are the materials of choice for micro/nanopatterning and device fabrication but are rarely used as a self-assembly material. We report for the first time a novel interplay of self-assembly and photolithography for fabrication of hierarchical and ordered micro/nano structures. We create self-organized structures by the intensified dewetting of unstable thin (∼10 nm to 1 μm) photoresist films by annealing them in an optimal solvent and nonsolvent liquid mixture that allows spontaneous dewetting to form micro/nano smooth dome-like structures. The density, size (∼100 nm to millimeters), and curvature/contact angle of the dome/droplet structures are controlled by the film thickness, composition of the dewetting liquid, and time of annealing. Ordered dewetted structures are obtained simply by creating spatial variation of viscosity by ultraviolet exposure or by photopatterning before dewetting. Further, the structures thus fabricated are readily photopatterned again on the finer length scales after dewetting. We illustrate the approach by fabricating several three-dimensional structures of varying complexity with secondary and tertiary features.

Gravity-driven instability of a thin liquid film underneath a soft solid

The gravity-driven instability of a thin liquid film located underneath a soft solid material is considered. The equations and boundary conditions governing the solid deformation are systematically converted from a Lagrangian representation to an Eulerian representation, which is the natural framework for describing the liquid motion. This systematic conversion reveals that the continuity-of-velocity boundary condition at the liquid-solid interface is more complicated than has previously been assumed, even in the small-strain limit. We then make clear the conditions under which the commonly used simplified version of this boundary condition is valid. The small-strain approximation, lubrication theory, and linear stability analysis are applied to derive an expression for the growth rate of small-amplitude perturbations. Asymptotic analysis reveals that the coupling between the liquid and solid manifests itself as a lower effective liquid-air interfacial tension that leads to larger instability growth rates. Although this suggests that it is more difficult to maintain a stable liquid coating underneath a soft solid, the effect is expected to be weak for cases of practical interest.

Wetting-dewetting films: the role of structural forces

The liquid wetting and dewetting of solids are ubiquitous phenomena that occur in everyday life. Understanding the nature of these phenomena is beneficial for research and technological applications. However, despite their importance, the phenomena are still not well understood because of the nature of the substrate's surface energy non-ideality and dynamics. This paper illustrates the mechanisms and applications of liquid wetting and dewetting on hydrophilic and hydrophobic substrates. We discuss the classical understanding and application of wetting and film stability criteria based on the Frumkin-Derjaguin disjoining pressure model. The roles of the film critical thickness and capillary pressure on the film instability based on the disjoining pressure isotherm are elucidated, as are the criteria for stable and unstable wet films. We consider the film area in the model for the film stability and the applicable experiments. This paper also addresses the two classic film instability mechanisms for suspended liquid films based on the conditions of the free energy criteria originally proposed by de Vries (nucleation hole formation) and Vrij-Scheludko (capillary waves vs. van der Waals forces) that were later adapted to explain dewetting. We include a discussion of the mechanisms of nanofilm wetting and dewetting on a solid substrate based on nanoparticles' tendency to form a 2D layer and 2D inlayer in the film under the wetting film's surface confinement. We also present our view on the future of wetting-dewetting modeling and its applications in developing emerging technologies. We believe the review and analysis presented here will benefit the current and future understanding of the wetting-dewetting phenomena, as well as aid in the development of novel products and technologies.

Electro-hydrodynamic instability of stressed viscoelastic polymer films

We study the stability of a viscoelastic thin polymer film under two destabilization factors: the application of an electric field normal to the surface--as in typical electro-hydrodynamic destabilization experiments--and the presence of a frozen-in internal residual stress, stemming from the preparation process of the film, typically spin-coating. At the film-substrate interface we consider a general boundary condition, containing perfect gliding on slippery substrates, as well as perfect sticking of the film to the substrate as limiting cases. We show that the interplay of the two sources of stress, the viscoelasticity and the boundary condition, leads to a rich behavior, especially as far as the fastest growing wave number (or wavelength) is concerned. The latter determines the initial growth of the instability, and often also the final pattern obtained in small capacitor gaps, and is the main experimental observable.

Self-organized pathways to nanopatterns exploiting the instabilities of ultrathin confined bilayers

Self-organized interfacial instabilities of an ultrathin bilayer confined between a pair of rigid surfaces is explored. The bilayers are classified based on the macroscopic dewetting behaviors of the liquid films sandwiched between a pair of confining surfaces having surface energy higher or lower than the liquid films. Linear and nonlinear analyses employing the governing equations originating from the continuum description together with molecular dynamics (MD) simulations unveil the salient spatiotemporal features of the dewetting process. The study uncovers that, under the destabilizing influence of the intermolecular interactions, the interface of a confined bilayer can deform into interesting embedded and encapsulated patterns with nanoscale periodicity. The continuum and MD simulations collectively show the detailed route to dewetting starting from the formation of holes in the early stage, their growth to achieve equilibrium contact angle at the intermediate phase, and then to evolve into the equilibrium morphologies at the later stage. Examples are shown where the length and the time scales of the simulated nanostructures from both the continuum and MD approaches are found to agree with the same obtained from the linear stability analysis. We also highlight the deviations that are observed in the continuum and MD approaches. The study confirms that the reduced stabilizing interfacial tension at the liquid-liquid interface together with enhanced intermolecular interaction because of the thinness of the layers can be an alternative strategy for pattern miniaturization exploiting the instabilities of a thin confined bilayer. Further, the study shows that use of topographical patterns on the bounding surfaces can impose periodic order to the holes, droplets, columns, and channels, which can find important applications in the diverse areas of nanotechnology.

Stability and dewetting of metal nanoparticle filled thin polymer films: control of instability length scale and dynamics

We investigate the influence of gold nanoparticle addition on the stability, dewetting, and pattern formation in ultrathin polymer-nanoparticle (NP) composite films by examining the length and time scales of instability, morphology, and dynamics of dewetting. For these 10-50 nm thick (h) polystyrene (PS) thin films containing uncapped gold nanoparticles (diameter approximately 3-4 nm), transitions from complete dewetting to arrested dewetting to absolute stability were observed depending on the concentration of the particles. Experiments show the existence of three distinct stability regimes: regime 1, complete dewetting leading to droplet formation for nanoparticle concentration of 2% (w/w) or below; regime 2, partial dewetting leading to formation of arrested holes for NP concentrations in the range of 3-6%; and regime 3, complete inhibition of dewetting for NP concentrations of 7% and above. Major results are (a) length scale of instability, where lambdaH approximately hn remains unchanged with NP concentration in regime 1 (n approximately 2) but increases in regime 2 with a change in the scaling relation (n approximately 3-3.5); (b) dynamics of instability and dewetting becomes progressively sluggish with an increase in the NP concentration; (c) there are distinct regimes of dewetting velocity at low NP concentrations; (d) force modulation AFM, as well as micro-Raman analysis, shows phase separation and aggregation of the gold nanoparticles within each dewetted polymer droplet leading to the formation of a metal core-polymer shell morphology. The polymer shell could be removed by washing in a selective solvent, thus exposing an array of bare gold nanoparticle aggregates.

A unified theory of instabilities in viscoelastic thin films: from wetting to confined films, from viscous to elastic films, and from short to long waves

A general unified theory of field (van der Waals, electric, etc.)-induced surface instabilities in thin viscoelastic films that accounts for a destabilizing field and stabilizing effects of elastic strain and surface energy is presented. The present theory seamlessly covers the instability and its different regimes in films ranging from elastic to viscous, from adhesive (confined) to wetting (free surface), and from short- to long-wave instabilities. The critical conditions for the onset of instability are found to be strongly dependent on elastic properties such as the shear modulus of the film, but the dominant wavelength is strikingly independent of the film rheology. Different regimes based on a nondimensional parameter (gamma/mu h) are uncovered, where gamma is the surface energy, mu is the elastic shear modulus, and h is the film thickness. A short-wave, elasticlike response with wavelength lambda approximately = 2.96 h is obtained for gamma/mu h < 0.1, whereas long waves that depend nonlinearly on the field strength and surface energy are obtained for gamma/mu h > 1. Owing to their small critical thickness, wetting films destabilized by intermolecular forces always display long-wave instability regardless of their viscoelasticity. Furthermore, our numerical simulations based on energy minimization for unstable wetting elastic films show the formation of islands for ultrathin films and a morphological phase transition to holes embedded in the film for relatively thicker films. Unlike viscous films, however, unstable elastic films do not display a unique dominant wavelength but a bimodal distribution of wavelengths.

The effect of viscoelasticity on the stability of a pulmonary airway liquid layer

The lungs consist of a network of bifurcating airways that are lined with a thin liquid film. This film is a bilayer consisting of a mucus layer on top of a periciliary fluid layer. Mucus is a non-Newtonian fluid possessing viscoelastic characteristics. Surface tension induces flows within the layer, which may cause the lung's airways to close due to liquid plug formation if the liquid film is sufficiently thick. The stability of the liquid layer is also influenced by the viscoelastic nature of the liquid, which is modeled using the Oldroyd-B constitutive equation or as a Jeffreys fluid. To examine the role of mucus alone, a single layer of a viscoelastic fluid is considered. A system of nonlinear evolution equations is derived using lubrication theory for the film thickness and the film flow rate. A uniform film is initially perturbed and a normal mode analysis is carried out that shows that the growth rate g for a viscoelastic layer is larger than for a Newtonian fluid with the same viscosity. Closure occurs if the minimum core radius, R(min)(t), reaches zero within one breath. Solutions of the nonlinear evolution equations reveal that R(min) normally decreases to zero faster with increasing relaxation time parameter, the Weissenberg number We. For small values of the dimensionless film thickness parameter epsilon, the closure time, t(c), increases slightly with We, while for moderate values of epsilon, ranging from 14% to 18% of the tube radius, t(c) decreases rapidly with We provided the solvent viscosity is sufficiently small. Viscoelasticity was found to have little effect for epsilon>0.18, indicating the strong influence of surface tension. The film thickness parameter epsilon and the Weissenberg number We also have a significant effect on the maximum shear stress on tube wall, max(tau(w)), and thus, potentially, an impact on cell damage. Max(tau(w)) increases with epsilon for fixed We, and it decreases with increasing We for small We provided the solvent viscosity parameter is sufficiently small. For large epsilon approximately 0.2, there is no significant difference between the Newtonian flow case and the large We cases.

Electric-field-induced patterns in soft viscoelastic films: from long waves of viscous liquids to short waves of elastic solids

We show that the electric field driven surface instability of viscoelastic films has two distinct regimes: (1) The viscoelastic films behaving like a liquid display long wavelengths governed by applied voltage and surface tension, independent of its elastic storage and viscous loss moduli, and (2) the films behaving like a solid require a threshold voltage for the instability whose wavelength always scales as approximately 4xfilm thickness, independent of its surface tension, applied voltage, loss and storage moduli. Wavelength in a narrow transition zone between these regimes depends on the storage modulus.

Dewetting dynamics of stressed viscoelastic thin polymer films

Ultrathin polymer films that are produced, e.g., by spin coating are believed to be stressed since polymers are "frozen in" into out-of-equilibrium configurations during this process. In the framework of a viscoelastic thin-film model, we study the effects of lateral residual stresses on the dewetting dynamics of the film. The temporal evolution of the height profiles and the velocity profiles inside the film as well as the dissipation mechanisms are investigated in detail. Both the shape of the profiles and the importance of frictional dissipation vs viscous dissipation inside the film are found to change in the course of dewetting. The interplay of the nonstationary profiles, the relaxing initial stress, and the changes in the dominance of the two dissipation mechanisms caused by nonlinear friction with the substrate is responsible for the rich behavior of the system. In particular, our analysis sheds a different light on the occurrence of the unexpected maximum in the rim width obtained recently in experiments on polystyrene-polydimethylsiloxane systems.

Anisotropic dewetting on stretched elastomeric substrates

We study the instability of a very thin liquid film resting on a uniformly stretched soft elastomeric substrate driven by van der Waals forces. A linear stability analysis shows that the critical fluctuation wavelength in the tensile direction is larger than those in the other directions. The magnitudes of the critical wavelengths are adjustable in the sense that they depend on the principal stretch of the substrate. For example, when the principal stretch of the substrate varies from 1.0 (unstretched) to 3.0, the range of the critical wavelength in the tensile direction increases by 7.0% while that normal to the tensile direction decreases by 8.7%. Therefore, the phenomenon may find potential applications in creating tunable topographically patterned surfaces with nano- to microscale features.