Slippage of Newtonian liquids: influence on the dynamics of dewetting thin 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.

Signatures of slip in dewetting polymer films

Thin polymer films on hydrophobic substrates are susceptible to rupture and hole formation. This, in turn, initiates a complex dewetting process, which ultimately leads to characteristic droplet patterns. Experimental and theoretical studies suggest that the type of droplet pattern depends on the specific interfacial condition between the polymer and the substrate. Predicting the morphological evolution over long timescales and on the different length scales involved is a major computational challenge. In this study, a highly adaptive numerical scheme is presented, which allows for following the dewetting process deep into the nonlinear regime of the model equations and captures the complex dynamics, including the shedding of droplets. In addition, our numerical results predict the previously unknown shedding of satellite droplets during the destabilization of liquid ridges that form during the late stages of the dewetting process. While the formation of satellite droplets is well known in the context of elongating fluid filaments and jets, we show here that, for dewetting liquid ridges, this property can be dramatically altered by the interfacial condition between polymer and substrate, namely slip. This work shows how dissipative processes can be used to systematically tune the formation of patterns.

Tuning relaxation dynamics and mechanical properties of polymer films of identical thickness

Using dewetting as a characterization tool, we demonstrate that physical properties of thin polymer films can be regulated and tuned by employing variable processing conditions. For different molecular weights, the variable behavior of polystyrene films of identical thickness, prepared along systematically altered pathways, became predictable through a single parameter P, defined as the ratio of time required over time available for the equilibration of polymers. In particular, preparation-induced residual stresses, the corresponding relaxation times as well as the rupture probability of such films (of identical thickness) varied by orders of magnitude following scaling relations with P. Our experimental findings suggest that we can predictably enhance properties and hence maximize the performance of thin polymer films via appropriately chosen processing conditions.

Prospects for Clinical Applications of Polymer-Coated Haemoconcentrator on Extracorporeal Circuit in Cardiopulmonary Bypass Surgeries

Purpose

Extracorporeal circulation circuits used in cardiopulmonary bypass surgeries are increasingly being coated with polymer materials to reduce the thrombogenicity of extracorporeal devices. However, a haemoconcentrator, which corrects haematocrit and electrolyte imbalances, is not coated with polymers. In this study, we sought to assess the filtration performance of polymer-coated haemoconcentrators in order to obtain insight into their prospects for use in clinical applications.

Methods

In vitro experiments were performed to evaluate the water pressure and flow properties of polymer-coated haemoconcentrators by comparing 3 polymer-coated haemoconcentrators with 3 non-coated haemoconcentrators. The cross-sectional surfaces of both types of haemoconcentrators were observed using a scanning electron microscope (SEM).

Results

The slopes of the regression lines for estimating the filtrated fluid flow as a function of the transmembrane pressure were 6.286 ± 0.320 for polymer-coated haemoconcentrators and 3.712 ± 0.170 for non-coated haemoconcentrators. These slopes were found to be significantly different and indicate that the filtration velocity is enhanced in polymer-coated haemoconcentrators over that in non-coated haemoconcentrators. However, the hollow fibre damage observed by SEM was not shown to contribute to higher filtration flow in the polymer-coated haemoconcentrator. Taking these results into consideration, we hypothesise that a polymer coating makes a foreign surface on a hollow fibre slippery, owing to the hydrophobicity of the polymer, thereby enhancing the velocity of the filtration.

Conclusions

The results of this preliminary investigation suggest that a polymer coating can enhance the filtration performance of a haemoconcentrator and that polymer-coated haemoconcentrators might be useful in clinical applications.

Hydraulic transport across hydrophilic and hydrophobic nanopores: Flow experiments with water and n-hexane

We experimentally explore pressure-driven flow of water and n-hexane across nanoporous silica (Vycor glass monoliths with 7- or 10-nm pore diameters, respectively) as a function of temperature and surface functionalization (native and silanized glass surfaces). Hydraulic flow rates are measured by applying hydrostatic pressures via inert gases (argon and helium, pressurized up to 70 bar) on the upstream side in a capacitor-based membrane permeability setup. For the native, hydrophilic silica walls, the measured hydraulic permeabilities can be quantitatively accounted for by bulk fluidity provided we assume a sticking boundary layer, i.e., a negative velocity slip length of molecular dimensions. The thickness of this boundary layer is discussed with regard to previous capillarity-driven flow experiments (spontaneous imbibition) and with regard to velocity slippage at the pore walls resulting from dissolved gas. Water flow across the silanized, hydrophobic nanopores is blocked up to a hydrostatic pressure of at least 70 bar. The absence of a sticking boundary layer quantitatively accounts for an enhanced n-hexane permeability in the hydrophobic compared to the hydrophilic nanopores.

Instability, self-organization and pattern formation in thin soft films

The free surface of a thin soft polymer film is often found to become unstable and self-organizes into various meso-scale structures. In this article we classify the instability of a thin polymer film into three broad categories, which are: category 1: instability of an ultra-thin (<100 nm) viscous film engendered by amplification of thermally excited surface capillary waves due to interfacial dispersive van der Waals forces; category 2: instability arising from the attractive inter-surface interactions between the free surface of a soft film exhibiting room temperature elasticity and another rigid surface in its contact proximity; and category 3: instability caused by an externally applied field such as an electric field or a thermal gradient, observed in both viscous and elastic films. We review the salient features of each instability class and highlight how characteristic length scales, feature morphologies, evolution pathways, etc. depend on initial properties such as film thickness, visco-elasticity (rheology), residual stress, and film preparation conditions. We emphasize various possible strategies for aligning and ordering of the otherwise isotropic structures by combining the essential concepts of bottom-up and top-down approaches. A perspective, including a possible future direction of research, novelty and limitations of the methods, particularly in comparison to the existing patterning techniques, is also presented for each setting.

Micropatterned Surfaces for Atmospheric Water Condensation via Controlled Radical Polymerization and Thin Film Dewetting

Inspired by an example found in nature, the design of patterned surfaces with chemical and topographical contrast for the collection of water from the atmosphere has been of intense interest in recent years. Herein we report the synthesis of such materials via a combination of macromolecular design and polymer thin film dewetting to yield surfaces consisting of raised hydrophilic bumps on a hydrophobic background. RAFT polymerization was used to synthesize poly(2-hydroxypropyl methacrylate) (PHPMA) of targeted molecular weight and low dispersity; spin-coating of PHPMA onto polystyrene films produced stable polymer bilayers under appropriate conditions. Thermal annealing of these bilayers above the glass transition temperature of the PHPMA layer led to complete dewetting of the top layer and the formation of isolated PHPMA domains atop the PS film. Due to the vastly different rates of water nucleation on the two phases, preferential dropwise nucleation of water occurred on the PHPMA domains, as demonstrated by optical microscopy. The simplicity of the preparation method and ability to target polymers of specific molecular weight demonstrate the value of these materials with respect to large-scale water collection devices or other materials science applications where patterning is required.

Capillary droplet propulsion on a fibre

A viscous liquid film coating a fibre becomes unstable and decays into droplets due to the Rayleigh-Plateau instability (RPI). Here, we report on the generation of uniform droplets on a hydrophobized fibre by taking advantage of this effect. In the late stages of liquid column breakup, a three-phase contact line can be formed at one side of the droplet by spontaneous rupture of the thinning film. The resulting capillary imbalance leads to droplet propulsion along the fibre. We study the dynamics and the dewetting speed of the droplet as a function of molecular weight as well as temperature and compare to a force balance model based on purely viscous dissipation.

Onset of Area-Dependent Dissipation in Droplet Spreading

We probe the viscous relaxation of structured liquid droplets in the partial wetting regime using a diblock copolymer system. The relaxation time of the droplets is measured after a step change in temperature as a function of three tunable parameters: droplet size, equilibrium contact angle, and the viscosity of the fluid. Contrary to what is typically observed, the late-stage relaxation time does not scale with the radius of the droplet-rather, relaxation scales with the radius squared. Thus, the energy dissipation depends on the contact area of the droplet, rather than the contact line.

Influence of slip on the Plateau-Rayleigh instability on a fibre

The Plateau-Rayleigh instability of a liquid column underlies a variety of fascinating phenomena that can be observed in everyday life. In contrast to the case of a free liquid cylinder, describing the evolution of a liquid layer on a solid fibre requires consideration of the solid-liquid interface. Here we revisit the Plateau-Rayleigh instability of a liquid coating a fibre by varying the hydrodynamic boundary condition at the fibre-liquid interface, from no slip to slip. Although the wavelength is not sensitive to the solid-liquid interface, we find that the growth rate of the undulations strongly depends on the hydrodynamic boundary condition. The experiments are in excellent agreement with a new thin-film theory incorporating slip, thus providing an original, quantitative and robust tool to measure slip lengths.

Fast membrane hemifusion via dewetting between lipid bilayers

The behavior of lipid bilayers is important to understand the functionality of cells like the trafficking of ions. Standard procedures to explore the properties of lipid bilayers and hemifused states typically use supported membranes or vesicles. Both techniques have several shortcomings in terms of bio-relevance or accessibility for measurements. In this article, the formation of individual free standing hemifused states between model cell membranes is studied using an optimized microfluidic scheme which allows for simultaneous optical and electrophysiological measurements. In the first step, two model membranes are formed at a desired location within a microfluidic device using a variation of the droplet interface bilayer (DiB) technique. In the second step, the two model membranes are brought into contact forming a single hemifused state. For all tested lipids, the hemifused state between free standing membranes forms within hundreds of milliseconds, i.e. several orders of magnitude faster than those reported in literature. The formation of a hemifused state is observed as a two stage process, whereas the second stage can be explained as a dewetting process under no-slip boundary conditions. The formed hemifusion states have a long lifetime and a single fusion event can be observed when triggered by an applied electric field as demonstrated for monoolein.

Nanofluidics of thin polymer films: linking the slip boundary condition at solid-liquid interfaces to macroscopic pattern formation and microscopic interfacial properties

If a thin liquid film is not stable, different rupture mechanisms can be observed causing characteristic film morphologies: spinodal dewetting and dewetting by nucleation of holes. This rupturing entails liquid flow and opens new possibilities to study microscopic phenomena. Here we use this process of dewetting to gain insight on the slip boundary condition at the solid-liquid interface. Having established hydrodynamic models that allow for the determination of the slip length in a dewetting experiment based on nucleation, we move on to the quantification and molecular description of slip effects in various systems. For the late stage of the dewetting process involving the Rayleigh-Plateau instability, several distinct droplet patterns can be observed. We describe the importance of slip in determining what pattern may be found. In order to control the slip length, we use polymeric liquids on different hydrophobic coatings of silicon wafers. We find that subtle changes in the coating can lead to large changes in the slip length. Thus, we gain insight into the question of how the structure of the substrate affects the slip length.

Influence of slip on the Rayleigh-Plateau rim instability in dewetting viscous films

A dewetting viscous film develops a characteristic fluid rim at its receding edge due to mass conservation. In the course of the dewetting process, the rim becomes unstable via an instability of Rayleigh-Plateau type. An important difference exists between this classic instability of a liquid column and the rim instability in a thin film as the growth of the rim is continuously fueled by the receding film. We explain how the development and macroscopic morphology of the rim instability are controlled by the slip of the film on the substrate. A single thin-film model captures quantitatively the characteristics of the complete evolution of the rim observed in the experiments.

Molecular transport and flow past hard and soft surfaces: computer simulation of model systems

The equilibrium and flow of polymer films and drops past a surface are characterized by the interface and surface tensions, viscosity, slip length and hydrodynamic boundary position. These parameters of the continuum description are extracted from molecular simulations of coarse-grained models. Hard, corrugated substrates are modelled by a Lennard-Jones solid while polymer brushes are studied as prototypes of soft, deformable surfaces. Four observations are discussed. (i) If the surface becomes strongly attractive or is coated with a brush, the Navier boundary condition fails to describe the effect of the surface independently of the strength and type of the flow. This failure stems from the formation of a boundary layer with an effective, higher viscosity. (ii) In the case of brush-coated surfaces, flow induces a cyclic, tumbling motion of the tethered chain molecules. Their collective motion gives rise to an inversion of the flow in the vicinity of the grafting surfaces and leads to strong, non-Gaussian fluctuations of the molecular orientations. The flow past a polymer brush cannot be described by Brinkman's equation. (iii) The hydrodynamic boundary condition is an important parameter for predicting the motion of polymer droplets on a surface under the influence of an external force. Their steady-state velocity is dictated by a balance between the power that is provided by the external force and the dissipation. If there is slippage at the liquid-solid interface, the friction at the solid-liquid interface and the viscous dissipation of the flow inside the drop will be the dominant dissipation mechanisms; dissipation at the three-phase contact line appears to be less important on a hard surface. (iv) On a soft, deformable substrate like a polymer brush, we observe a lifting-up of the three-phase contact line. Controlling the grafting density and the incompatibility between the brush and the polymer liquid we can independently tune the softness of the surface and the contact angle and thereby identify the parameters for maximizing the deformation at the three-phase contact.

Wetting morphologies and their transitions in grooved substrates

When exposed to a partially wetting liquid, many natural and artificial surfaces equipped with complex topographies display a rich variety of liquid interfacial morphologies. In the present article, we focus on a few simple paradigmatic surface topographies and elaborate on the statics and dynamics of the resulting wetting morphologies. It is demonstrated that the spectrum of wetting morphologies increases with increasing complexity of the groove structure. On elastically deformable substrates, additional structures in the liquid morphologies can be observed, which are caused by deformations of the groove geometry in the presence of capillary forces. The emergence of certain liquid morphologies in grooves can be actively controlled by changes in wettability and geometry. For electrically conducting solid substrates, the apparent contact angle can be varied by electrowetting. This allows, depending on groove geometry, a reversible or irreversible transport of liquid along surface grooves. In the case of irreversible liquid transport in triangular grooves, the dynamics of the emerging instability is sensitive to the apparent hydrodynamic slip at the substrate. On elastic substrates, the geometry can be varied in a straightforward manner by stretching or relaxing the sample. The imbibition velocity in deformable grooves is significantly reduced compared to solid grooves, which is a result of the microscopic deformation of the elastic groove material close to the three phase contact line.

Imbibition in mesoporous silica: rheological concepts and experiments on water and a liquid crystal

We present, along with some fundamental concepts regarding imbibition of liquids in porous hosts, an experimental, gravimetric study on the capillarity-driven invasion dynamics of water and of the rod-like liquid crystal octyloxycyanobiphenyl (8OCB) in networks of pores a few nanometers across in monolithic silica glass (Vycor). We observe, in agreement with theoretical predictions, square root of time invasion dynamics and a sticky velocity boundary condition for both liquids investigated. Temperature-dependent spontaneous imbibition experiments on 8OCB reveal the existence of a paranematic phase due to the molecular alignment induced by the pore walls even at temperatures well beyond the clearing point. The ever present velocity gradient in the pores is likely to further enhance this ordering phenomenon and prevent any layering in molecular stacks, eventually resulting in a suppression of the smectic phase in favor of the nematic phase.

Impact of slippage on the morphology and stability of a dewetting rim

In this study lubrication theory is used to describe the stability and morphology of the rim that forms as a thin polymer film dewets from a hydrophobized silicon wafer. Thin film equations are derived from the governing hydrodynamic equations for the polymer to enable the systematic mathematical and numerical analysis of the properties of the solutions for different regimes of slippage and for a range of timescales. Dewetting rates and the cross sectional profiles of the evolving rims are derived for these models and compared to experimental results. Experiments also show that the rim is typically unstable in the spanwise direction and develops thicker and thinner parts that may grow into 'fingers'. Linear stability analysis as well as nonlinear numerical solutions are presented to investigate shape and growth rate of the rim instability. It is demonstrated that the difference in morphology and the rate at which the instability develops can be directly attributed to the magnitude of slippage. Finally, a derivation is given for the dominant wavelength of the bulges along the unstable rim.

Slip effects in polymer thin films

Probing the fluid dynamics of thin films is an excellent tool for studying the solid/liquid boundary condition. There is no need for external stimulation or pumping of the liquid, due to the fact that the dewetting process, an internal mechanism, acts as a driving force for liquid flow. Viscous dissipation, within the liquid, and slippage balance interfacial forces. Thus, friction at the solid/liquid interface plays a key role towards the flow dynamics of the liquid. Probing the temporal and spatial evolution of growing holes or retracting straight fronts gives, in combination with theoretical models, information on the liquid flow field and, especially, the boundary condition at the interface. We review the basic models and experimental results obtained during the last several years with exclusive regard to polymers as ideal model liquids for fluid flow. Moreover, concepts that aim to explain slippage on the molecular scale are summarized and discussed.

Reduced interfacial entanglement density affects the boundary conditions of polymer flow

Hydrodynamic boundary conditions play a crucial role in the flow dynamics of thin films and can be probed by the analysis of liquid front profiles. For long-chained polymer films it was reported that a deviation from a symmetric profile is a result of viscoelastic effects. In this Letter, however, evidence is given that merely a slip-boundary condition at the solid-liquid interface can lead to an asymmetric profile. Variation of molecular weight shows that slippage is directly linked to chain entanglements. We find a reduced entanglement density at the solid-liquid interface (factors 3 to 4), which stresses the importance of considering nonbulk polymer properties in the vicinity of an interface.

Spinodal dewetting of thin films with large interfacial slip: implications from the dispersion relation

We compare the dispersion relations for spinodally dewetting thin liquid films for increasing magnitude of interfacial slip length in the lubrication limit. While the shape of the dispersion relation, in particular the position of the maximum, are equal for no-slip up to moderate-slip lengths, the position of the maximum shifts to much larger wavelengths for large slip lengths. Here, we discuss the implications of this fact for recently developed methods to assess the disjoining pressure in spinodally unstable thin films by measuring the shape of the roughness power spectrum. For polystyrene (PS) films on octadecyltrichlorosilane (OTS) covered Si wafers (with slip length b approximately 1 microm), we predict a 20% shift of the position of the maximum of the power spectrum which should be detectable in experiments.