Linear stability analysis of a sharp-interface model for dewetting thin films

The stability of the receding front at the growing rim of a thin liquid film dewetting from a substrate is studied. The underlying forces that drive the dewetting motion are given by the intermolecular potential between the liquid film and the substrate. The role of slippage in the emerging instability is studied via a sharp-interface model for the dewetting thin film, which is derived from the lubrication model via matched asymptotic expansions. Using the separation of the time-scale for the slow growth of the rim and the time-scale on which the rim destabilises, the sharp-interface results are compared to earlier results for the lubrication model and good agreement for the unstable modes is obtained. The main advantage of the sharp-interface model is that it allows for the derivation of traveling solutions for the base state and subsequently a systematic linear stability analysis via normal modes. Interestingly, unlike the dispersion relations that are typically encountered for the well-known finger-instability in thin-film flows, where the dependence of the growth rate on the wave number is quadratic, here it is linear.     

Wetting of3He-4He mixtures on alkali metal substrates

From available information concerning the wetting behavior of pure³He and pure⁴He on alkali metal substrates, as well as the known properties of bulk³He-⁴He mixtures, the complete wetting phase diagrams for such mixtures, showing prewetting, isotopic separation and lambda transitions for the film phases have been derived. We predict new phenomena such as a triple-point induced dewetting transition, and the absence of a superfluid film wetting Cs, Rb and K walls under concentrated³He solutions.     

Achieving Large‐Area Planar Perovskite Solar Cells by Introducing an Interfacial Compatibilizer

Despite the recent unprecedented increase in the power conversion efficiencies (PCEs) of small‐area devices (≤0.1 cm²), the PCEs deteriorate drastically for PSCs of larger areas because of the incomplete film coverage caused by the dewetting of the hydrophilic perovskite precursor solutions on the hydrophobic organic charge‐transport layers (CTLs). Here, an innovative method of fabricating scalable PSCs on all types of organic CTLs is reported. By introducing an amphiphilic conjugated polyelectrolyte as an interfacial compatibilizer, fabricating uniform perovskite films on large‐area substrates (18.4 cm²) and PSCs with the total active area of 6 cm² (1 cm² × 6 unit cells) via a single‐turn solution process is successfully demonstrated. All of the unit cells exhibit highly uniform PCEs of 16.1 ± 0.9% (best PCE of 17%), which is the highest value for printable PSCs with a total active area larger than 1 cm².     

Two-dimensional nanoparticle arrays formed by dewetting of thin gold films deposited on pre-patterned substrates

We demonstrate the formation of accurate 2D gold nanoparticle arrays via solid-state dewetting on a pre-patterned substrate. The annealing-induced dewetting of Au film on both flat and pre-patterned SiO₂ substrates is investigated. The pre-patterned structures affect clearly the formation of nanoparticles, and there is a depth effect of the pre-patterned grooves on the formation of nanoparticles during dewetting. Especially in pre-patterned areas with deep grid grooves (depth 150 nm) there is almost one single particle formed in the flat areas of every unit square, thus resulting in a very periodic 2D structure of gold nanoparticles.     

Rimming flows within a rotating horizontal cylinder: asymptotic analysis of the thin-film lubrication equations and stability of their solutions

It is well-known that a standard lubrication analysis of the equations of motion in thin liquid films coating the inside surface of a rotating horizontal cylinder leads, under creeping-flow conditions, to a cubic equation for the film thickness profile which, depending on the fluid properties of the liquid, the speed of rotation and the fill fraction F, has either (a) a continuous, symmetric (homogeneous) solution; (b) a solution containing a shock; or (c) no solution below a certain speed. By means of an asymptotic analysis of the recently proposed “modified lubrication equation” (MLE) [M. Tirumkudulu and A. Acrivos, Phys. Fluid 13 (2000) 14–19], it is shown that the solutions of the cubic equation referred to above correctly describe the film-thickness profiles although, when shocks are involved, under exceedingly restrictive conditions, typically F~ 10⁻³ or less. In addition, using the MLE, the linear stability of these film profiles is investigated and it is shown that: the “homogeneous” profiles are neutrally stable if surface-tension effects are neglected but, if the latter are retained, the films are asymptotically stable to two-dimensional disturbances and unstable to axial disturbances; on the other hand, the non-homogeneous profiles are always asymptotically stable, thus confirming results given earlier [T.B. Benjamin, W.G. Pritchard, and S.J. Tavener (preprint, 1993)] on the basis of the standard lubrication analysis.     

Slip in Quantum Fluids

In this review we describe theoretical and experimental investigations of general slip phenomena in context with the flow of the quantum liquids³He,⁴He and their mixtures at low temperatures. The phenomenon of slip is related to a boundary effect. It occurs when sufficiently dilute gases flow along the wall of an experimental cell. A fluid is said to exhibit slip when the fluid velocity at the wall is not equal to the wall’s velocity. Such a situation occurs whenever the wall reflects the fluid particles in a specular-like manner, and/or if the fluid is describable in terms of a dilute ordinary gas (classical fluid) or a dilute gas of thermal excitations (quantum fluid). The slip effect in quantum fluids is discussed theoretically on the basis of generalized Landau-Boltzmann transport equations and generalized to apply to a regime of ballistic motion of the quasiparticles in the fluid. The central result is that the transport coefficient of bulk shear viscosity, which typically enters in the Poiseuille flow resistance and the transverse acoustic impedance, has to be replaced by geometry dependent effective viscosity, which depends on the details of the interaction of the fluid particles with the cell walls. The theoretical results are compared with various experimental data obtained in different geometries and for both Bose and Fermi quantum fluids. Good agreement between experiment and theory is found particularly in the case of pure normal and superfluid³He, with discrepancies probably arising because of deficiencies in characterization of the experimental surfaces.     

Surface Effects of 4He Coating on the Viscosity and the Slip Length of Normal and Superfluid 3He

We have measured the viscosity, , and the slip length, , of normal and superfluid ³ He using a torsional oscillator with a thick sample space. We coated the oscillating surface with 2.5 layers of ⁴ He film to study how the ⁴ He thin film changes the scattering mechanism of ³ He quasiparticles at the cell wall at 5 bar and 21 bar. In the normal phase, the temperature dependence of the viscosity was changed a little by the ⁴ He film at 21 bar but no change was observed at 5 bar. The slip length was enhanced by ⁴ He coating at 5 bar. This enhancement indicates the increase of specularity of ³ He quasiparticles scattering at the oscillating surface. On the other hand, a reduction of the slip length was observed at 21 bar. In the superfluid phase, the temperature dependence of supports the existence of Andreev reflection even with ⁴ He film on the surface at 5 bar and 21 bar.     

The propagation and basal solidification of two-dimensional and axisymmetric viscous gravity currents

The effect of basal solidification on viscous gravity currents is analysed using continuum models. A Stefan condition for basal solidification is incorporated into the Navier-Stokes equations. A simplified version of this model is determined in the lubrication and large-Bond-number limit. Asymptotic solutions are obtained in three parameter régimes. (i) A similarity solution is possible in the following cases: the two-dimensional problem when volume per unit length (V) is proportional to time (t) raised to the power 7/4(V = qt ^7/4) and the Julian number (v ³ g ² /q ⁴ ) is large, where v is kinematic viscosity, q is a constant of proportionality and g is the acceleration due to gravity; the axisymmetric problem when volume is proportional to time raised to the power 3 (V = Qt ³) and the dimensionless group vg/Q is large, where Q is a constant of proportionality. In both cases, the front is found to depend on time raised to the power 5/4, as it does in the absence of solidification, but the constant of proportionality satisfies a modified system of equations. (ii) In the case of large Stefan number and small modified Peclet number (Pe ² 1, where Pe is the Peclet number and is the aspect ratio), asymptotic and numerical methods are combined to produce the most revealing results. The temperature of the fluid approaches the melting point over a short time-scale. Over the long time-scale, the solid/liquid interface is determined from the conduction of latent heat into the solid. Strong coupling is observed with the basal solidification modifying the flow at leading order. The solidification may retard and eventually arrest the front motion long before complete phase change has taken place. (iii) In the case of constant volume and large modified Peclet number (Pe ² 1), similarity solutions are found for the solidification at the base of the gravity current on the short time-scale. The coupling is weak on this time-scale with the solidification being dependent on the front position but not influencing the fluid motion at leading order. Over the long time-scale, the drop completely solidifies. Analytical solutions are not obtained on this time-scale, but scalings are deduced.     

Scale effect on flow and thermal boundaries in micro‐/nano‐channel flow using molecular dynamics–continuum hybrid simulation method

The molecular dynamics (MD)–continuum hybrid simulation method has been developed in two aspects in the present work: (1) The energy equation has been combined into the coupling method in order to obtain the hybrid temperature profile and (2) the coupling method has been improved by the local linearization to obtain a smoother parametric profile. The developed method is primarily validated by analytical solutions and full MD results. Then, it is employed to study the scale effect on the flow and thermal boundaries in micro‐/nano‐channel flow. The hybrid velocity and temperature profiles are obtained with the channel height (H) ranging from 60σ to 2014σ and the solid–liquid coupling (β) ranging from 0.1 to 50. Scale effect has shown strong influence on the boundaries. Obvious slip characteristics can be found in the profiles, i.e. velocity slip and temperature jump, when H is small and β is large. However, the results also show that the profiles can be well predicted to converge to the macroscale non‐slip/non‐jump analytical solutions when H is large enough, where the effect of β can be omitted and the slip characteristics disappear. Correlations of relative slip length, relative temperature jump and pressure gradient with H are fitted from the simulation results. Copyright © 2009 John Wiley & Sons, Ltd.     

NMR in pure3He films on a Nuclepore substrate

The properties of³He films on a Nuclepore substrate have been measured by pulsed NMR at a Larmor frequency of 10 MHz between 1.3 and 4.2 K. The³He film thickness was varied from 0.14 to 2 layers. The spin-spin relaxation timeT ₂ agrees well with previous measurements of³He films on Mylar and Vycor glass at low temperatures. The spin-lattice relaxation timeT ₁ for submonolayer films shows a strong temperature dependence consistent with a thermally activated process. This behavior has not previously been observed on amorphous substrates. The spin diffusion coefficient was measured for the thickest films at 4.2 and 2.6 K and found to be consistent with free atom motion of the³He in the vapor. In thin films or at low temperatures, the diffusion was too small to be observed. The magnetic coupling between the³He nuclei in a film and the protons in the Nuclepore substrate was determined from the effect of the³He on the proton-lattice relaxation time. It is about 100 times weaker than the interaction between³He and the fluorine nuclei in a Teflon substrate.     

Mixed State Hall Resistivity in YBCO c-Axis-Oriented Thin Films

Hall voltage measurements on YBCO c-axis-oriented thin films in the mixed state were carried out. The films were grown on MgO substrates utilising evaporation technique followed by relatively low heating temperature. Hall voltage was measured in low magnetic fields perpendicular to the film surface, in which sign reversal near T _c was observed. Relatively large transverse voltage was found to be insensitive to the magnetic field inversion (even Hall effect). This effect is discussed in terms of the vortices guided motion model which is argued to give a reasonable explanation for the even Hall effect in type II superconductors.     

Slip initiation on frictional fractures

Direct shear tests and biaxial compression tests are conducted to investigate the onset of slip along a non-homogeneous frictional surface and to determine the effect of specimen thickness and confining stress on slip initiation and propagation. The specimens are made of two and three acrylic blocks with the contact surfaces between blocks having on their upper half a frictional strength smaller than on their lower half. This creates a “weak” surface on the upper half and a “strong” surface on the lower half. The specimens are then loaded in direct shear or biaxial compression with confining pressures ranging from 0.7 to 3.5 MPa. The onset of slip, slip propagation, and the stress field generated at the front and center of the blocks interfaces are monitored using a photoelastic technique where a thin photoelastic film is placed at the location where observations are made. The onset of slip at the weak-strong zone interface is treated as propagation of a frictional crack under Mode II loading. The critical stress intensity factor, K_IIC, at the onset of slip is obtained from photoelastic techniques. The results show a weak dependency of K_IIC on the normal stress applied and no influence of the specimen size for specimens thicker than 25.4 mm; for thinner specimens the K_IIC values are smaller because the boundaries of the specimen prevent the full development of the stress field ahead of the crack tip. The experiments show a linear increase of the critical energy release rate with normal stress which is explained with linear elastic fracture mechanics theories.     

Meso-patterning of thin polymer films by controlled dewetting: from nano-droplet arrays to membranes

Controlled dewetting of thin polymer films on physically heterogeneous substrates is employed as a new soft lithography route to obtain various types of ordered meso-scale structures, including nano-membranes and ordered arrays of nano-droplets. Dewetting of a thin polymer film on a defect free homogeneous surface occurs by a randomly placed collection of holes and droplets with a well-defined spacing. In contrast, on a physically patterned surface, strong influence of the underlying pattern is observed on the dewetting pathways as well as on the ordering and size of the resulting meso-scale structures. The imposed periodicity of the substrate pattern vis-à-vis the spinodal length scale of dewetting provides a powerful tool for the morphology and size control. The thickness of the film and the kinetics of dewetting are the other important parameters that govern the morphology of the resulting structures.     

Self-organized patterned arrays of Au and Ag nanoparticles by thickness-dependent dewetting of template-confined films

In this work we report on the formation of self-organized and multimodal sized patterned arrays of Au and Ag nanoparticles on SiO₂ surface exploiting the thickness-dependent solid-state dewetting properties of template-confined deposited nanoscale films. In this approach, the Au and Ag surface pattern order, on the SiO₂ substrate, is established by the template confined deposition on a micrometric scale, while the solid-state dewetting phenomenon is induced by thermal processes (below the Au and Ag melting temperature). The deposited films have not an uniform thickness. They, instead, present a controlled thickness due to shadowing mask effects during depositions. Such an inhomogeneity can be further controlled by changing the deposition angle. After the dewetting process, scanning electron microscopy analyses allowed us to correlate the mean diameter 〈D〉 and spacing 〈s〉 of the formed nanoparticles by the thickness h of the deposited films. Despite the dewetting process of the Au and Ag films occurs in the solid state, relations describing the evolution of 〈D〉 and 〈s〉 with 〈h〉 typical of the linear hydrodynamic spinodal dewetting process of liquid films, 〈D〉 ∝ h ^5/3 and 〈s〉 ∝ h ², were verified within a 20 % experimental error. As a consequence we call this process “pseudo-spinodal dewetting”.     

Measurement of vortex diffusivity and lifetime below the Kosterlitz-Thouless transition in helium films

Using vortex pair motion, we have measured the vortex diffusivity below the Kosterlitz-Thouless transition temperature (T _KT) in atomically thin superfluid helium films on both argon and neon substrates. The diffusivities are on the order of/m nearT _KT and then fall rapidly to10 ^–3 /m near0.1 K for argon and to0.03 /m for neon. However, for the thinnest helium film on neon, the diffusivity is large and independent of temperature. At small flow velocities, dissipation due to unpaired vortices indicates a vortex lifetime on the order of seconds for a neon substrate near0.1 K.     

Role of Wetting Front in Dewetting of Liquid Solder Drop on Cu Thin Films

The thermodynamic conditions for dewetting of a liquid solder drop on copper thin films were examined under a hot-stage optical microscope in a flowing protective atmosphere.Dewetting of liquid solder was found to depend strongly on the copper film thickness and preceded by spalling of Cu 6 Sn 5 intermetallic compounds.However,the loss of interfacial bonding by spalling was not sufficient to cause immediate dewetting of solder drops if the wetting tip was still strongly bonded to the copper film.By introducing a pinning force on the wetting front,a sufficient condition was found from a force balance analysis for dewetting of the liquid solder drop,in general agreement with the experimental results.     

Vertical ZnO Nanotube Transistor on a Graphene Film for Flexible Inorganic Electronics

The bottom‐up integration of a 1D–2D hybrid semiconductor nanostructure into a vertical field‐effect transistor (VFET) for use in flexible inorganic electronics is reported. Zinc oxide (ZnO) nanotubes on graphene film is used as an example. The VFET is fabricated by growing position‐ and dimension‐controlled single crystal ZnO nanotubes vertically on a large graphene film. The graphene film, which acts as the substrate, provides a bottom electrical contact to the nanotubes. Due to the high quality of the single crystal ZnO nanotubes and the unique 1D device structure, the fabricated VFET exhibits excellent electrical characteristics. For example, it has a small subthreshold swing of 110 mV dec^?1, a high I_max/I_min ratio of 10⁶, and a transconductance of 170 nS µm^?1. The electrical characteristics of the nanotube VFETs are validated using 3D transport simulations. Furthermore, the nanotube VFETs fabricated on graphene films can be easily transferred onto flexible plastic substrates. The resulting components are reliable, exhibit high performance, and do not degrade significantly during testing.     

Multi‐linearity algorithm for wall slip in two‐dimensional gap flow

Wall slip has been observed in a micro/nanometer gap during the past few years. It is difficult to make a mathematical analysis for the hydrodynamics of the fluid flowing in a gap with wall slip because the fluid velocity at the liquid–solid interface is not known a priori. This difficulty is met especially in a two‐dimensional slip flow due to the non‐linearity of the slip control equation. In the present paper we developed a multi‐linearity method to approach the non‐linear control equation of the two‐dimensional slip gap flow. We used an amended polygon to approximate the circle yield (slip) boundary of surface shear stress. The numerical solution does not need an iterative process and can simultaneously give rise to fluid pressure distribution, wall slip velocity and surface shear stress. We analysed the squeeze film flow between two parallel discs and the hydrodynamics of a finite slider gap with wall slip. Our numerical solutions show that wall slip is first developed in the large pressure gradient zone, where a high surface shear stress is easily generated, and then the slip zone is enlarged with the increase in the shear rate. Wall slip dramatically affects generation of the hydrodynamic pressure. Copyright © 2006 John Wiley & Sons, Ltd.     

Potential flow of a film down an inclined plate

Summary The flow of a liquid film along a semi-infinite flat plate due to gravity is considered, the fluid being assumed inviscid and incompressible. When the Froude numberFr, based on the initial film thickness and velocity, is large compared to unity, solutions can be found by the method of matched asymptotic expansions. The fluid speed and deflection, and the pressure gradient are found toO(Fr ^–2). Hydraulic theory enters as the first term in the outer expansion, which is valid far downstream from the leading edge. When the liquid falls vertically, the motion represents half of a freely falling jet.