Slippery Substrate Research Articles

Sensitivity and stability improvement on slippery surface-aggregated substrate for trace heavy metals detection using NELIBS

The sensitive and stable detection of trace heavy metals in liquid is crucial given its profound impact on various aspects of human life. Currently, nanoparticle-enhanced laser-induced breakdown spectroscopy (NELIBS) with dried droplet method (DDM) is widely applied for heavy metals detection. Nevertheless, the coffee ring effect (CRE) in DDM affects the stability, accuracy, and sensitivity of NELIBS. Here, we developed a slippery surface-aggregated substrate (SS substrate) to suppress the CRE and enrich analytes, and form a plasmonic platform for NELIBS detection. The SS substrate was prepared by infiltrating perfluorinated lubricant into the pores of PTFE membrane. The droplet, with targeted elements and gold nanoparticles, was dried on the SS substate to form the plasmonic platform for NELIBS analysis. Then, trace heavy metal elements copper (Cu) and manganese (Mn) were analyzed by NELIBS. The results of Cu (RSD = 5.60%, LoD = 3.72 μg/L) and Mn (RSD = 7.42%, LoD = 6.37 μg/L), illustrated the CRE suppression and analytes enrichment by the SS substrate. The results verified the realization of stable, accurate and sensitive NELIBS detection. And the LoDs succeeded to reach the standard limit of China (GB/T 14848-2017). Furthermore, the results for groundwater detection (relative error: 5.92% (Cu) and 4.74% (Mn)), comparing NELIBS and inductively coupled plasma mass spectrometry (ICP-MS), validated the feasibility of the SS substrate in practical applications. In summary, the SS substrate exhibits immense potential for practical application such as water quality detection and supervision.

A controllable sliding law for thin-film flows over slippery fluid-saturated substrates: theory and experiments

We develop a theoretical and experimental framework for generating slip underneath thin-film flows of viscous fluids in the laboratory, with the ability to control slip as desired. Such a framework is useful for large-scale fluid-mechanical experiments in which basal sliding is important. In particular, we consider the flow of a thin film of viscous fluid spreading over a structured, slippery substrate, involving a sequence of two-dimensional cavities that are prewetted with a fluid of smaller viscosity. By averaging over small-scale inhomogeneities, we demonstrate that such a substrate gives rise to a macroscopic linear sliding law, or Navier slip condition, that is effectively homogeneous on the large scale. The slip length, determining the slipperiness of the substrate, is proportional to the viscosity ratio and width of each cavity. As such, the slipperiness of the substrate can be controlled by altering the viscosity ratio, as desired. Two asymptotic regimes arise, describing flow over very slippery substrates and flow over no-slip substrates. The former regime is valid for early times, when the depth of the overlying fluid is much less than the slip length, and the latter is valid for late times, when the depth is much greater than the slip length. Solutions to the full model approach similarity solutions describing the two regimes for early and late times. We confirm our theoretical predictions by conducting a series of analogue laboratory experiments.

Thermocapillary thin film flows on a slippery substrate with odd viscosity effects

This study investigates the behavior of a thin liquid with odd viscosity effects as it flows down a uniformly heated, slippery inclined plane, where the liquid’s time-reversal symmetry is broken. The breaking of symmetry results in interesting effects, as the antisymmetric part of the fluid stress tensor does not vanish. Two models, the Benney-type equation model (BEM) and the weighted residual model (WRM), are constructed to account for the combined effects of slip length, thermocapillarity, and odd viscosity. A detailed stability analysis determines both models’ critical Reynolds numbers Rec. For small slip lengths, the first-order WRM is better at capturing the instability threshold than the first-order BEM. While both models account for the effects of odd viscosity and thermocapillarity, only the Rec of WRM incorporates the wall slip effects. Another significant finding is that the BEM effectively avoids the issue of finite-time blow-up by incorporating odd viscosity. Additionally, employing a weakly nonlinear stability analysis with multiple scales uncovers four flow regions in BEM: supercritical stable, subcritical unstable, unconditional stable, and explosive zones. Two separate bifurcation scenarios emerge for various wave numbers: supercritical within a specific range and subcritical for larger wave numbers. The presence of odd viscosity alleviates the reduction of the unconditional stable zone and the increase in the explosive zone, which are caused by the combined influence of slip and thermal effects. Numerical investigation of traveling wave solutions of WRM shows that wave height is promoted by slip and thermal effects but reduced with increasing odd viscosity coefficient. Further numerical simulations of WRM on a larger domain demonstrate the stabilizing effects of odd viscosity and its interaction with destabilizing slip and thermocapillary effects.

Shear imposed falling liquid films on a slippery substrate with Marangoni effects: Effect of odd viscosity

We investigate the behavior of a thin fluid with disrupted time-reversal symmetry on a uniformly heated inclined surface under external shear stress using modified Navier–Stokes equations, an energy conservation equation, and incorporating a Navier slip condition. Critical conditions for instability onset are determined by a linear stability analysis within the Orr–Sommerfeld framework. We derive a first-order Benney-type evolution equation to study long-wave instabilities. We find slippery substrate, imposed shear stress along the flow direction, and Marangoni number consistently destabilize the flow, while odd viscosity and imposed counter-flow shear stabilize it. A weakly nonlinear analysis using multiple scales reveal distinct zones of instability. Marangoni number, slip length, odd viscosity, and imposed shear direction significantly impact stability and instability regions. Numerical simulations of the free surface evolution equation of a flow system under consideration provide clear evidence of the contributions of thermocapillary, slip length, odd viscosity, and imposed shear direction. Furthermore, our analysis of linear and weakly nonlinear stability, as well as our numerical simulations, exhibit remarkable consistency.

Falling liquid films on a slippery substrate with variable fluid properties

We investigate the stability of a gravity-driven, thin, Newtonian liquid flowing on a uniformly heated slippery inclined plane. We construct a mathematical model of the flow that comprises the Navier–Stokes equation coupled with the equation of energy. While the rest of the boundary conditions are standard for thin-film problems, we apply a Navier slip boundary condition at the solid–liquid interface. We assume that the fluid thermophysical properties — density, dynamical viscosity, surface tension, and thermal diffusivity vary linearly with temperature as long as the change in temperature is small. In the analysis part, we follow the standard long-wave theory and construct a nonlinear evolution equation for the film thickness. This is followed by a linear and weakly nonlinear stability analysis. The linear analysis allows us to compute the critical Reynolds number of our problem and from this study, we conclude that the slippery substrate destabilizes the film flow. The weakly nonlinear stability analysis finds a finer description of various stable/unstable zones. Finally, we perform a numerical simulation of the evolution equation in a periodic domain using spectral methods. Our numerical results support the analytical predictions of the instability threshold using the linear and weakly nonlinear theories. The influence of the small Biot number is also investigated in presence of the slip length together with the variable fluid properties.

(Invited, Digital Presentation) Understanding Interfacial Chemo-Mechanics of Two-Dimensional Materials-Based Heterogeneous Functional Materials for Energy Storage

Two-dimensional (2D) materials and their heterostructures (2D + nD, n = 0,1,2,3) attracted enormous interest in wide range of applications including electrochemical systems, e.g., batteries. Electro-chemo-mechanics, the coupling of mechanics and electrochemistry, plays a crucial role in designing these systems. This talk considers battery as a model system and demonstrates the role of 2D materials in overcoming various interfacial electro-chemo-mechanical challenges. 2D materials are engineered as the van der Waals (vdW) “slippery” interface. For example, silicon (Si) electrodes can be placed over the graphene-coated current collector for Lithium-Ion Batteries (LIBs). This arrangement provides less stress build-up and less stress “cycling” on the vdW slippery substrate instead of a fixed interface. 2D materials such as MXenes can also be used to replace polymer binders, e.g., in Si-based LIBs. Our DFT studies show more stable performance and higher Coulombic efficiency for Si films deposited on graphene-coated nickel (i.e., slippery interface) than conventional nickel current collectors. The interface strength of monoclinic Se (selenium) is 0.43 J/m2, which is similar in magnitude in amorphous Si with graphene (0.41 J/m2). However, the interface strength of c-Se on a 3D aluminum (Al) current collector is higher (0.99 J/m2), suggesting a stronger adhesion for 3D/3D interface than 3D/2D interface. Furthermore, interface strength variation between a-Si and Ti3C2Tx MXenes are determined for various surface functional groups (Tx). The completely hydroxylated Ti3C2 has the highest interface strength of 0.60 J/m2 with a-Si. The talk also summarizes our recent efforts in developing High Dimensional Deep Learning Potential (HDDLP) to study interfacial electro-chemo-mechanics in 2D materials-based systems. Our computational results are in good agreement with experiments. Besides batteries, our comprehensive interface analyses are beneficial in advancing understanding of other 2D materials-based systems, e.g., sensors, fuel cells, solar cells, nanomedicine, soft-actuators, etc.

Weakly viscoelastic film on a slippery slope

We study the stability of weakly viscoelastic film (Walter's B″) flowing down under gravity along a slippery inclined plane. The focus is to investigate the interaction of the bottom slip with the viscoelastic parameter as well as the influence of the other flow parameters on the stability of the flow. For the slippery substrate, we use the Navier-slip boundary condition at the solid–liquid interface. The dimensionless slip length β is first assumed to be small and its order is considered same as the order of the film aspect ratio ϵ=H/L, where H is the mean film thickness and L is a typical wavelength. To discuss the coupled effect of slip length β and viscoelastic parameter γ, we have used the classical Benney equation model (BEM) as well as the weighted residual method (WRM). For linear stability, the normal mode analysis is carried out to capture the instability threshold. The critical Reynolds numbers (Rec) are obtained for BEM and WRM separately for the system. We found that the first-order WRM is a better choice to capture the instability threshold in comparison with a first-order BEM when β is small. Another noteworthy result we obtain is that, in the absence of β, WRM and BEM yield the same expression for the critical Reynolds number. Further, we have extended the study for moderate values of β, that is, β of order unity and it is found that both BEM and WRM are able to capture the effects of β and γ. We derive the Orr–Sommerfeld (OS) type eigenvalue problem and an asymptotic analysis is performed for small perturbation wavenumbers, which gives an expression for the critical Reynolds number for the instability of very long perturbations. The critical Reynolds number obtained by the OS eigenvalue problem exactly matches with that obtained by BEM. Finally, we validate our analytical predictions by performing a direct numerical simulation of the WRM and good agreement between the results of the linear stability analysis, weighted residual model, and the numerical simulations is found.

Multi-bioinspired and Multistructural Integrated Patterned Nanofibrous Surface for Spontaneous and Efficient Fog Collection

Harvesting water from untapped fog is a potential and sustainable solution to freshwater shortages. However, designing high-efficiency fog collectors is still a critical and challenging task. Herein, learning from the unique microstructures and functionalities of the Namib desert beetle, honeycomb, and pitcher plant, we present a multi-bioinspired patterned fog collector with hydrophilic nanofibrous bumps and a hydrophobic slippery substrate for spontaneous and efficient fog collection. Interestingly, hydrophilic nanofibrous bumps display a honeycomb-like cellular grid structure self-assembled from electrospun nanofibers. Notably, the patterned nanofibrous fog collector exhibits superior water-collecting efficiency of 1111 mg cm-2 h-1. The hydrophilic nanofibrous bumps increase the effective fog-collecting area, and the hydrophobic slippery substrate promotes quick transport of collected water in the desired direction reducing the secondary water evaporation, finally achieving rapid directional transport of tiny droplets and high-efficiency water collection. This work opens a new avenue to collect water efficiently and provides clues to research on the multi-bioinspired synergistical optimization strategy.

Influence of the odd viscosity on a falling film down a slippery inclined plane

The stability of a thin viscous Newtonian fluid with broken time-reversal-symmetry draining down a slippery inclined plane is examined. The presence of the odd part of the Cauchy stress tensor with an odd viscosity coefficient brings new characteristics in fluid flow as it gives rise to new terms in the pressure gradient of the flow. By odd viscosity, it is meant that apart from the well-known coefficient of shear viscosity, a classical liquid with broken time-reversal symmetry is endowed with a second viscosity coefficient. The model implements a Navier slip condition at the solid–liquid interface with the slip length being the parameter that measures the deviation from the no-slip condition. The classical long-wave expansion technique is performed and a nonlinear evolution equation of Benney-type is derived in terms of film thickness h(x, t), which is significantly modified due to the presence of odd viscosity in the liquid. The parameters governing the film flow system and the slippery substrate strongly influence the waveforms and their amplitudes and hence the stability of the fluid. The linear stability analysis is performed using the normal mode approach and a critical Reynolds number is obtained. The results of the linear stability analysis reveal that larger odd viscosity leads to the higher critical Reynolds number while the higher slip length makes the critical Reynolds number lower. In other words, odd viscosity has a stabilizing effect while the slip length promotes instability. Based on the method of multiple scales, a weakly nonlinear stability analysis is carried out, which shows that there is a range of wave numbers with a supercritical bifurcation and a range of larger wave numbers with a subcritical bifurcation. Different instability zones are also demarcated. The weakly nonlinear study shows that with an increase in the odd viscosity, the supercritical stable region and the explosion area shrink, whereas the unconditional stable and the subcritical unstable regions increase. It has also been shown that the spatial uniform solution corresponding to the sideband disturbance may be stable in the unstable region. The spatiotemporal evolution of the model has been analyzed numerically by employing the Crank–Nicolson method in a periodic domain for different values of the odd viscosity and slip length. The nonlinear simulations are found to be in good agreement with the linear and weakly nonlinear stability analysis. The authors of the article agree to the retraction of the article effective 29 June 2022.

Thermocapillary instability on a film falling down a non-uniformly heated slippery incline

A gravity-driven, thin, incompressible liquid film flow on a non-uniformly heated, slippery inclined plane is considered within the framework of the long-wave approximation method. A mathematical model incorporating variation in surface tension with temperature has been formulated by coupling the Navier–Stokes equation, governing the flow, with the equation of energy. For the slippery substrate, the Navier slip boundary condition is used at the solid–liquid interface. An evolution equation is formed in terms of the free surface, which includes the effects of inertia, thermocapillary as well as slip length. Using the normal mode approach, linear stability analysis is carried out and a critical Reynolds number is obtained, which reflects its dependence on the Marangoni number Mn as well as slip length δ. This depicts that δ and Mn both have the destabilization effect on the flow field. The linear study also reveals that the inertia force has a negligible effect compare to the thermocapillary or slip. In addition, the study highlights a critical Marangoni number at which the instability sets in when the thermocapillary stress attains a critical value. The method of multiple scales is used to investigate the weakly nonlinear stability analysis of the flow. The study interprets that the variation of Mn and δ have substantial effects on different stable/unstable zones. It also shows that within a considered parametric domain, the unconditional stable zone completely vanishes for any value of Mn, when the slip length δ attains a critical value. The study also divulges that in the subcritical unstable (supercritical stable) zone the threshold amplitude (ζa) decreases (increases) with the increment of Mn and δ. Further, we discussed the spatial uniform solution of the complex Ginzburg–Landau equation for sideband disturbances. Employing the Crank–Nicolson method, the nonlinear evolution equation of the free surface is solved numerically in a periodic domain, considering the sinusoidal initial perturbation of small amplitude. The nonlinear simulations are found to be in good agreement with the linear and weakly nonlinear stability analysis. The evolution of the maximum hmax and minimum hmin thickness amplifies, for small change of Mn and δ. Further, it shows that the influence of the thermocapillary force amplifies the destabilizing nature of δ. The traveling wave solution confirms the existence of a fixed point for the considered parametric domain, chosen from the experimental data. Finally, the Hopf bifurcation of the fixed point exhibits that the nonlinear wave speed at the transcritical point increases as δ increases but decreases as Mn increases. The noteworthy result which arises from the study is that a transcritical Hopf bifurcation exists if the slip length δ>max16Mn−13,12Mn−23−Mn.

Effect of porous layer on the Faraday instability in viscous liquid

A linear stability analysis of a viscous liquid on a vertically oscillating porous plane is performed for infinitesimal disturbances of arbitrary wavenumbers. A time-dependent boundary value problem is derived and solved based on the Floquet theory along with the complex Fourier series expansion. Numerical results show that the Faraday instability is dominated by the subharmonic solution at high forcing frequency, but it responds harmonically at low forcing frequency. The unstable regions corresponding to both subharmonic and harmonic solutions enhance with the increasing value of permeability and yields a destabilizing effect on the Faraday instability. Further, the presence of porous layer makes faster the transition process from subharmonic instability to harmonic instability in the wavenumber regime. In addition, the first harmonic solution shrinks gradually and becomes an unstable island, and ultimately disappears from the neutral curve if the porous layer thickness is increased. In contrast, the first and second subharmonic solutions coalesce, and the onset of Faraday instability is dominated by the subharmonic solution. In a special case, the study of Faraday instability of a viscous liquid on a porous substrate can be replaced by a study of Faraday instability of a viscous liquid on a slippery substrate when the permeability of the porous substrate is very low. Further, the Faraday instability can be destabilized by introducing a slip effect at the bottom plane.

Rivulet flow down a slippery substrate

A detailed analysis of small-scale locally unidirectional gravity-driven rivulet flow with prescribed volume flux down an inclined slippery substrate for a rivulet with either constant width (i.e., pinned contact lines) or constant contact angle is undertaken. In particular, we determine the effect of varying the Navier slip length λ (i.e., the strength of the slip at the solid–fluid interface) on the rivulet. The present analysis shows that the shape and size of the rivulet and the velocity within it depend strongly on the value of λ. Increasing the value of λ reduces the viscous resistance at the substrate and, hence, leads to a larger velocity within the rivulet, and so the prescribed flux is achieved with a smaller rivulet. In particular, in the limit of strong slip, λ → ∞, for a rivulet of a perfectly wetting fluid and a rivulet with constant width, the velocity becomes large and plug-like like O(λ1/2) ≫ 1, and the rivulet becomes shallow like O(λ−1/2) ≪ 1, while for a rivulet with positive constant contact angle, the velocity becomes large and plug-like like O(λ2/3) ≫ 1, and the rivulet becomes narrow like O(λ−1/3) ≪ 1 and shallow like O(λ−1/3) ≪ 1.

Contact line instability of gravity driven thin films flowing down an inclined plane with wall slippage

Coating liquid films exist widely in nature and industrial processes, such as lava flows, falling-film evaporators, and microfabrication processes. In this paper, we aim to give a comprehensive study on contact line instability of thin film flows on a slippery substrate, which has different slippery lengths in the streamwise direction and the spanwise direction. It is reported here for thin film flows with contact lines, the streamwise slippery effect plays an opposite role compared with the spanwise slippery effect, different from the conclusion by Ding and Wong that the wall slippage always promoted the instability of the thin film flow [Ding and Wong, Int. J. Heat Mass Tran. 90, 2015]. The evolution equation of the thin film flow is derived by the lubrication theory, and traveling wave solutions are obtained, showing that with a larger streamwise slippery length, the traveling wave speed is promoted and a higher capillary ridge is induced. Linear stability analysis (LSA) and energy analysis are carried out to elucidate the mechanism of the flow instability. Results indicate that for thin film flows with dynamic contact lines, the slippery effect in the streamwise and spanwise direction plays different roles in the flow instability. The wall slippage in the streamwise direction suppresses the wave height of traveling waves and impedes the instability of the flow, while the wall slippage in the spanwise direction promotes the instability with a smaller cut off wavenumber. Besides, numerical simulations for thin film flows are performed, and the flow phenomenon agrees well with the prediction by the LSA. Our findings offer insight into the influence of the wall slippage on the dynamics of thin films coating on biomaterials and compliant substrates.

Droplet Retention and Shedding on Slippery Substrates.

A significant limitation for droplet mobility on solid surfaces is to overcome the inherent pinning of the droplet's contact line that occurs because of chemical/physical heterogeneities. A recent innovation is to use surface texture or porosity to create a stabilized lubricant surface. Droplets on such slippery liquid-infused porous surfaces (SLIPS)/lubricant-impregnated surfaces (LIS) are highly mobile because of the lubricant layer. Low pinning of the contact line reduces the energy required to move a droplet; however, it makes it difficult to accurately position the droplet or to stop its motion altogether. In this paper, a simple structure (step), as small as a few microns in height, is used to introduce controlled droplet pinning on a slippery substrate. The key effect is identified as the capillary force, arising from the interaction between the lubricant menisci created by the step and droplet. The effect of changing step height, lubricant thickness, and initial position on step-droplet interactions has been investigated, showing that droplets can both be repelled from and attracted to the step. To measure the adhesion strength, we report droplet detachment angle measurements under gravity and scaling of force with the lubricant thickness/step height ratio. Under certain conditions, the interaction strength is sufficient to ensure droplet-step attachment even when the surface is rotated to an upside-down orientation. These findings can motivate the design of SLIPS structures, capable of shedding or retaining droplets preferentially, for example, according to the size or wettability, relevant to applications from microfluidics to fog harvesting.

Hydrophobic Slippery Surface-Based Surface-Enhanced Raman Spectroscopy Platform for Ultrasensitive Detection in Food Safety Applications.

Collecting highly diluted target analytes into specific hot spot regions is vital for ultrasensitive surface-enhanced Raman spectroscopy (SERS) applications. In this work, a hydrophobic slippery platform was employedas a concentrator to construct colloidal SERS-active substrates regardless of the diffusion limits during droplet evaporation. Within only 140 s, sufficient absorption between the analytes and colloidal Au nanoparticles (Au NPs) was observed by fluorescence imaging. This effect resulted in excellent SERS sensitivity and stability. Compared with the common metal colloid-based SERS substrates, e.g.,drying on a silicon wafer or detection in colloidal solutions, this preconcentrated method showed lower detection limits and the lowest detectionconcentration of crystal violet molecule down to 10-12 M with a portable Raman spectrometer. Such high signal enhancement was mainly ascribed to the condensation effect of Au colloids/analytes on the hydrophobic slippery substrate, by which almost all probe molecules were guided into the "hot spot" regions of aggregated Au NPs. Using the SERS platform, various illegal additives in realistic food and health-care products, for example, malachite green (1 ppb) added in fish and morphine (0.1 ppm) added in a chafing dish, could be sensitively detected. Therefore, our protocol is a general SERS platform that may provide a simple, fast, and cost-effective approach for trace molecular sensing.

Utilizing van der Waals Slippery Interfaces to Enhance the Electrochemical Stability of Silicon Film Anodes in Lithium-Ion Batteries.

High specific capacity anode materials such as silicon (Si) are increasingly being explored for next-generation, high performance lithium (Li)-ion batteries. In this context, Si films are advantageous compared to Si nanoparticle based anodes since in films the free volume between nanoparticles is eliminated, resulting in very high volumetric energy density. However, Si undergoes volume expansion (contraction) under lithiation (delithiation) of up to 300%. This large volume expansion leads to stress build-up at the interface between the Si film and the current collector, leading to delamination of Si from the surface of the current collector. To prevent this, adhesion promotors (such as chromium interlayers) are often used to strengthen the interface between the Si and the current collector. Here, we show that such approaches are in fact counter-productive and that far better electrochemical stability can be obtained by engineering a van der Waals "slippery" interface between the Si film and the current collector. This can be accomplished by simply coating the current collector surface with graphene sheets. For such an interface, the Si film slips with respect to the current collector under lithiation/delithiation, while retaining electrical contact with the current collector. Molecular dynamics simulations indicate (i) less stress build-up and (ii) less stress "cycling" on a van der Waals slippery substrate as opposed to a fixed interface. Electrochemical testing confirms more stable performance and much higher Coulombic efficiency for Si films deposited on graphene-coated nickel (i.e., slippery interface) as compared to conventional nickel current collectors.

Stability of viscosity stratified flows down an incline: Role of miscibility and wall slip

The effects of wall velocity slip on the linear stability of a gravity-driven miscible two-fluid flow down an incline are examined. The fluids have the matched density but different viscosity. A smooth viscosity stratification is achieved due to the presence of a thin mixed layer between the fluids. The results show that the presence of slip exhibits a promise for stabilizing the miscible flow system by raising the critical Reynolds number at the onset and decreasing the bandwidth of unstable wave numbers beyond the threshold of the dominant instability. This is different from its role in the case of a single fluid down a slippery substrate where slip destabilizes the flow system at the onset. Though the stability properties are analogous to the same flow system down a rigid substrate, slip is shown to delay the surface mode instability for any viscosity contrast. It has a damping/promoting effect on the overlap modes (which exist due to the overlap of critical layer of dominant disturbance with the mixed layer) when the mixed layer is away/close from/to the slippery inclined wall. The trend of slip effect is influenced by the location of the mixed layer, the location of more viscous fluid, and the mass diffusivity of the two fluids. The stabilizing characteristics of slip can be favourably used to suppress the non-linear breakdown which may happen due to the coexistence of the unstable modes in a flow over a substrate with no slip. The results of the present study suggest that it is desirable to design a slippery surface with appropriate slip sensitivity in order to meet a particular need for a specific application.

Steady solution and spatial stability of gravity-driven thin-film flow: reconstruction of an uneven slippery bottom substrate

Steady solutions of an inverse problem relevant to gravity-driven film flows over an undulated slippery bottom are considered. Given a target free surface shape, the goal is to obtain the corresponding bottom topography of a slippery substrate which causes the specified free surface shape for a film flowing over it. The approaches followed by Sellier (Phys Fluids 20:062106, 2008) for creeping films and by Heining and Aksel (Phys Fluids 21:083605, 2009) for inertial films for reconstructing a rigid bottom topography for a target free surface profile are extended to the reconstruction of a slippery bottom topography. The model equations for film thickness above the bottom topography are derived for creeping flows under lubrication approximation and for inertial films using the weighted-residual integral boundary layer method and are solved numerically. The influence of inertia, slip parameter and surface tension on the shape of the reconstructed bottom topography is analyzed for different prescribed free surface shapes (sinusoidal, trench and bell-shaped). It is observed that the nonlinearities that appear in the reconstructed rigid bottom substrate with no slip at the substrate are suppressed by seeking the bottom substrate to be reconstructed as a slippery substrate. A spatial linear stability analysis of the corresponding direct problem is examined using Floquet theory, and the results reveal that the slip parameter and surface tension have a high influence on the critical Reynolds number. The results provide a strategy for controlling surface defects in a gravity-driven film over a substrate; namely, in order to achieve a target free surface profile, one can design the bottom substrate to be an undulated rough/textured/grooved or a superhydrophobic surface which can be modelled as an undulated smooth substrate with velocity slip at the substrate.

Fatigue-free, superstretchable, transparent, and biocompatible metal electrodes

Next-generation flexible electronics require highly stretchable and transparent electrodes. Few electronic conductors are both transparent and stretchable, and even fewer can be cyclically stretched to a large strain without causing fatigue. Fatigue, which is often an issue of strained materials causing failure at low strain levels of cyclic loading, is detrimental to materials under repeated loads in practical applications. Here we show that optimizing topology and/or tuning adhesion of metal nanomeshes can significantly improve stretchability and eliminate strain fatigue. The ligaments in an Au nanomesh on a slippery substrate can locally shift to relax stress upon stretching and return to the original configuration when stress is removed. The Au nanomesh keeps a low sheet resistance and high transparency, comparable to those of strain-free indium tin oxide films, when the nanomesh is stretched to a strain of 300%, or shows no fatigue after 50,000 stretches to a strain up to 150%. Moreover, the Au nanomesh is biocompatible and penetrable to biomacromolecules in fluid. The superstretchable transparent conductors are highly desirable for stretchable photoelectronics, electronic skins, and implantable electronics.

Falling liquid films on a slippery substrate with Marangoni effects

This paper investigates the dynamics of liquid films of mean thickness h0 flowing down a uniformly heated slippery substrate. The dimensionless slippery length β is small and is assumed to have the same order as the film parameter ∊=h0/l where l is a typical wave length. A weighted-residual model and a Benney-type model are derived to discuss the influences of slippery length β, Reynolds number Re, Marangoni number M and Biot number Bi on the dynamics of the film. It is found that, when Reynolds number is small (Re<1) and the wall is non-slip, the Benney-type model, weighted-residual model are in good agreements with the linearized Navier–Stokes equations (LNS). However, when the wall is slip or the Reynolds number is moderate, the Benney-type model does not agree with LNS. Our results show that, for a small slippery effect at the substrate, the weighted-residual model compares well with LNS at moderate Re. It demonstrates that the weighted-residual model is more reasonable than the Benney-type model. A critical Reynolds number obtained by the weighted-residual model for this system is Rec=35(1-3β)46(7-67β+159β2)Wek2+cotα-3MBi2(1+Bi)2 (α is the inclined angle and We is the Weber number). Linear stability analysis shows that, the instability is enhanced as the slippery length β and the Reynolds number Re increase. In the long-wave range, the linear wave speed c=1+2β. When the wall is heated, the instability is reinforced. The instability is impeded when the substrate is cooled. Nonlinear analysis by the traveling wave solutions shows that, the wave speed and wave height of traveling waves are promoted by the slippery and fluid inertial effects. Nonlinear study shows that the traveling wave speed is promoted by a heated substrate and is reduced by a cooled substrate. It shows that the speed of fast waves is larger than the linear wave speed and the higher the wave is the faster it travels. Direct numerical simulation of the weighted residual model supports the linear stability analysis and the nonlinear analysis of traveling wave solutions.