Thin film dynamics on a vertically rotating disk partially immersed in a liquid bath

The axisymmetric flow of a thin liquid film is considered for the problem of a vertically rotating disk that is partially immersed in a liquid bath. A model for the fully three-dimensional free-boundary problem of the rotating disk, that drags a thin film out of the bath is set up. From this, a dimension-reduced extended lubrication approximation that includes the meniscus region is derived. This problem constitutes a generalization of the classic drag-out and drag-in problem to the case of axisymmetric flow. The resulting nonlinear fourth-order partial differential equation for the film profile is solved numerically using a finite element scheme. For a range of parameters steady states are found and compared to asymptotic solutions. Patterns of the film profile, as a function of immersion depth and angular velocity are discussed.Comment: 31 pages, 19 figures accepted: Applied Mathematical Modellin

Marangoni-driven liquid films rising out of a meniscus onto a nearly horizontal substrate

We revisit here the situation of a thin liquid film driven up an inclined substrate by a thermally induced Marangoni shear stress against the counter-acting parallel component of gravity. In contrast to previous studies, we focus here on the meniscus region, in the case where the substrate is nearly horizontal, so there is a significant contribution from the normal component of gravity. Our numerical simulations show that the time-dependent lubrication model for the film profile can reach a steady state in the meniscus region that is unlike the monotonic solutions found in [Münch, SIAM J. Appl. Math., 62(6):2045-2063, 2002]. A systematic investigation of the steady states of the lubrication model is carried out by studying the phase space of the corresponding third order ODE system. We find a rich structure of the phase space including multiple non-monotonic solutions with the same far-field film thickness

Dynamics of a surface-gradient-driven liquid film rising from a reservoir onto a substrate

On a tilted heated substrate, surface tension gradients can draw liquid up out of a reservoir. The resulting film thickness profile is controlled by the tilt of the substrate, the imposed temperature gradient, and the thickness of a postulated thin precursor layer. We study the evolution of this film in time, using a lubrication model. A number of distinct behaviours are possible as the substrate tilt angle and other parameters are varied. We use recent results for the multiple stationary profiles possible near the meniscus and examine how these can interact with the advancing front. We show that it is in fact possible to systematically determine the evolution of the entire film profile from the meniscus to the apparent contact line. This allows a categorisation of the range of behaviours for a transversely-uniform profile, in a two-dimensional parameter space. In addition to combinations of meniscus profiles involving capillary fronts and double shock structures, we describe a new combination of a Type I meniscus with a rarefaction fan, and either undercompressive or classical waves for the advancing front, that arises for certain ranges of large substrate tilt and of precursor thickness

A theory for undercompressive shocks in tears of wine

We revisit the tears of wine problem for thin films in water-ethanol mixtures and present a new model for the climbing dynamics. The new formulation includes a Marangoni stress balanced by both the normal and tangential components of gravity as well as surface tension which lead to distinctly different behavior. The prior literature did not address the wine tears but rather the behavior of the film at earlier stages and the behavior of the meniscus. In the lubrication limit we obtain an equation that is already well-known for rising films in the presence of thermal gradients. Such models can exhibit non-classical shocks that are undercompressive. We present basic theory that allows one to identify the signature of an undercompressive (UC) wave. We observe both compressive and undercompressive waves in new experiments and we argue that, in the case of a pre-coated glass, the famous "wine tears" emerge from a reverse undercompressive shock originating at the meniscus

Behavior of thin colloidal films and fundamental studies of convective deposition

Colloidal assembly is emerging in different avenues of modern technology like photonics, membrane, quantum dots, and molecular adsorption devices. Fabricating network of colloidal particle is governed by the surface energy and fluid flows. As you go smaller in size, fundamental understanding of the process is crucial. Previous research in our group was focused on the different applications of using the particle networks. Fabricating these structures on a desired substrate, with a choice of particles, and a desirable number of layers is a tedious task. It demands the thorough understanding of process parameters and different interactions in the thin colloidal film. In the following work, we have separated the convective deposition into two parts. One is governed by thin film stability of solvent, particle interactions with substrate and interface, and interfacial properties, on the other hand, the second part is governed by the solvent flow through a porous structure of particles network. Separating one process into two bits helps in probing for more details. Previous models of convective deposition capture the essential physics over narrow ranges of parameters, however, there is much room for developing robust models over broader deposition conditions and understanding instabilities in this system. In the convective deposition, the suspension flow is driven by solvent evaporation. The widely used Nagayama equation for the convective deposition defines the evaporation loss as the product of the evaporation rate (Je) and drying length ( ). Here, is the hydrodynamic length scale, which for many years’ have been assumed as a constant. Even though it is safe to assume a constant value for in a small region of substrate velocity, it fails to predict the coating thickness over wide velocity range. Following the work done by Y. Jung et al. we have derived an analytical expression for the drying length in the convective deposition for a more general geometry, treating a system as a Darcy flow. This analysis allows the prediction of coating thickness over a wider range of substrate velocities. In depositing a thicker or smaller particles colloidal crystals, the evaporation driven hydrodynamic stress in the thin film causes crack formation. In such cases, the crack spacing varies with the thickness. This phenomenon is not new and has been observed in all length scales. It has been shown that, in a colloidal crystal, a crack spacing scales up with a hydrodynamic stress. Interestingly, the simultaneous 1D drying and particle deposition in convective deposition results in highly linear uniform cracks. We have shown that the crack spacing can be easily tuned with the deposition speed or the substrate temperature. These fundamental studies enable optimizing deposition conditions to produce various thin film structures for a given particle size, solvent, and stabilizing agent. As is done in many previous studies of convective deposition and evaporating droplets, an addition of a surfactant can significantly change the mode of deposition to be nearly independent of the evaporation rate and deposition velocity by altering this length scale and thin film flow. At lower surfactant concentrations, the added surfactant had no effects on the assembly. At higher surfactant concentrations above the critical micelle concentration, the marangoni stresses become the main driving force for the flow inside the thin film. This Marangoni flow which can be much stronger than that driven by the evaporation may be tailored to produce the desired particle depositions over a wide range of velocities. The direction of marangoni flow is important. We have studied the mixture of water-ethanol as a choice of solvent, which allows completely reverse results that of the excess surfactant concentration. We also have studied the particle-particle and particle-substrate interactions, which play a crucial role in the convective deposition. Following results demonstrates the non-trivial effects of varying surface charge and ionic strength of monosized silica microspheres in the water on the quality of the deposited monolayer. The increase in particle surface charge results in a broader range of parameters that result in monolayer deposition which can be explained considering the particle-substrate electrostatic repulsion in solution. Resulting changes in the coating morphology and microstructure at different solution conditions were observed using confocal microscopy enabling correlation of order to disorder transitions with relative particle stability. The following work discusses the novel way of isolating the inherent streaking instabilities happening in the convective deposition. With hydrophobic treating substrate in periodic areas allows one to separate these instabilities, leaving an ideal coating in between. The final part of this thesis is devoted to a relatively new scale-up technique of continuous particle assembly. We have studied the limitations on microstructure at higher substrate velocities as well as a smaller improvement in microstructure using a bidisperse silica suspension

The Meniscus-Guided Deposition of Semiconducting Polymers

The electronic devices that play a vital role in our daily life are primarily based on silicon and are thus rigid, opaque, and relatively heavy. However, new electronics relying on polymer semiconductors are opening up new application spaces like stretchable and self-healing sensors and devices, and these can facilitate the integration of such devices into our homes, our clothing, and even our bodies. While there has been tremendous interest in such technologies, the widespread adoption of these organic electronics requires low-cost manufacturing techniques. Fortunately, the realization of organic electronics can take inspiration from a technology developed since the beginning of the Common Era: printing. This review addresses the critical issues and considerations in the printing methods for organic electronics, outlines the fundamental fluid mechanics, polymer physics, and deposition parameters involved in the fabrication process, and provides future research directions for the next generation of printed polymer electronics

Dynamic unbinding transitions and deposition patterns in dragged meniscus problems

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.We sketch main results of our recent work on the transfer of a thin liquid film onto a flat plate that is extracted from a bath of pure non-volatile liquid. Employing a long-wave hydrodynamic model, that incorporates wettability via a Derjaguin (disjoining) pressure, we analyse steady-state meniscus profiles as the plate velocity is changed. We identify four qualitatively different dynamic transitions between microscopic and macroscopic coatings that are out-of-equilibrium equivalents of equilibrium unbinding transitions. The conclusion briefly discusses how the gradient dynamics formulation of the problem allows one to systematically extend the employed one-component model into thermodynamically consistent two-component models as used to describe, e.g., the formation of line patterns during the Langmuir-Blodgett transfer of a surfactant layer