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

Collapsed heteroclinic snaking near a heteroclinic chain in dragged meniscus problems

We study a liquid film that is deposited onto a flat plate that is inclined at a constant angle to the horizontal and is extracted from a liquid bath at a constant speed. We additionally assume that there is a constant temperature gradient along the plate that induces a Marangoni shear stress. We analyse steady-state solutions of a long-wave evolution equation for the film thickness. Using centre manifold theory, we first obtain an asymptotic expansion of solutions in the bath region. The presence of the temperature gradient significantly changes these expansions and leads to the presence of logarithmic terms that are absent otherwise. Next, we obtain numerical solutions of the steady-state equation and analyse the behaviour of the solutions as the plate velocity is changed. We observe that the bifurcation curve exhibits snaking behaviour when the plate inclination angle is beyond a certain critical value. Otherwise, the bifurcation curve is monotonic. The solutions along these curves are characterised by a foot-like structure that is formed close to the meniscus and is preceded by a thin precursor film further up the plate. The length of the foot increases along the bifurcation curve. Finally, we explain that the snaking behaviour of the bifurcation curves is caused by the existence of an infinite number of heteroclinic orbits close to a heteroclinic chain that connects in an appropriate three-dimensional phase space the fixed point corresponding to the precursor film with the fixed point corresponding to the foot and then with the fixed point corresponding to the bath.Comment: Final revised version. 18 pages. To be published in Eur. Phys. J.

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

Thin water films driven by air through surface roughness

The interaction between thin films and roughness surfaces has been studied when the thin viscosity-dominated films are driven by the air shear stress in the context of a high Reynolds number boundary layer theory. A number of properties of this model are examined, such as transport and pooling of water in a roughness field, heat transfer of film/roughness combinations, and rivulet formation. For rivulet formation due to the instability of two-dimensional film fronts, a general formula for the largest unstable wavelength, the fastest temporal growth rate, and the neutral wavelength has been developed from the linear instability analysis. This formula is validated using experimental data for film fronts on flat surfaces which are driven by constant surface tension gradients. This formula is also validated using numerical simulations of film fronts moving through various roughened surfaces.;To describe a water bead on a precursor film, a new disjoining pressure model is developed from a modified classical long-distance disjoining pressure model. This model satisfies the requirement that the disjoining pressure on the precursor film is larger than zero. Another advantage of this modified model is that an effective distance used in classical long-distance disjoining pressure models is avoided even when a water bead is on a dry surface. This model is validated using experimental data from aircraft icing tests

Modelling of driven free surface liquid films

In several types of coating processes a solid substrate is removed at a controlled velocity U from a liquid bath. The shape of the liquid meniscus and the thickness of the coating layer depend on U. These dependencies have to be understood in detail for non-volatile liquids to control the deposition of such a liquid and to lay the basis for the control in more complicated cases (volatile pure liquid, solution with volatile solvent). We study the case of non-volatile liquids employing a precursor film model that describes partial wettability with a Derjaguin (or disjoining) pressure. In particular, we focus on the relation of the deposition of (i) an ultrathin precursor film at small velocities and (ii) a macroscopic film of thickness h ∝ U^(2/3) (corresponding to the classical Landau Levich film). Depending on the plate inclination, four regimes are found for the change from case (i) to (ii). The different regimes and the transitions between them are analysed employing numerical continuation of steady states and saddle-node bifurcations and simulations in time. We discuss the relation of our results to results obtained with a slip model. In connection with evaporative processes, we will study the pinning of a droplet due to a sharp corner. The approach employs an evolution equation for the height profile of an evaporating thin film (small contact angle droplet) on a substrate with a rounded edge, and enables one to predict the dependence of the apparent contact angle on the position of the contact line. The calculations confirm experimental observations, namely that there exists a dynamically produced critical angle for depinning that increases with the evaporation rate. This suggests that one may introduce a simple modification of the Gibbs criterion for pinning that accounts for the non-equilibrium effect of evaporation

Visualization and modeling of evaporation from pore networks by representative 2D micromodels

Evaporation is a key process for the water exchange between soil and atmosphere, it is controlled by the internal water fluxes and surface vapor fluxes. The focus of this thesis is to visualize and quantify the multiphase flow processes during evaporation from porous media. The retained liquid films in surface roughness (thick-film flow) and angular corners (corner flow) have been found to facilitate and dominate evaporation. Using the representative 2D micromodels (artificial pore networks) with different surface roughness and pore structures, this thesis gives visualizations of the corner and thick-film flow during the evaporation process, presents the enhanced hydraulic continuity by corner and thick-film flow, and tests the validity of the SSC-model which assumes corner flow is dominant for the mass transport during evaporation. Surface roughness and wettability are proved both experimentally and theoretically to play a key role for the time and temperature behaviors of the evaporation process, besides, this thesis shows that for a consistent description of the time-dependent mass loss and the geometry of the corner/thick-film flow region, the fractality of the evaporation front must be taken into account