Stability of evaporating two-layered liquid film in the presence of surfactant—III. Non-linear stability analysis
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Disjoining pressure
ABSTRACT The extended thin film evaporation is analyzed during the constant drying rate period. The extended thin film is defined as the liquid film which the disjoining pressure dominates the fluid flow field and works as the driving force of replenishing the evaporating liquid. The results of the analysis show that the extended thin film evaporation can compensate the reduction of evaporation rate due to the increase of dry spots and keep the evaporation rate nearly constant. Experimental data in the literature are in good agreement with the results of this work. This implies that the extended thin film evaporation may be an important part of the mechanism for drying.
Disjoining pressure
Constant (computer programming)
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We explore the effect of disjoining pressure on a thin film equation in the presence of a non-uniform body force, motivated by a model describing the reverse draining of a magnetic film. To this end, we use a combination of numerical investigations and analytical considerations. The disjoining pressure has a regularizing influence on the evolution of the system and appears to select a single steady-state solution for fixed height boundary conditions; this is in contrast with the existence of a continuum of locally attracting solutions that exist in the absence of disjoining pressure for the same boundary conditions. We numerically implement matched asymptotic expansions to construct equilibrium solutions and also investigate how they behave as the disjoining pressure is sent to zero. Finally, we consider the effect of the competition between forcing and disjoining pressure on the coarsening dynamics of the thin film for fixed contact angle boundary conditions.
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Forcing (mathematics)
Zero (linguistics)
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Disjoining pressure
Line (geometry)
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We experimentally study steady Marangoni-driven surfactant transport on the interface of a deep water layer. Using hydrodynamic measurements, and without using any knowledge of the surfactant physico-chemical properties, we show that sodium dodecyl sulphate and Tergitol 15-S-9 introduced in low concentrations result in a flow driven by adsorbed surfactant. At higher surfactant concentration, the flow is dominated by the dissolved surfactant. Using Camphoric acid, whose properties are {\it a priori} unknown, we demonstrate this method's efficacy by showing its spreading is adsorption dominated.
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In film coating and other applications involving thin liquid films, surfactants are typically employed to suppress the usually undesirable instabilities driven by surface phenomena. Yet, in the present study a mechanism of Marangoni instability in evaporating thin films is presented and analyzed, which has its origin on the effects of a soluble surfactant. As the film thins due to evaporation, thickness perturbations lead to surfactant concentration perturbations, which in turn drive film motion and tend to enhance uneven drying. A thin-film analysis is applied and evolution equations for the film thickness and the surfactant concentration are derived and analyzed by the techniques of linear stability and numerical simulation. In the linear analysis a nonautonomous system is obtained for the film thickness and surfactant concentration perturbations, which shows that the instability will manifest itself provided that an appropriate Marangoni number is relatively large and the surfactant solubility in the bulk is large as well. On the other hand, low solubility in the bulk, diffusion, and the effect of surfactant on interfacial mobility through the surface viscosity are found to suppress disturbance growth. Direct numerical simulations of the full nonlinear evolution equations confirm those results and add to the picture obtained for the physical system behavior. Estimates of the relevant dimensionless parameters suggest that the conditions for instability may be met in relatively thick films, on the order of tens of microns, for which the effects of molecular forces and disjoining pressure are not dominant. Moreover, the stabilizing effects of diffusion and interfacial mobility are not likely to become significant unless the films are much thinner, i.e., on the order of 1 μm or below.
Disjoining pressure
Marangoni number
Dimensionless quantity
Lubrication theory
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Disjoining pressure
Marangoni number
Lubrication theory
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Disjoining pressure
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Development of disjoining pressure was performed to study the symmetric, Lennard-Jones (LJ) free thin films using molecular modelling. A methodology rooted from film thermodynamics was established to derive the disjoining pressure isotherm [Formula: see text], which is based on the surface tension at varied film thicknesses and can be viewed as a post-processing technique. The results showed that the disjoining pressure of LJ fluid is purely attractive. Compared with the complicated method reported previously, this methodology is demonstrated to be more convenient and readily applicable for other liquid films (e.g. water, aqueous thin films containing electrolyte or surfactants), meanwhile it can be applied at both low and high temperatures.
Disjoining pressure
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Disjoining pressure
Marangoni number
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