Browsing by Subject "Thermocapillarity"

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Investigations into the evolution of heated liquid films
(2024-08) Mohamed, Omair A. A.
The evolution of the free surface of a heated liquid film is directly tied to the performance and efficiency of various industrial systems. Therefore, we investigate the spatiotemporal evolution of heated liquid films across a range of different settings by formulating distinct of hydro-thermal models taking into account the effects of inertia, thermocapillarity, evaporation, gas shear, and thermal radiation, where we direct our modeling efforts in each problem on the most dominant physical phenomena. In liquid flows characterized by relatively low Reynolds numbers belonging to the drag-gravity flow regime, we model the hydrodynamics of the film using the long-wave expansion (LWE) methodology and perform linear stability analyses focused on the thermocapillary and evaporative instabilities, as they have a primary influence on the film’s evolution in this flow regime. Consequently, the evaporation process is governed by the competition between thermodynamic disequilibrium and diffusion effects dependent on the interface’s curvature. We modify the kinetic-diffusion evaporation model of Sultan et al. [Sultan et al., J. Fluid Mech. 543, 183, (2005)] and combine it with long-wave theory to derive a governing equation encapsulating the coupled dynamics. We then utilize linear stability theory to derive the system’s dispersion relationship, in which the Marangoni effect has two components. The first results from surface tension gradients driven by the uneven heat flux, while the second arises from surface tension gradients caused by imbalances in vapor diffusion. These two components interact with evaporative mass loss and vapor recoil in a rich and complex manner. Moreover, we identify an evaporation regime where a volatile film is devoid of evaporation instabilities. Furthermore, we investigate the effect of film thinning on its stability at the two opposing limits of the evaporation regime, where we find its impact in the diffusion-limited regime to be dependent on the intensity of evaporative phenomena. Finally, we conduct a spatiotemporal analysis which indicates that vapor diffusion effects are correlated with a shift towards absolute instability. In the second problem, we study the spatiotemporal evolution of an evaporating liquid film sheared by a gas and consider both the inertial and thermal instability modes, where the shearing gas is modeled by imposing a constant shear stress along the liquid’s interface. Interestingly, it’s inclusion in the problem allows the utilization of a one-sided evaporation model, which is precisely the transfer-rate-limited case of the first system we investigated. Once more long-wave theory is used to derive the an evolution for the liquid film which incorporates the role of the shearing gas. Afterwards, linear stability theory is used to investigate the temporal and spatiotemporal characteristics of the flow, where it is found that the evaporation of the film promotes absolute instabilities and can cause convective/absolute transitions. We also find that counter-flowing shearing gas can suppress the inertial instability affirming similar conclusions found by previous studies for a strongly confined isothermal film. Furthermore, the evolution interface equation was solved numerically to explore the film’s nonlinear stability. Moreover, we employ self-similarity analysis to probe the shear stress’s effect on the film’s rupture mechanics. In the third problem we research, the liquid flow’s Reynolds number is relatively high, and hence we utilize the weighted-residual integral boundary layer (WIBL) technique [C. Ruyer-Quil and P. Manneville,” Eur. Phys. J. B, 15, 357, (2000)], and direct our attention at directly simulating the temperature field across the film using reduced models. The WIBL hydrodynamic equations are derived expressions obtained via the boundary layer approximation, while the thermal profile is modeled by employing an asymptotic expansion which produces a hierarchy of models in which enhanced sophistication is offset by higher complexity and computational cost. These models are solved numerically revealing how the temperature field across the film is governed by a balance between the conduction across both the liquid film and the solid surface, and their respecitve radiative emissions, wherein these two transfer phenomena are linked through two corresponding dimensionless numbers associated with both the liquid film and the solid surface.
Open Access
An iterative solution approach to coupled heat and mass transfer in a steadily fed evaporating water droplet
(American Society of Mechanical Engineers, 2019) Akkuş, Y.; Çetin, Barbaros; Dursunkaya, Z.
Inspired by the thermoregulation of mammals via perspiration, cooling strategies utilizing continuously fed evaporating droplets have long been investigated in the field, yet a comprehensive modeling capturing the detailed physics of the internal liquid flow is absent. In this study, an innovative computational model is reported, which solves the governing equations with temperature-dependent thermophysical properties in an iterative manner to handle mass and heat transfer coupling at the surface of a constant shape evaporating droplet. Using the model, evaporation from a spherical sessile droplet is simulated with and without thermocapillarity. An uncommon, nonmonotonic temperature variation on the droplet surface is captured in the absence of thermocapillarity. Although similar findings were reported in previous experiments, the temperature dip was attributed to a possible Marangoni flow. This study reveals that buoyancy-driven flow is solely responsible for the nonmonotonic temperature distribution at the surface of an evaporating steadily fed spherical water droplet.
Open Access
Linear stability analysis of evaporating falling liquid films
(Elsevier, 2020) Mohamed, Hammam; Biancofiore, Luca
We consider the linear stability of evaporating thin films falling down an inclined plate. The one sided-model presented first by “Burelbach, J.P., Bankoff, S.G., Davis, S.H., 1988, Nonlinear stability of evaporating/condensing liquid films, Journal of Fluid Mechanics 195, 463–494. ” was implemented to decouple the dynamics of the liquid than those of the vapor at the interface, at which the evaporation is modeled based on a thermal equilibrium approach. We consider the base state solution derived by “Joo, S., Davis, S.H., Bankoff, S., 1991, Long-wave instabilities of heated falling films: two-dimensional theory of uniform layers, Journal of Fluid Mechanics 230, 117–146. ” which is based on the slow evaporation assumption. In previous works, only low dimensional models. i.e. the long wave theory, have been analysed for evaporating liquid films. Conversely in this paper, we extend the Orr-Sommerfeld eigenvalue problem for a film falling down a heated wall to include evaporation effects namely, vapor recoil and mass loss. As expected, we observe that the long wave theory fails in predicting the correct behavior when the inertia is strong or the wavenumber k is large. We confirm that the instability induced by vapor recoil (E-mode) behaves in a similar fashion to the instability due to the thermocapillary effect (S-mode). Both the S-mode and the E-mode can enhance each other, specially, at low Reynolds numbers Re. Moreover, we examine the perturbation energy budget to have an insight into the instabilities mechanism. We show that the presence of evaporation adds a new term corresponding to the work done by vapor recoil at the interface (VRE). We also find that the main contributor to the perturbation kinetic energy in the unstable E-mode is the work done by shear stress while VRE is negligible, unless Re << 1. Simpler analytical expressions of the energy balance terms near the instability threshold are obtained by using a long wave approximation.
Open Access
Modeling of evaporation from a sessile constant shape droplet
(ASME, 2017) Akkuş, Y.; Çetin, Barbaros; Dursunkaya, Z.
In this study, a computational model for the evaporation from a sessile liquid droplet fed from the center to keep the diameter of the droplet constant is presented. The continuity, momentum and energy equations are solved with temperature dependent thermo-physical properties using COMSOL Multi-physics. At the surface of the droplet, convective heat and evaporative mass fluxes are assigned. Since the flow field is affected by evaporative flux, an iterative scheme is built and the computation is automated using COMSOL-MATLAB interface. Correlations are implemented to predict the convective heat transfer coefficients and evaporative flux. Three different wall temperatures are used in simulations. The results show that the flow inside the droplet is dominated by buoyancy when the effect of the thermo-capillarity is neglected. The resulting flow generates a circulation pattern emerging from the entrance to the apex, along the surface of the droplet to the bottom heated wall and back to the entrance.
Open Access
A theoretical framework for comprehensive modeling of steadily fed evaporating droplets and the validity of common assumptions
(Elsevier, 2020) Akkuş, Y.; Çetin, Barbaros; Dursunkaya, Z.
A theoretical framework is established to model the evaporation from continuously fed droplets, promising tools in the thermal management of high heat flux electronics. Using the framework, a comprehensive model is developed for a hemispherical water droplet resting on a heated flat substrate incorporating all of the relevant transport mechanisms: buoyant and thermocapillary convection inside the droplet and diffusive and convective transport of vapor in the gas domain. At the interface, mass, momentum, and thermal coupling of the phases are also made accounting for all pertinent physical aspects including several rarely considered interfacial phenomena such as Stefan flow of gas and the radiative heat transfer from interface to the surroundings. The model developed utilizes temperature dependent properties in both phases including the density and accounts for all relevant physics including Marangoni flow, which makes the model unprecedented. Moreover, utilizing this comprehensive model, a nonmonotonic interfacial temperature distribution with double temperature dips is discovered for a hemispherical droplet having internal convection due to buoyancy in the case of high substrate temperature. Proposed framework is also employed to construct several simplified models adopting common assumptions of droplet evaporation and the computational performance of these models, thereby the validity of commonly applied simplifying assumptions, are assessed. Benchmark simulations reveal that omission of gas flow, i.e. neglecting convective transport in gas phase, results in the underestimation of evaporation rates by 23–54%. When gas flow is considered but the effect of buoyancy is modeled using Boussinesq approximation instead of assigning temperature dependent density throughout the gas domain, evaporation rate can be underestimated by up to 16%. Deviation of simplified models tends to increase with increasing substrate temperature. Moreover, presence of Marangoni flow leads to larger errors in the evaporation rate prediction of simplified models.