Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session F12: Drops: Heat Transfer and Evaporation IIIDrops

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Chair: Alvaro Marin, Max Planck + University of Twente Center for Complex Fluid Dynamics Room: 505 
Monday, November 20, 2017 8:00AM  8:13AM 
F12.00001: Effect of wettability and topological features of Namib beetle inspired bumps on dropwise condensation. SHAKEEL AHMAD, Hui Tang, Haimin Yao The Stenocara beetle lives in arid desert environment where the only available source of water is fog droplets. The beetle contains many hydrophobic/hydrophilic bumps on its back. Water collection occurs on the hydrophilic patches. Once the droplet reaches the critical volume, it sheds down due to gravity. Although a number of studies on condensation and water collection on beetle inspired structures have been reported in literature, most of them were on micro/nano scale textures. However, in nature the beetle bumps are in millimeter scale. At this scale the role of topological features and gravity becomes crucial for early droplet shedding. Therefore, in this work we numerically investigated the effects of bump shape, wettability contrast, surface slope and hydrophilic patch to total area ratio on droplet shedding volume and time. A threedimensional lattice Boltzmann method (LBM) based numerical framework was used for the simulations. Compared with bumps of other shapes such a cube or a circular cylinder, faster droplet shedding was obtained over a hemispherical bump. Furthermore, it was found that larger hydrophilic patch to total area ratio for the hemispherical bump significantly increased the droplet shedding time. [Preview Abstract] 
Monday, November 20, 2017 8:13AM  8:26AM 
F12.00002: Lubrication model for evaporation of binary sessile drops Adam Williams, Pedro Sáenz, George Karapetsas, Omar Matar, Khellil Sefiane, Prashant Valluri Evaporation of a binary mixture sessile drop from a solid substrate is a highly dynamic and complex process with flow driven both thermal and solutal Marangoni stresses. Experiments on ethanol/water drops have identified chaotic regimes on both the surface and interior of the droplet, while mixture composition has also been seen to govern drop wettability. Using a lubricationtype approach, we present a finite element model for the evaporation of an axisymmetric binary drop deposited on a heated substrate. We consider a thin drop with a moving contact line, taking also into account the commonly ignored effects of inertia which drives interfacial instability. We derive evolution equations for the film height, the temperature and the concentration field considering that the mixture comprises two ideally mixed volatile components with a surface tension linearly dependent on both temperature and concentration. The properties of the mixture such as viscosity also vary locally with concentration. We explore the parameter space to examine the resultant effects on wetting and evaporation where we find qualitative agreement with experiments in both these areas. This enables us to understand the nature of the instabilities that spontaneously emerge over the drop lifetime. [Preview Abstract] 
Monday, November 20, 2017 8:26AM  8:39AM 
F12.00003: 3D unsteady computations of evaporative instabilities in a sessile drop of ethanol on a heated substrate David Brutin, Sergey Semenov, Florian Carle, Marc Medale Droplets are ubiquitous and have been studied for century. However, the flow pattern and instabilities occurring during evaporation are still under investigations and their origin is still debated. In this letter, we are comparing an ethanol drop evaporating onto a heated substrate under weightlessness conditions and with pinned contact line with a 3D unsteady computation of thermoconvective instabilities to determine with accuracy the type of instabilities. Our onesided model, devoid of fitting parameters, demonstrates quantitative agreement with experimental data and confirms that experimentally observed instabilities are driven by thermocapillary stress, and not by the gas convection. By creating creating a numerical infrared image, we can conclude with certitude that the experimentally observed thermoconvective instabilities in evaporating sessile drops of volatile liquids, which in infrared spectrum look similar to hydrothermal waves, are actually nothing else than unsteady B\'{e}nardMarangoni instability. [Preview Abstract] 
Monday, November 20, 2017 8:39AM  8:52AM 
F12.00004: Droplet evaporation and combustion in a liquidgas multiphase system METIN MURADOGLU, Muhammad Irfan Droplet evaporation and combustion in a liquidgas multiphase system are studied computationally using a fronttracking method. One field formulation is used to solve the flow, energy and species equations with suitable jump conditions. Both phases are assumed to be incompressible; however, the divergencefree velocity field condition is modified to account for the phase change at the interface. Both temperature and species gradient driven phase change processes are simulated. Extensive validation studies are performed using the benchmark cases: The Stefan and the sucking interface problems, $d^2$ law and wet bulb temperature comparison with the psychrometric chart values. The phase change solver is then extended to incorporate the burning process following the evaporation as a first step towards the development of a computational framework for spray combustion. We used detailed chemistry, variable transport properties and ideal gas behaviour for a nheptane droplet combustion; the chemical kinetics being handled by the CHEMKIN. An operatorsplitting approach is used to advance temperature and species mass fraction in time. The numerical results of the droplet burning rate, flame temperature and flame standoff ratio show good agreement with the experimental and previous numeric [Preview Abstract] 
Monday, November 20, 2017 8:52AM  9:05AM 
F12.00005: Numerical investigation of the droplet condensation on the horizontal surface with patterned wettability JaeYong Cho, JoonSang Lee The condensation is the one of the efficient heat transfer phenomenon that transfers the heat along an interface between two phases. This condensation is affected by the wettability of surface. Heat transfer rate can be improved by controlling the wettability of surface. Recently, the researches with patterned wettability, which is composed by a combination of hydrophilic and hydrophobic surface, have been performed to improve the heat transfer rate of condensation. In this study, we performed numerical simulation for condensation of droplet on the patterned wettability, and we analyze condensation phenomenon on the wettability pattered surface through the kinetic energy, heat flux curve, and droplet shape in the vicinity of the droplet. When we performed numerical simulations and analyzing the condensation with patterned wettability, we used the lattice Boltzmann method for the base model, and phase change was solved by PengRobinson equation of sate. We can find that the droplet is generated at the bottom surface and high condensation rate can be maintained on the patterned wettability. [Preview Abstract] 
Monday, November 20, 2017 9:05AM  9:18AM 
F12.00006: Structure evolution in the evaporation of complex fluids Urvashi Gupta, Arandeep S. Uppal, Richard V. Craster, Omar K. Matar Thixotropy has been of increasing interest for a variety of applications. Ideal thixotropy is defined as a reduction in viscosity during flow and subsequent recovery during rest and is usually attributed to a dynamic internal structure within the fluid, typically modelled by the inclusion of an extra parameter, $\lambda$, denoting the level of internal structure development. Complex particleladen fluids exhibit thixotropy and furthermore can undergo gelation during evaporation. Hence, we consider the evaporation of thixotropic droplets, where we build upon previous models and link structure evolution to the particle concentration. The model is further extended to include a yield stress and thus an evolving pseudoplug is observed during the evaporative process, and a systematic parametric study is undertaken. [Preview Abstract] 
Monday, November 20, 2017 9:18AM  9:31AM 
F12.00007: Diffusive boundary layers at the bottom of gaps and cracks Merlin A Etzold, Julien R Landel, Stuart B Dalziel This work is motivated by the chemical decontamination of droplets of chemical warfare agents trapped in the gaps and cracks found in most manmade objects. We consider axial laminar flow within gaps with both straight and angled walls. We study the diffusive mass transfer from a source (e.g. a droplet surface) located at the bottom of the gap. This problem is similar to boundary layers and Graetztype problems (heat transfer in pipe flow) with the added complication of a nonuniform lateral concentration profile due to the lateral variation of the velocity profile. We present 3D solutions for the diffusive boundary layer and demonstrate that a 2D meanfield model, for which we calculate series and similarity solutions, captures the essential physics. We demonstrate the immediate practical relevance of our findings by comparing decontamination of a droplet located in a gap and on an exposed surface [Landel et al., JFM (2016), vol. 789, pp. 630668]. [Preview Abstract] 
Monday, November 20, 2017 9:31AM  9:44AM 
F12.00008: Simplified conditions holding at the gasliquid interface during evaporation S.J.S. Morris We show that on the gas side of the interface between a pure liquid and a binary mixture of its vapour with an insoluble gas, the normal derivative of vapour partial pressure $p_v$ satisfies $ \frac{\partial p_v}{\partial n} +\frac{\alpha c}{2\pi pD}(Pp_v)(pp_v)=0. $ Constants $\alpha$, $c$, $D$ denote the dimensionless accommodation coefficient, a molecular speed and the diffusivity. Provided the continuum approximation holds within the gas, and $\alpha=O(1)$, this boundary condition implies that evaporation can take one of two forms. (a) If the coexistence pressure $P$ evaluated at the interface is less than the constant total gas pressure $p$, liquid at the interface is in local thermodynamic equilibrium with its vapour, and the evaporation rate is determined by diffusion through the gas. (b) Conversely, if $P>p$, gas at the interface consists of pure vapour, and the evaporation rate is determined by processes within the liquid. In the Wayner theory of the heated evaporating meniscus, such as that in a heat pipe, case (b) is assumed. As an application of our result, we show that some of the published experiments intended to test the Wayner theory instead operate under conditions in which case (a) holds. As a result, they do not perform the test intended. [Preview Abstract] 
Monday, November 20, 2017 9:44AM  9:57AM 
F12.00009: Evaporation of a sessile droplet on a slope Amir Jarrahi Darban, Saeed Jafari Kang, Hassan Masoud We theoretically examine the drying of a droplet sitting stationary on an incline, assuming that the effect of gravity relative to the surface tension is weak, i.e., Bond number (Bo) is small. We express the shape of the drop and the vapor concentration field as perturbation expansions in terms of Bo. We suppose that the evaporation results from a purely diffusive transport of the vapor phase and that the contact line is a pinned circle. At the zerothorder (Bo $=$ 0), the droplet takes the form of a spherical (or cylindrical in 2D) cap, for which the vapor concentration field is already known. Here, the YoungLaplace and Laplace equations are solved analytically to calculate the firstorder corrections to the shape and concentration field, respectively. Perhaps surprisingly, we find that, to the leading order in Bo, the asymmetry caused by the component of gravity parallel to the slop does not contribute to the total evaporation rate. This result can also be obtained using the reciprocal theorem without even solving for the firstorder correction to the concentration field. Finally, comparison with direct numerical simulations indicates that considering only the leading order corrections provides estimates that are valid well beyond the limit of very small Bo. [Preview Abstract] 
Monday, November 20, 2017 9:57AM  10:10AM 
F12.00010: Halfspace problem of weak evaporation and condensation Takeru Yano The halfspace problem of weak evaporation and condensation is considered on the basis of the numerical solution of Boltzmann–Krook–Welander equation. The problem has been studied extensively by Sone and his colleagues for the case of completecondensation condition. In a previous paper (Fluid Dynamics Research 40 (2008) 474–484), the author has introduced a generalized boundary condition and shown that the solution of the problem with the generalized boundary condition can be transformed into the solution with the completecondensation condition. In the present study, using accurate numerical solutions, we investigate the relation among the data at infinity and the temperature at the interface in the case of the generalized boundary condition, which serves as the boundary condition for the equations of fluid dynamics when weak evaporation or condensation takes place at the interface. [Preview Abstract] 
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