Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session A4: Drops I |
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Chair: Stephen Morris, University of California, Berkeley Room: 23C |
Sunday, November 18, 2012 8:00AM - 8:13AM |
A4.00001: Effects of microscale inertia on heat or mass transfer from a drop Deepak Krishnamurthy, Ganesh Subramanian Heat or mass transport from suspensions of solid particles or drops is ubiquitous in many industrial processes. In the zero inertia limit the transport is diffusion limited owing to the presence of closed streamlines around each particle. A small but finite amount of inertia though, results in a vastly different picture, greatly enhancing transport by destroying the closed streamline configuration. We develop a theoretical formulation to study the effects of weak inertia on transport from a density-matched drop in a 2D linear flow. It is shown that, unlike a solid particle, the near-surface streamlines are closed only when the viscosity ratio \textit{($\lambda )$} exceeds a critical value \textit{$\lambda $}$_{c}$\textit{=2$\alpha $/(1-$\alpha )$}, where $\alpha $ is the linear flow parameter measuring relative magnitudes of extension and vorticity. The velocity field on the drop surface can be characterized using a complex-valued analogue of the \textit{(C,$\tau )$} coordinate system used to describe Jeffrey orbits of an axisymmetric particle. In the open-streamline case \textit{($\lambda <\lambda $}$_{c})$, convective transport occurs even with zero inertia, and for large Peclet number (\textit{Pe}) (the relative magnitude of convective to diffusive transport), the Nusselt number (dimensionless rate of heat transfer) is expected to scale as \textit{F($\alpha $,$\lambda )$Pe}$^{1/2}$ and is determined via a boundary layer analysis in the \textit{(C,$\tau )$} coordinate system. In the closed streamline case \textit{($\lambda >\lambda $}$_{c})$, similar to the solid particle, inertia plays a crucial role, and the Nusselt number must scale as \textit{G($\alpha $,$\lambda$Re}$^{1/2}$\textit{Pe}$^{1/2}$. A methodology is developed to analyze the convection along spiraling streamlines using a physically motivated choice of coordinate system on the drop surface. [Preview Abstract] |
Sunday, November 18, 2012 8:13AM - 8:26AM |
A4.00002: When a water drop freezes before it solidifies Pirouz Kavehpour, Stephen Davis, Faryar Tavakoli When a drop of liquid is placed on a substrate which temperature is below the melting point of the liquid, one would expect the drop to solidify instantaneously. However, many liquids, such as water, must be subcooled to solidify below its melting temperature due to homogeneous nucleation's high activation energy. Most of the drop solidification research, particularly for water, phase change is assumed to occur at equilibrium freezing temperature; however, this is not the case. We found that after a certain degree of supercooling, a kinetic based nucleation begins and latent heat of fusion is suddenly liberated, causing an increase in liquid temperature. At the end of this stage, approximately 20\% of the drop is crystallized. This phenomenon is known among metallurgists as recalescence. This is followed by a slow solidification process at the melting point. As a water droplet spreads on a cold substrate, its contact line stops just prior to freezing inception from the liquid-solid interface. In this study, we assert that recalescence prior to solidification may be the cause of water's sudden immobility, which results in a fixed contact angle and droplet diameter. In our experiments, the nucleation front initiates from the trijunction point and propagates to the drop volume. [Preview Abstract] |
Sunday, November 18, 2012 8:26AM - 8:39AM |
A4.00003: Fluid Dynamics of Condensed Droplets on Hybrid Surfaces Chun Wei Yao, Jorge Alvarado, Charles Marsh, Anthony Jacobi Droplets impinging on hybrid surfaces consisting of a micropillar array of hydrophobic and hydrophilic sites exhibit a distinct wetting behavior that can be estimated using a surface energy-based model. However, condensed droplets display a quite different wetting behavior when they grow on hybrid surfaces. In this study, hybrid surfaces with four different spacing ratios were tested in a condensation cell. For hybrid surfaces with spacing ratio below 2, initial droplets form on the top of the micropillars, and then grow and coalesce with adjacent droplets, which shed after they reach a given size. After shedding, the top surface remains partially dry which allows for faster droplet re-nucleation. Droplet growth and coalescence continue until very large droplets are formed which is a characteristic behavior of Wenzel droplets For hybrid surfaces with spacing ratio equal to 2, a quite interesting wetting behavior is observed when droplets coalesce. The coalesced droplets form a thin liquid film, which sheds eventually under the right conditions. The results indicate that spacing ratio is the key factor for having different fluid dynamics of condensed droplets on hybrid surfaces. [Preview Abstract] |
Sunday, November 18, 2012 8:39AM - 8:52AM |
A4.00004: Evaporation control of a drop on fibers Camille Duprat, Alison D. Bick, Howard A. Stone The evaporation dynamics of mist from a fibrous material has important industrial and environmental consequences. In order to understand the drying kinetics of a fiber array, we study a drop sitting on two parallel fibers and, in particular, investigate how the structure and mechanical properties of the material affect the drying dynamics. A drop deposited on two parallel fibers can adopt different shapes, depending on the drop volume, the interfiber distance, the surface tension of the liquid and the fiber radius and elasticity. A given volume of liquid on a given pair of fibers can adopt two distinct morphologies. These two states exhibit different drying kinetics that greatly affects the overall drying time. In addition, flexible fibers undergo deformation that leads to spontaneous spreading, hence to an increased drying rate. The drying kinetics is thus controlled by the fiber elasticity. Furthermore, during evaporation, the drop can change morphology, which counterintuitively results in an increased wetted area during drying. [Preview Abstract] |
Sunday, November 18, 2012 8:52AM - 9:05AM |
A4.00005: Directional motion of evaporating droplets on gradient surfaces Shuhuai Yao, Li Xu, Zhigang Li Droplet evaporation on surfaces has various applications in drying problems such as ink-jet printing, pesticide spraying, chemical or biological detection, and DNA microarray spotting technology. Controlling evaporating droplets via substrate morphology and/or wetting properties allows for efficient deposition of sample molecules in these applications. In this work, evaporation of sessile water droplets on surfaces with wettability gradients was studied. The wettability gradient was generated by fabricating non-uniformly distributed cylindrical micropillars on silicon surfaces. During the evaporation, it was found, along the wettability gradient, that the contact line on one side was strongly pinned, while the contact line on the other side depinned and gradually receded, making the center of mass of the droplet move either in or against the direction the wettability gradient, depending on the configuration of the micropillars. The theoretical criterion predicting the moving direction was derived based on the excess free energy and the energy barrier during the evaporation. The theoretical predications agreed well with the experimental observations. The results provide a parametric design basis to control the contact line dynamics and directional transport of evaporating droplets. [Preview Abstract] |
Sunday, November 18, 2012 9:05AM - 9:18AM |
A4.00006: Apparent contact angle of an evaporating drop S.J.S. Morris In experiments by Poulard et al. (2005), a sessile drop of perfectly wetting liquid evaporates from a non--heated substrate into an under--saturated mixture of vapour with an inert gas; evaporation is limited by vapour diffusion. The system exhibits an apparent contact angle $\theta$ that is a flow property. Under certain conditions, the apparent contact line was stationary relative to the substrate; we predict $\theta$ for this case. Observed values of $\theta$ are small, allowing lubrication analysis of the liquid film. The liquid and vapour flows are coupled through conditions holding at the phase interface; in particular, vapour partial pressure there is related to the local value of liquid pressure through the Kelvin condition. Because the droplet is shallow, the interfacial conditions can be transferred to the solid--liquid interface at $y=0$. We show that the dimensionless partial pressure $p(x,y)$ and the film thickness $h(x)$ are determined by solving $\nabla^2 p =0$ for $y>0$ subject to a matching condition at infinity, and the conditions $-p={\cal L} h_{xx} + h^{-3}$ and $(h^3 p_x)_x + 3 p_y=0$ at $y=0$. The parameter $\cal L$ controls the ratio of Laplace to disjoining pressure. We analyse this b.v.p. for the experimentally--relevant case ${\cal L}\to 0$. [Preview Abstract] |
Sunday, November 18, 2012 9:18AM - 9:31AM |
A4.00007: Thermal Effects of the Substrate on Water Droplet Evaporation Benjamin Sobac, David Brutin Since a few decades, the evaporation of a drop deposited onto a substrate has been subject to numerous research activities due to the increase of the range of applications underpinned by this phenomenon. However, this process today is always a challenging problem in soft matter physics due to the complexity of present couplings: fluid dynamic, physical chemistry of the substrate, heat and mass transfer. The originality of the presented experiment is to decouple the effects of wetting properties and thermal properties of the substrate. Thus, whereas we previously presented the role of wetting properties on evaporation by changing the surface energy and the roughness while maintaining the thermal properties constant thanks to nanoscale coatings on the substrate surface (B. Sobac and D. Brutin, Langmuir 27, 14999 (2011)), we investigate here the influence of the thermal properties of the substrate while keeping the wetting properties the same (B. Sobac and D. Brutin, Phys. Rev. E, underpress). We experimentally investigate the behavior of a pinned droplet evaporating into air. The influences of the substrate temperature and substrate thermal properties on the evaporation process are studied in both hydrophilic and hydrophobic conditions. Experimental data are compared to the quasi-steady diffusion-driven evaporation model assuming the isothermia of the drop at the substrate temperature. This comparison permits to highlights several thermal mechanisms linked to evaporation and their respective contributions in regard of pure mass diffusion mechanism. The range of validity of the classical evaporation model is also discussed. [Preview Abstract] |
Sunday, November 18, 2012 9:31AM - 9:44AM |
A4.00008: Dropwise condensation on a cold gradient substrate Ashley Macner, Susan Daniel, Paul Steen Distributions of drops that arise from dropwise condensation evolve by nucleation, growth, and coalescence of drops. An understanding of how surface-energy gradients applied to the substrate affect drop growth and coalescence is needed for design of effective surfaces for large-scale dropwise condensation. Transient dropwise condensation from a vapor phase onto a cold and chemically treated surface is reported. The surfaces were treated to deliver either a uniform contact-angle or a gradient of contact-angles by silanization. The time evolution of drop-size and number-density distributions is reported. For a typical condensation experiment, the drop distributions advance through two stages: an increase in drop density as a result of nucleation and a decrease in drop density as a result of larger scale coalescence events. Because the experiment is transient in nature, the shape of the distribution can be used to predict the number of drop generations and their stage of development. Preliminary results for gradient surfaces will be discussed and compared against observations of behavior on uniformly coated surfaces. [Preview Abstract] |
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