Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session ND: Rising and Spreading of Drops and Bubbles |
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Chair: Jacques Magnaudet, University of Toulouse Room: Hilton Chicago Continental A |
Tuesday, November 22, 2005 11:01AM - 11:14AM |
ND.00001: Dynamics of a rising bubble; Interactions between path, wake and shape oscillations Christian Veldhuis, Peter Van Oostrum, Arie Biesheuvel, Leen Van Wijngaarden, Detlef Lohse Single bubbles rising in quiescent purified water have been studied experimentally in the equivalent diameter range 1-6 millimeters. High speed recordings (500-1000 fr/s), in a stereoscopic Schlieren setup, provide insight on bubble path, shape and wake. Past research has been mainly on small bubbles. In the current research the bubble size is increased such that shape oscillations set in. Our experiments give information on the onset of bubble shape oscillations and the different wake structures that occur as the bubble diameter increases. The well-known double-threaded wakes are observed for smaller bubbles, shape oscillations are not observed in this regime (D$\sim$2mm), bubbles are axi-symmetric. Somewhat larger bubbles (D$\sim$3mm) show specific vortex shedding frequencies, shape oscillations set in and axi-symmetry breaks. Even larger bubbles (D$\sim$4mm) have a turbulent wake where no specific frequencies can be detected. Interesting observations are made with respect to the coupling of shape oscillations and wake structure. It turns out that there are two basic shape oscillation modes in the intermediate regime (D$\sim$3mm). These shape oscillations can be linked with oscillations in bubble velocity and wake structure. [Preview Abstract] |
Tuesday, November 22, 2005 11:14AM - 11:27AM |
ND.00002: Hydrodynamic interaction of a pair of bubbles rising in a quiescent liquid. Toshiyuki Sanada, Masao Watanabe Interaction effects on the motions of a pair of bubbles, which either rose in vertical line or side by side, in silicon oil pool were experimentally studied. A pair of bubbles rising in vertical line was generated by releasing bubbles successively from a single nozzle, while one rising side by side was generated, by releasing bubble simultaneously from a pair of horizontally placed orifices. Bubble diameter and liquid kinematic viscosity were taken as the experimental parameters. The motions of bubbles were recorded by a high-speed camera with 2000 fps. We observed that Reynolds number significantly affected the motions of a pair of bubbles rising both in vertical line and side by side. When a pair of bubbles rose in vertical line, the trailing bubble was attracted by the leading bubble wake, and then it collided with leading bubble, in the case of low Re, while a pair of bubbles kept a mutual equilibrium distance due to the balance between the leading bubble wake attractive force and potential repulsive force, in the case of intermediate Re. As Re further increased, the trailing bubble oscillated and then escaped from the vertical line. When a pair of bubbles rose side by side, they separated from each other as they rose in the case of low Re, while they attracted each other and then collided if the initial bubble horizontal distance was smaller than a critical value, in the case of large Re. [Preview Abstract] |
Tuesday, November 22, 2005 11:27AM - 11:40AM |
ND.00003: Boundary integral method for viscous potential flows: Three-dimensional dynamics of rising and oscillating bubbles. Kumar Bobba, Cheng Wang, Dan Joseph, Mory Gharib In this work a novel boundary integral method is developed for simulating viscous, potential flows (BEMVPF) containing evolving interfaces. The key idea is that, in potential flows the divergence of the shear stress tensor vanishes, but the shear stress tensor itself does not vanish. As a result of this, viscosity enters in the normal shear stress boundary condition, but not in the evolution equations. We show that this additional viscosity in the free boundary condition can be considered as a more general regularization procedure for the underlying equations. The boundary element method is implemented in the indirect form as a Fredholm integral equation of first kind with an immersed source boundary. This formulation circumvents the need for calculating the higher order derivatives of potential on the boundary, and allows for an optimal balance between the well-posedness of the operator and evaluating singular integrals. This new BEMVPF is applied to understand the three-dimensional and time dependent dynamics of a rising and oscillating bubble in a viscous ambient liquid in unbounded domain. The effect of an infinite rigid vertical boundary on the bubble motions is also studied numerically. The BEMVPF bubble computational results are excellent and are able to capture many new features that are not possible by traditional inviscid, potential flow bubble simulations. [Preview Abstract] |
Tuesday, November 22, 2005 11:40AM - 11:53AM |
ND.00004: The lift force on an oblate bubble rising in a shear flow Jacques Magnaudet, Richard Adoua, Dominique Legendre The flow about an oblate spheroidal bubble set fixed in a simple shear flow is studied using DNS. The bubble has a prescribed shape and its aspect ratio is varied from 1 to 2.5, while the Reynolds number is varied from some units to 2000. The dimensionless shear rate is also varied by one order of magnitude. The results indicate that for large enough aspect ratios, the lift force passes through a pronounced minimum for a Reynolds number of some hundreds. Within a finite range of Reynolds number about this minimum, the lift force may even be negative, making the bubble migrate in a direction opposite to that predicted by inviscid theory. In contrast, the positive value of the lift force predicted by this theory is recovered at large enough Reynolds number. An analysis of the flow field reveals that the asymmetry of the separated near wake (which for a clean bubble exists only for large enough aspect ratios) is responsible for the lift reversal. Within a certain range of Reynolds number the wake is unstable, so that the lift force due to the shear combines with that due to the wake instability, resulting in an oscillating total lift force. [Preview Abstract] |
Tuesday, November 22, 2005 11:53AM - 12:06PM |
ND.00005: The motion of a clean bubble confined between two vertical walls B. Figueroa, R. Zenit, D. Legendre In nature, as well as in many engineering applications, the effects of confining walls on bubbly flows play an important role. Problems of practical interest where this situation occurs are such as underground water wells and naturally fractured oil reservoirs. Most fundamental studies do not include the effects of walls. The confinement effect on the drag over a bubble was investigated both experimentally and numerically. The experiments were performed with non polar liquids such that the bubble surface could be considered clean. Single bubble experiments and numerical simulations were performed for different Reynolds numbers and dimensionless distances between walls. It was found that the effect of confinement is very strong: the drag can be as much as two times that of a free rising bubble. The comparison between the simulations, performed with the JADIM code, showed good agreement with the experimental results. Both numerical and experimental drag coeficients were found to depend on the dimensionless distance $s=(a/R)$, where $a$ is the bubble radius and $R$ is the distance between walls. The form of this dependency fits closely the form $C_d/C_{d\infty}[1+8s^3+O(s^4)]$. Additionally, it was observed that for large $Re$ the bubble trajectory is unstable, in the sense that it begins to oscillate above certain critical Reynolds; In fact the bubble bounces back and forth from one wall to the other. This instability is different from that observed in freely rising bubbles. [Preview Abstract] |
Tuesday, November 22, 2005 12:06PM - 12:19PM |
ND.00006: Trajectories of air bubbles rising in dense suspensions in a Hele-Shaw cell Ramon Sanchez, Ramon Herrera, Cesar Romo, Eduardo Ramos The motion of bubbles rising in a glass bead-water suspension is investigated experimentally. Observations have been conducted in a suspension confined between two vertical glass plates separated 3 mm. We report experimental results of the velocity and the path of air bubbles rising with various equivalent diameters in the range 1 to 4 mm and generation frequencies in the range 1 to 10 bubbles/s. The glass spheres in the suspension have diameters in the range 5 $\mu$m to 100$\mu$m and are hollowed with an effective density of 1.05 g/cm$^3$. Suspension concentrations used are up to 55$\%$ by weight. Observations indicate that bubble trajectories for concentrations of 30$\%$ and higher are composed by the general ascending trend plus rapid zigzagging displacements superimposed to a relative slow horizontal oscillation. This dynamics contrasts with the almost rectilinear paths of bubbles of the same diameter rising in pure water. We have also observed that for low concentrations, the bubble rising velocity depends on the departing frequency at the bottom of the cell. [Preview Abstract] |
Tuesday, November 22, 2005 12:19PM - 12:32PM |
ND.00007: A Diffuse Interface Model for Electrowetting Droplets In a Hele-Shaw Cell Hsiang-Wei Lu, Glasner Karl, Andrea Bertozzi, Chang-Jin Kim Electrowetting has recently been explored as a mechanism for moving small amounts of fluid in confined spaces. We propose a diffuse interface model for droplet motion, due to electrowetting, in Hele-Shaw geometry. In the limit of small interface thickness, asymptotic analysis shows the model is equivalent to Hele-Shaw flow with a voltage-modified Young-Laplace boundary condition on the free surface. We show that details of the contact angle significantly affect the timescale of motion in the model. We measure receding and advancing contact angles in the experiments and derive their influences through a reduced order model. These measurements suggest a range of timescales in the Hele-Shaw model which include those observed in the experiment. The shape dynamics and topology changes in the model agree well with the experiment, down to the length scale of the di®use interface thickness. [Preview Abstract] |
Tuesday, November 22, 2005 12:32PM - 12:45PM |
ND.00008: Multiscale modeling in the numerical computation of isothermal nonwetting Marc K. Smith, G. Paul Neitzel A state of permanent, isothermal nonwetting of a solid surface by a normally wetting liquid may be achieved by having the surface move tangential to a liquid drop being pressed against it. Surrounding gas is swept into the space between the liquid and solid, creating a lubricating film that prevents wetting. The length scales of the drop and the film are typically three or more orders of magnitude different, making numerical simulation difficult from a resolution standpoint. A hybrid computational approach employing lubrication theory for the thinnest portions of the gas film and a finite element simulation for the liquid and outer gas phases is presented. The model problem is a steady, two-dimensional flow between parallel solid surfaces with the drop attached to the upper surface. Results are presented for a silicone oil drop with air as the surrounding gas. The drop shape, flow field, and forces on the drop are determined as functions of the Reynolds number, the flow rate through the system, and the solid surface separation distance. As the drop approaches the lower surface, both leftward-leaning and rightward-leaning drop shapes are possible, but there is a range of flow rates where steady solutions are not found. When the separation distance is less than the radius of the undisturbed hemispherical drop, only left-leaning drop shapes are found. The reasons for this behavior are explained in terms of the lubrication pressure field beneath the drop. [Preview Abstract] |
Tuesday, November 22, 2005 12:45PM - 12:58PM |
ND.00009: Advancing contact line in presence of colloids. Laurent Limat, Emmanuelle Rio, Adrian Daerr, Fran\c{c}ois Lequeux Coating a solid with colloids often involves an advancing moving contact line that leaves behind a thin film progressively evaporating. We have investigated the interaction between wetting and colloids on a simple experiment: a drop of colloid is pushed at constant speed over a solid. Depending on the drop velocity V and on the colloid concentration c, different behaviours are observed. At low c or high V, the contact line remains stationary. At high c or low V, a stick-slip motion of the contact line is observed. This induces irregularities of the colloid deposition, explored by transmission electron microscopy. We have investigated these phenomena varying drop speed and colloid concentration, and proposed a simple physical model of the stick-slip appearance and of its properties. [Preview Abstract] |
Tuesday, November 22, 2005 12:58PM - 1:11PM |
ND.00010: Contact angle saturation in electrocapillary effect Shaun Berry, Jakub Kedzierski, Behrouz Abedian Electrocapillary behavior results from a reduction of the surface energy at the solid/liquid interface due to an applied electrical potential. The effect causes the contact angle of a hydrophobic liquid droplet to decrease and wet the solid surface. Controlling this effect has potential applications in microfluidic devices. A limiting behavior is contact angle saturation. Contact angle saturation occurs when a high enough voltage is applied to the liquid phase resulting in a limiting contact angle beyond which there is no change in the droplet shape regardless of the applied voltage. This paper presents recent experimental results of our investigation into the parameters effecting electrocapillary behavior of the alkane/water/surfactant system. We also present a model explaining contact angle saturation and provide results on parameters such as surfactant concentration and temperature on this phenomenon. [Preview Abstract] |
Tuesday, November 22, 2005 1:11PM - 1:24PM |
ND.00011: Variational Approach to Modeling Droplet Spreading/Recoiling and Comparison with Experiments Manish Tiwari, Ilker Bayer, Constantine Megaridis The dynamics of droplet spreading and recoiling on a flat substrate is modeled through the variational approach, based on the work of Kim and Chun (2001). The geometry of the droplet after impact is modeled separately as either a cylinder or a truncated sphere. The effect of variation of dynamic contact angle with contact line velocity is included. The molecular kinetic theory by Blake and Haynes (1969), and the hydrodynamic theory by Cox (1998) have been adopted to model wetting dynamics. Systematic parameter studies are carried out to demonstrate the effect of substrate surface energy, liquid surface tension and other rheological properties. The droplet wetting and dewetting dynamics is observed to be very sensitive to the specific dynamic contact angle relationship. The parametric values are tuned to match the experimental data, thus producing molecular kinetic and hydrodynamic parameters for different substrate/liquid combinations. The parameters so obtained compare well with data published in the literature. The experimental data seem to be bounded between the cylindrical and truncated sphere model results and appear to provide a convenient tool for understanding the physics of competition among kinetic, potential and viscous dissipation of energy when a droplet strikes a substrate. [Preview Abstract] |
Tuesday, November 22, 2005 1:24PM - 1:37PM |
ND.00012: Shear flow past 2D droplets pinned or moving on an adhering channel wall at moderate Reynolds numbers Peter Spelt Numerical simulations are presented of shear flow past two-dimensional droplets on an adhering wall, at moderate Reynolds numbers. The results have been obtained using a novel extension of a level-set method to simulate moving contact lines (with measures to eliminate any errors in the conservation of mass of droplets). First, the case is considered of droplets whose contact lines are pinned. Data are presented for the critical value of the dimensionless shear rate (a Weber number, \textit{We}), beyond which no steady state is found, as a function of Reynolds number, \textit{Re}. It is shown that, as \textit{Re} is increased, the critical value of \textit{We} (denoted by a subscript $c)$ changes from \textit{We}$_{c}\sim $\textit{Re} to \textit{We}$_{c}$=const., and that the deformation of droplets at \textit{We} just above \textit{We}$_{c}$ changes fundamentally from a gradual to a sudden dislodgement. In the second part of the presentation, contact lines are allowed to move. The contact-line singularity is removed by using a Navier-slip boundary condition. It is shown that macroscale contact angles can be defined that are primarily a function of the capillary number based on the contact-line speed, not of the value of \textit{We} and \textit{Re }of the shear flow. In a third part of the presentation, results are presented for droplets moving on a wall with position-dependent sliplength or contact-angle hysteresis, in an effort to stabilize or destabilize droplets. [Preview Abstract] |
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