Bulletin of the American Physical Society
61st Annual Meeting of the APS Division of Fluid Dynamics
Volume 53, Number 15
Sunday–Tuesday, November 23–25, 2008; San Antonio, Texas
Session HG: Drops V |
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Chair: Shaoping Quan, Institute of High Performance Computing, Singapore Room: 101A |
Monday, November 24, 2008 10:30AM - 10:43AM |
HG.00001: Reversed trajectories of interacting pair of drops in a steady shear at finite inertia Kausik Sarkar, Peter Olapade, Rajesh Singh Interactions between viscous drops in a steady shear are numerically simulated using front tracking finite difference method. The results match well at low Reynolds number with the experimental observations of Guido and Simione (1998). At finite inertia, the drops behave differently from that in Stokes flow. Two drops placed initially flow-direction and shear-direction offsets do not pass each other. Instead, the drops upon interaction reverse their trajectories. Such behaviors were already reported for freely rotating solid particles, where it is ascribed to the reversed streamlines around a particle at finite inertia. However, drop deformation critically affects the trajectories, in that for some values of Reynolds numbers, drops pass each other at low and high capillary numbers, but reverse their motion at intermediate capillary numbers. The results are due to the increased drop inclination in the flow direction at increased capillary number. [Preview Abstract] |
Monday, November 24, 2008 10:43AM - 10:56AM |
HG.00002: Equilibrium shapes and stability of a coupled interface system consisting of a liquid bridge and a pendant drop Santhosh Ramalingam, Osman Basaran A capillary switch, which is a continuous volume of liquid where a sessile drop is connected to a pendant drop through a liquid-filled circular hole in a plate, is an example of a coupled interface system, i.e. a sessile and a pendant drop. In certain microfluidic applications involving transport of small liquid volumes, the sessile drop of the switch is grown at the expense of the pendant drop so that it coalesces with a second pendant drop hanging from a rod placed above the plate. The result is another coupled interface system wherein a liquid bridge is now connected to a pendant drop through the circular hole in the plate. Here, we investigate the equilibrium shapes and stability of this coupled interface system. The equilibrium shapes are determined numerically by finite element analysis and families of equilibrium shapes are tracked using first order continuation. Shape stability is determined by (i) exploiting the connectivity of the shape families and (ii) tracking numerically the fate of volume preserving perturbations by a transient hydrodynamic analysis. Locations of turning and bifurcation points are identified as functions of system volume, pressure difference between the gas phases above and below the plate, and bridge height. [Preview Abstract] |
Monday, November 24, 2008 10:56AM - 11:09AM |
HG.00003: Investigation of drop coalescence using tomographic PIV Cecilia Ortiz-Duenas, Jungyong Kim, Ellen Longmire High-speed tomographic PIV was used to obtain evolving volumetric velocity fields of the coalescence of single drops and two side-by-side drops through liquid/liquid interfaces. Reynolds numbers (Re=$\rho _{s}$U$_{\sigma }$D/$\mu _{s})$ based on surface tension velocity (U$_{\sigma }$=D/t$_{\sigma })$ and surrounding ambient fluid were 8-10, and the viscosity ratio between the fluid drop and surrounding fluid was 0.14. The coalescence process investigated is driven by gravity and thus the initial drops are non-spherical and the interface is deformed by the drops. Previously, Mohamed-Kassim {\&} Longmire (2004) showed that under these conditions, the film rupture typically occurs off-axis, and therefore the flow is three-dimensional. For a single drop, volumetric velocity vector fields are used to characterize the asymmetric film rupture occurring for 0$<$t/t$_{\sigma }<$0.1 and the subsequent symmetric development of the velocity and vorticity fields for 0.1$<$t/t$_{\sigma }<$1.6. It is shown that even though the film rupture occurs off-axis, the capillary waves and the collapse of the drop into a vortex ring are relatively axisymmetric. For two side-by-side drops, the first drop to coalesce ruptures off-axis on the side closest to the second drop. The volumetric velocity and vorticity fields indicate an asymmetric collapse of the drop for 0.1$<$t/t$_{\sigma }<$1.6 due to the deformation of the interface by the second drop while the capillary waves are axisymmetric. [Preview Abstract] |
Monday, November 24, 2008 11:09AM - 11:22AM |
HG.00004: Numerical simulations of relaxation and breakup of an elongated droplet Jing Lou, Shaoping Quan The relaxation and breakup of an initially elongated droplet in a viscous fluid is studied using a moving mesh interface tracking (MMIT) / finite volume method. The interface is zero thickness and moves with the fluid. Mesh adaptations are employed to allow large deformation and to capture the changing curvature, and mesh separation is implemented to permit pinch-off. Detailed investigations of the relaxation and breakup process are performed. It is found that the vortex rings play an important role in the relaxation and pinch-off process, and they are created and collapsed during the process. It is shown that the fluid velocity field and the neck shape are distinctly different for viscosity ratios larger and smaller than $\mathcal{O}$(1), and thus a different end-pinching mechanism is observed for each regime. The length ratio also significantly influences the velocity distributions, but not the neck shape. The effects of the density ratio on the relaxation and breakup process are minimal. However, the droplet evolution is retarded. The formation of a satellite droplet is observed, and the size of the droplet depends strongly on the length ratio and the viscosity ratio. [Preview Abstract] |
Monday, November 24, 2008 11:22AM - 11:35AM |
HG.00005: Partial and total coalescence of drops in presence of a surface Francois Blanchette, Laura Messio, John Bush The coalescence of a drop with a liquid reservoir of a different fluid is investigated numerically and experimentally. Drops are gently deposited on the surface of the reservoir and coalesce with negligible initial vertical velocity. Depending on the drop size and reservoir composition, partial or total coalescence may occur. The difference in surface tension between the drop and the reservoir is of particular importance in determining the type of coalescence observed through the tangential motion it generates (Marangoni effect). If the surface tension of the drop is much larger than that of the reservoir, a new type of coalescence occurs: a droplet is ejected from the top of the drop, while satellite droplets are left in its wake. These regimes are delineated numerically or experimentally. [Preview Abstract] |
Monday, November 24, 2008 11:35AM - 11:48AM |
HG.00006: Drop Break-up in Concentrated Surfactant Solutions Itai Cohen, John Savage, Patrick Spicer, Marco Caggioni Droplets break-up in air is a common phenomenon that occurs all around us. At the point of break-up, the drop radius shrinks to zero in a finite amount of time. The pressure exerted by the interface is inversely proportional to the minimum radius and becomes singular at break-up. In Newtonian fluids, this finite time singularity gives rise to universal features in the breakup process that can be described by similarity solutions for the fluid air interface. In this talk I will address the question of how this process is altered when observed in concentrated surfactant solutions. Remarkably we find that breakup in these systems is a mix between universal and non-universal behavior. [Preview Abstract] |
Monday, November 24, 2008 11:48AM - 12:01PM |
HG.00007: The effect of surface deformation on droplet collisions Paul Van Noordt, Carlos Hidrovo Microfluidics has proven to be of great value in many engineering and scientific applications. Because of the small scales involved, microfluidics requires only small sample sizes, which can result in shorter reaction and analysis times, relatively cheap costs, and little waste. The present study will investigate the coalescence of two liquid droplets with the ultimate goal of applying the results to the design of a pneumatic-based impact-coalescence mixing microreactor. When two droplets collide, several outcomes are possible, namely bouncing, coalescence, disruption, and fragmentation. The outcome is influenced by several parameters, including the impact parameter, the droplet-size ratio, and the film thickness between the droplets. We will consider the transfer of energy via viscous dissipation from the high-speed droplets to the deforming surfaces. We examine the relationship between the kinetic energy and the surface energy of the droplets as they collide as a governing factor affecting the outcome of the collisions. By considering various conditions, a preliminary criterion has been established for each possible outcome. [Preview Abstract] |
Monday, November 24, 2008 12:01PM - 12:14PM |
HG.00008: Head-on collision of viscous drops Robert Schroll, Christophe Josserand, Stephane Zaleski, Wendy Zhang When a liquid drop hits a solid wall at several m/s, the no-slip boundary condition at the wall causes a viscous boundary layer to develop. Numerical results on the impact of a viscous liquid drop reveal that the presence of this viscous boundary layer causes the thin liquid sheet ejected by impact to attain a pancake shape, characterized by a uniform thickness everywhere except at the rim. Here we examine a scenario where the viscous boundary layer is absent and show that, consistent with our expectation from solid-wall impact, the ejected sheet has a different shape. Specifically we simulate head-on collision of two viscous liquid drops of equal size. Air effects are reduced to a level where they are insignificant. Because the collision plane corresponds to essentially a free-stress surface, the viscous boundary layer is absent. Consistent with this absence, we find that the thin liquid sheet ejected by the collision does not evolve towards a pancake shape, but instead thins continuously with distance from the collision center. Reducing the strength of surface tension increases the radial extent of the sheet at a given time after collision. [Preview Abstract] |
Monday, November 24, 2008 12:14PM - 12:27PM |
HG.00009: An Analytical Criterion for Separation-Driven Coalescence of Droplets Ann Lai, Howard Stone Recent experiments by Bremond \emph{et al.} [1], along with simulations by Yoon \emph{et al.} [2], have demonstrated that two droplets coalesce as they are separating rather than upon their collision. We analyze the experimental configuration in the limit that the continuous phase is more viscous than the droplet phase by applying lubrication analysis followed by the method of domain perturbations to determine the evolution of the deformation as a function of time. We find that there is a universal shape for the deformed droplet at the time of contact. In particular, for two droplets of radius, $R$, moving apart according to $h_0(t)=h_0(0)+\alpha t^2$, where $2h_0(t)$ is the separation distance, we define a nondimensional parameter, $A=\frac{3\mu R^2\sqrt{\alpha}}{\gamma [h_0(0)]^{3/2}}$, where $\mu$ is the viscosity of the continuous phase and $\gamma$ is the interfacial tension. There exists a critical value, $A_{crit}=3.0792$, below which coalescence cannot occur. \\ \\ $[1]$ N. Bremond, A.R. Thiam, and J. Bibette 2008 \emph{Phys. Rev. Lett.} 100, 024501. \\ $[2]$ Y. Yoon, F. Baldessari, H. Ceniceros, and L.G. Leal 2007 \emph{Phys. Fluids} 19, 102102. [Preview Abstract] |
Monday, November 24, 2008 12:27PM - 12:40PM |
HG.00010: Droplet Merging by Use of Droplet Velocity Difference due to Viscosity or Size Difference Byungju Jin, Young Won Kim, Jung Yul Yoo We observe that two droplets of the same size but of different viscosities are merged by velocity difference induced as they are transported with the carrier fluid. Further, it is noted that two droplets of the same viscosity but of different size can be readily merged. Thus, the objective of the present study is to propose a simple and highly efficient nanoliter- or picoliter-size droplet-merging method which uses velocity difference induced by droplet viscosity or size difference in a microfluidic channel. To make viscosity difference, the mass ratio of water and glycerol is varied. Two droplets of the same size or of different sizes are generated alternatingly in the cross channel by controlling flowrates. For the quantitative measurement of the velocity difference of the droplets, micro-PIV is used. This droplet merging method can be used to mix or encapsulate one target sample with another material, so that it can be applied to cell lysis, particle synthesis, drug discovery, hydrogel-bead production, and so on. [Preview Abstract] |
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