Bulletin of the American Physical Society
62nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 54, Number 19
Sunday–Tuesday, November 22–24, 2009; Minneapolis, Minnesota
Session GH: Drops IV: Breakup |
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Chair: Osman Basaran, Purdue University Room: 101H |
Monday, November 23, 2009 8:00AM - 8:13AM |
GH.00001: Contraction of Asymmetric Newtonian Liquid Filaments Patrick McGough, Krishnaraj Sambath, Santosh Appathurai, Pradeep Bhat, Michael Harris, Osman Basaran Understanding the dynamics of satellite drops is important in several industrial applications involving drop formation including inkjet printing, electrospraying and atomization. The precursor to these satellite drops is a slender liquid filament that connects an about-to-form drop to the rest of the liquid in the nozzle. Once a filament is formed, it either contracts into a single satellite or breaks into multiple satellites, due to surface tension. Our understanding of the contraction of Newtonian filaments in a passive ambient fluid has improved greatly over the past two decades thanks to the numerical analyses of Schulkes (1996) and Notz and Basaran (2004) who modeled the filaments as cylinders that are terminated by two identical spherical caps. However, in many situations, the filament shapes at the onset of formation may not be symmetric as in the aforementioned studies. To improve our understanding of the fluid mechanics of contraction of such asymmetric filaments, we study here the recoil of filaments whose initial shapes are sections of tapered axisymmetric cones that are terminated by two unequal spherical caps. The dynamics are studied by both a 2-D analysis and a 1-D slender-jet analysis, and the results are summarized by constructing phase diagrams involving the dimensionless groups governing the dynamics. [Preview Abstract] |
Monday, November 23, 2009 8:13AM - 8:26AM |
GH.00002: Effect of initial shape on contraction dynamics of Newtonian filaments Krishnaraj Sambath, Patrick McGough, Santosh Appathurai, Pradeep Bhat, Michael Harris, Osman Basaran Slender liquid filaments arise in a number of applications involving drop formation, atomization, and cloud physics. Under the action of surface tension, a filament either contracts into a single drop or breaks into multiple drops as it recoils. Our understanding of the contraction of Newtonian filaments in a passive ambient fluid has improved greatly over the past two decades thanks to the numerical analyses of Schulkes (1996) and Notz and Basaran (2004) who modeled the filaments as cylinders that are terminated by two identical hemispherical caps. However, in many situations, the initial shape of a filament may resemble more that of two unequal globular or spherical drops that are connected by a slender cylinder. The dynamics of contraction of such filaments are studied here by both a two-dimensional analysis and a one-dimensional slender-jet analysis, and the results are summarized by constructing phase diagrams involving the dimensionless groups governing the dynamics. [Preview Abstract] |
Monday, November 23, 2009 8:26AM - 8:39AM |
GH.00003: Droplet formation from the breakup of micron-sized liquid jets Wim van Hoeve, Arjan van der Bos, Michel Versluis, Jacco Snoeijer, Michael P. Brenner, Detlef Lohse Droplet formation from the breakup of a liquid jet emerging from a micron-sized circular nozzle is investigated with ultra high-speed imaging at 1 million frames per second and within a lubrication approximation model [Eggers and Dupont, Phys. Rev. Lett. 262, 1994, 205-221]. The capillary time $\tau_c = \sqrt {\rho r^3 / \gamma}$ is extremely small -- of the order of $1\mu {}\mbox{s}$. In the analyzed low Reynolds number regime the jet breakup is driven by surface tension forces only. Rayleigh breakup is not influenced by the surrounding air. The high- speed imaging results and those from the model calculation perfectly agree for various liquid viscosities and jet velocities, confirming a universal scaling law also for diminutive Rayleigh jets. [Preview Abstract] |
Monday, November 23, 2009 8:39AM - 8:52AM |
GH.00004: Scaling in two-fluid pinch-off Chris Pommer, Ronald Suryo, Hariprasad Subramani, Michael Harris, Osman Basaran Two-fluid pinch-off is encountered when drops or bubbles of one fluid are ejected from a nozzle into another fluid or when a compound jet breaks. While the breakup of a drop in a passive environment and that of a passive bubble in a liquid are well understood, the physics of pinch-off when both the inner and outer fluids are dynamically active is inadequately understood. In this talk, the breakup of a compound jet whose core and shell are both incompressible Newtonian fluids is analyzed computationally by a method of lines ALE algorithm which uses finite elements with elliptic mesh generation for spatial discretization and adaptive finite differences for time integration. Pinch-off dynamics are investigated well beyond the limit of experiments set by the wavelength of visible light and that of various algorithms used in the literature. Simulations show that the minimum neck radius $r$ initially scales with time $\tau$ before breakup as $\tau^{\alpha}$ where $\alpha$ varies over a certain range. However, depending on the values of the governing dimensionless groups, this initial scaling regime may be transitory and, closer to pinch-off, the dynamics may transition to a final asymptotic regime for which $r \sim \tau^{\beta}$, where $\beta \neq \alpha$. [Preview Abstract] |
Monday, November 23, 2009 8:52AM - 9:05AM |
GH.00005: Single drop fragmentation is the source of raindrops size distribution Emmanuel Villermaux, Benjamin Bossa Like many natural objects, raindrops are distributed in size. By extension of what is known to occur inside the clouds, where small droplets grow by accretion of vapor and coalescence, raindrops in the falling rain at the ground level are believed to result from a complex mutual interaction with their neighbors. We show that the raindrops polydispersity, generically represented according to Marshall-Palmer's law, is quantitatively understood from the fragmentation products of non interacting, isolated drops. Both the shape of the drops size distribution, and its parameters are related from first principles to the dynamics of a single drop deforming as it falls in air, ultimately breaking into a dispersion of smaller fragments containing the whole spectrum of sizes observed in rain. The transformation is accomplished within a timescale much shorter than the typical collision time between the drops. [Preview Abstract] |
Monday, November 23, 2009 9:05AM - 9:18AM |
GH.00006: Droplet breakup past an obstacle Suzie Protiere, Dave Weitz, Howard Stone To investigate the transport of drops in a porous medium, we consider a model at the scale of an elementary event consisting of drop passing an obstacle in a microfluidic channel. We can thus observe the breakup process in a controlled way. We demonstrate that there exists an unstable situation for which a drop manages to pass the obstacle without breaking and define a critical value of the capillary number Ca* for which a drop will break. We also show that the obstruction dimensions play an important role in the breakup-non breakup transition. Finally we propose a model which describes the observed transition between breakup and non-breakup. [Preview Abstract] |
Monday, November 23, 2009 9:18AM - 9:31AM |
GH.00007: Production of ultra-small ink jet drops using drop-on-demand (DOD) drop formation Haijing Gao, Qi Xu, Michael Harris, Osman Basaran The formation of drops having radii that are smaller than the radii of the nozzle from which they are ejected is an active area of research in drop-on-demand (DOD) ink jet printing. In the last decade, Chen and Basaran (Phys Fluids, 2002; US patent, 2003) showed experimentally and computationally that several fold reduction in drop radius R (an order of magnitude reduction in drop volume V) is possible by judicious use of waveform modulation in which one or more intrinsic time scales such as capillary time, time for vorticity diffusion, and time for piezo actuation are varied. In this paper, we report the results of a computational study through which we have uncovered a novel method for achieving a factor of 5-10 reduction in R (about two to three orders of magnitude reduction in V). Scaling arguments are also developed which yield a simple expression for the size of the ultra-small drops formed as a function of the governing dimensionless groups. Formation of such small drops using DOD technology may prove especially attractive in applications involving direct printing of flexible electronics and solar cells. [Preview Abstract] |
Monday, November 23, 2009 9:31AM - 9:44AM |
GH.00008: Oscillations of a capillary switch used as a miniature opto-fluidic device Santhosh Ramalingam, Osman Basaran A capillary switch (CS) is a continuous volume of liquid consisting of a sessile and a pendant drop that are coupled through a liquid filled hole in a plate. When capillary force is much larger than body forces such as gravity, this simple, coupled interfacial system exhibits multiple equilibrium states beyond a critical volume. Owing to its extremely small size, and hence large curvature and highly spherical air-liquid interface, an oscillating CS can potentially be used as a variable focus liquid lens in MEMS devices. The dynamics of an oscillating CS are studied by solving the full 3D axi-symmetric or 2D Navier-Stokes equation using the Galerkin finite element method (G/FEM). Applying means of forcing such as oscillating the pressure in the gas surrounding the sessile (pendant) drop and vibrating the plate, modes of oscillation are identified from resonances observed during frequency sweeps. The shift in the frequencies of oscillation of lower modes due to changes in parameters such as liquid volume, plate thickness, and liquid viscosity and surface tension are also studied. Results are shown to agree well with experimental observations by Hirsa and coworkers. [Preview Abstract] |
Monday, November 23, 2009 9:44AM - 9:57AM |
GH.00009: Effects of viscoelasticity on retraction of a sheared drop Swarnajay Mukherjee, Kausik Sarkar The retraction of a sheared drop when either the drop or the matrix phase is Oldroyd B is investigated. The retraction is initially faster and later slower with increasing drop viscoelasticity. The initial faster relaxation of viscoelastic drops is due to inward pulling viscoelastic stresses at the drop tip and the later slowing down is due to the slowly relaxing viscoelastic stresses at the equator. The behavior is captured well by three model ODEs for two principal viscoelastic stresses (along the tip and equatorial directions) and the deformation. Matrix viscoelasticity slows the relaxation of a Newtonian drop right from the beginning because of the slow relaxation of stresses near the drop tip with increasing Deborah number. For drops sheared in supercritical conditions, when initially stretched beyond a certain length, relaxation leads to neck formation with two bulbous ends resulting in drop break-up, while for less stretching, it relaxes back to its spherical state. [Preview Abstract] |
Monday, November 23, 2009 9:57AM - 10:10AM |
GH.00010: Dynamics of contracting viscoelastic filaments Michael Harris, Santosh Appathurai, Pradeep Bhat, Osman Basaran Satellite drops are detrimental to many industrial applications involving the formation of viscoelastic drops including inkjet printing, DNA microarraying, and printing of flexible solar cells. The precursor to these satellite drops is a slender liquid filament that connects an about-to-form drop to the rest of the liquid in the nozzle.~ Once a filament is formed, it contracts due to surface tension. A filament may undergo further breakup during recoil. Whereas the contraction of Newtonian filaments in a passive ambient fluid is well understood (Schulkes 1996 and Notz and Basaran 2004), the contraction dynamics of viscoelastic filaments remains largely unexplored and is addressed in this presentation.~ Here the filament shape is idealized as an axisymmetric fluid cylinder terminated by hemispherical end-caps, and the conformation tensor formalism (Pasquali {\&} Scriven 2002) is used to model the viscoelasticity.~ The dynamics of contracting filaments are then analyzed by means of both a well-benchmarked two-dimensional finite element algorithm (Notz et al. 2001, Chen et al. 2002) and a one-dimensional slender-jet algorithm (Padgett et al. 1996).~ Regions of the parameter space are identified where recoiling filaments give rise to either a single satellite drop or multiple satellites. [Preview Abstract] |
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