Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session D4: Drops II: Numerical Simulations 
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Chair: Shu Takagi, The University of Tokyo Room: 307 
Sunday, November 20, 2011 2:10PM  2:23PM 
D4.00001: Modeling and Numerical Predictions of the Dynamic Contact Angle Using a Microscopic Forcing Term Gerry Della Rocca, Guillaume Blanquart The dynamic contact angle at the wall between two immiscible fluids has been shown to be a function of the static contact angle and the contact line velocity (or Capillary number). In numerical simulations of multiphase flows, this dynamic angle is often directly imposed from either an empirical model or a model based on the molecularkinetic theory of wetting. In contrast, a hydrodynamic viewpoint is used here to describe the flow around the contact line, and a microscopic forcing term is applied to simulate the molecular interactions at the boundary. The numerical simulations rely on a staggered arrangement of velocities, and a level set method is used to track the interface location. This framework has an inherent amount of slip which can be further supplemented by a Navierslip condition. For the pressure jump across the interface, a ghost fluid method is employed and the microscopic forcing term is added into the jump condition. An unresolved curvature model is proposed for the microscopic forcing term where a smooth circular arc connects the dynamic and static angles in the sub grid gap. This model does not rely on any underlying formula connecting the contact angles and the contact line velocity, but rather the dynamic angle evolves due to the nature of the flow. The model predictions for the dynamic contact angle are compared to experimental results. [Preview Abstract] 
Sunday, November 20, 2011 2:23PM  2:36PM 
D4.00002: Numerical Simulation and Scaling Analysis of Cell Printing Rui Qiao, Ping He Cell printing, i.e., printing three dimensional (3D) structures of cells held in a tissue matrix, is gaining significant attention in the biomedical community. The key idea is to use inkjet printer or similar devices to print cells into 3D patterns with a resolution comparable to the size of mammalian cells. Achieving such a resolution in vitro can lead to breakthroughs in areas such as organ transplantation. Although the feasibility of cell printing has been demonstrated recently, the printing resolution and cell viability remain to be improved. Here we investigate a unit operation in cell printing, namely, the impact of a cellladen droplet into a pool of highly viscous liquids. The droplet and cell dynamics are quantified using both direct numerical simulation and scaling analysis. These studies indicate that although cell experienced significant stress during droplet impact, the duration of such stress is very short, which helps explain why many cells can survive the cell printing process. These studies also revealed that cell membrane can be temporarily ruptured during cell printing, which is supported by indirect experimental evidence. [Preview Abstract] 

D4.00003: ABSTRACT WITHDRAWN 
Sunday, November 20, 2011 2:49PM  3:02PM 
D4.00004: Confined shear induces spatial ordering in an interacting pair of drops Rajesh Singh, Kausik Sarkar In a shear flow between two parallel walls, viscous interactions between deforming drops induce migration velocities away from the wall. Unlike free shear, the drops, after collision, come to the centerline of the domain, i.e. they experience a zero crossstream separation, and more importantly a fixed streamwise separation. We numerically investigate to find that the final streamwise separation depends on the degree of confinement, capillary number and viscosity ratio, but does not depend on the initial separation between drops. The streamwise separation varies as the square of the domain size and inversely with the capillary number. We present an asymptotic theory to explain these scalings. [Preview Abstract] 
Sunday, November 20, 2011 3:02PM  3:15PM 
D4.00005: Breakup of a Liquid Drop Falling Through a Quiescent Media: A DNS Study Maziyar Jalaal, Kian Mehravaran The breakup of falling liquid droplets in a stationary media is studied using Direct Numerical Simulations (DNS). An adaptive Volume of Fluid (VOF) method based on an octree Cartesian grid generation is employed, considerably reducing the computational cost. Fragmentations are followed reaching approximately stable clouds of droplets up to 1/1000 of the initial droplet diameter. Three different simulations are performed investigating the influence of the initial E\"{o}tv\"{o}s number. The mechanism of breakup, one of the most unclear phenomena in multiphase systems is described in detail. The wave growth over the bag, creation and retraction of punctures and ligament formation are presented and results are compared with recent theoretical investigations of (\textit{Savva {\&} Bush, J. Fluid. Mech. }\textbf{\textit{626}}\textit{: 211240.}) and (\textit{Bermond {\&} Villermaux, J. Fluid. Mech. }\textbf{\textit{524}}\textit{: 121130.}). The roles of RayleighTaylor and RayleighPlateau instabilities on breakup are also described and their influences on further clusteroffragments creation are shown. The outcomes can be used to develop current secondary atomization models. Moreover, the results can be used for better understanding of rain drop atomization during precipitation, as well as water droplet atomization in cooling towers. [Preview Abstract] 
Sunday, November 20, 2011 3:15PM  3:28PM 
D4.00006: Bare Shear Viscosity and Anomalous Fall Rate of Oil Droplets in Nitrogen Rodney Varley Experimental evidence of Kim and Fedele (1982) indicates a breakdown of the Millikan Law for the fall rate of oil droplets in Nitrogen gas over a pressure range of 115 atm. The discrepancy is most pronounced for smallest, 0.1 micron radius droplets for which the fall rate increases with pressure. The opposite behavior was observed by Millikan with larger drops in air of pressure at most one atm. We explain these results by arguing that the particle's motion, in particular Stokes' drag formula, is determined by the socalled bare shear viscosity which applies to micro fluid flows. This is in contrast with the usual theory which uses a renormalized shear viscosity and which is well approximated by the Enskog value. A mode coupling formula for the bare shear viscosity is discussed and a graphical comparison is made with the experimental results. Basically an increase in gas pressure produces a decrease in the bare shear viscosity and thus the fall rate increases. The idea that the shear viscosity is smaller for micro flows is consistent with the intuitive belief that on small enough spatial and time scales, fluid flows are conservative without dissipation. [Preview Abstract] 
Sunday, November 20, 2011 3:28PM  3:41PM 
D4.00007: Fluid Dynamics of Bottle Filling Patrick McGough, Haijing Gao, Santosh Appathurai, Osman Basaran Filling of bottles is a widely practiced operation in a large number of industries. Well known examples include filling of ``large'' bottles with shampoos and cleaners in the household products and beauty care industries and filling of ``small'' bottles in the pharmaceutical industry. Some bottle filling operations have recently drawn much attention from the fluid mechanics community because of the occurrence of a multitude of complex flow regimes, transitions, and instabilities such as mounding and coiling that occur as a bottle is filled with a fluid. In this talk, we present a primarily computational study of the fluid dynamical challenges that can arise during the rapid filling of bottles. Given the diversity of fluids used in filling applications, we consider four representative classes of fluids that exhibit Newtonian, shearthinning, viscoelastic, and yieldstress rheologies. The equations governing the dynamics of bottle filling are solved either in their full 3D but axisymmetric form or using the slenderjet approximation. [Preview Abstract] 
Sunday, November 20, 2011 3:41PM  3:54PM 
D4.00008: Do Liquid Drops on Inclined Surfaces Slide or Roll? Sumesh PT, Ignacio Pagonabarraga, Ronojoy Adhikari, Rama Govindarajan A solid sphere is likely to roll, while a rectangular box is likely to slide, on an inclined surface. Instead, a liquid drop can exhibit a variety of shapes and complex but interesting dynamics. We obtain global minimum energy static shapes first, for two realistic bases of potential energy, front and backpinned. We find that the free end always assumes Young's equilibrium angle. Using this clue, simple equations describing the angles and the maximum volume may be derived. Combining the lattice Boltzmann method for hydrodynamics and method of lines for a CahnHilliard equation, a hybrid numerical scheme is developed to study the dynamics of binary fluids on an inclined plate. The contribution of pure translation, and the vorticities associated with rolling and shearing motion are distinguished, using which the motion of the drop can be split into roll and slip. Surprisingly, as gravity increases, the fraction of motion due to roll decreases significantly for certain contact angles. The rolling motion is strongly dependent on the slip length which is in contrast to predictions by the lubrication approximation, where all dependence on the slip length is generally logarithamic. [Preview Abstract] 
Sunday, November 20, 2011 3:54PM  4:07PM 
D4.00009: Repellency of the Lotus Leaf: Resistance of Water Intrusion under Hydrostatic Pressure C.W. Extrand In an attempt to better understand the repellency of the lotus leaf, a model was constructed from hydrophobic hemispheres arranged on a hexagonal array. Two scenarios were considered. In the first, the hemispheres were smooth. In the second, the hemispheres had a secondary roughness. The model shows that without the secondary structure, the repellency of this surface geometry is relatively poor. The secondary structure directs the surface tension upward, allowing much greater resistance to penetration of water and prevents the loss of repellency. From the proposed model, the maximum intrusion pressure (or socalled CassieWenzel transition) of the lotus leaf is estimated to be 1215 kPa. The predicted maximum pressure agrees well with reported values from experimental measurements. [Preview Abstract] 
Sunday, November 20, 2011 4:07PM  4:20PM 
D4.00010: Surface and Bulk Oscillations of Sessile Drops: Clearing Up Confusion and Understanding Wind Sheared Drops Andrew J.B. Milne, Beatriz Defez Garcia, Miguel Cabrerizo Vilchez, Alidad Amirfazli Sessile drop oscillations are studied in the presence of a shearing airflow, and varying body force. The various possibilities for analysis, (center of mass or drop surface oscillations) are elucidated through presenting a unifying analysis framework based on wavenumber, frequency, and fluid properties. This work examines a range of fluid properties in a single study for the first time. A dispersion relation is found relating the frequency of centroid oscillation and capillarygravity wave number, depending on the ratio (surface tension/liquid density)$^{1/2}$, drop size$^{3/2}$ and contact angle. The effects of contact angle are more complex than previously suggested simplifications, or analytic solutions for axisymetric drops and must at present be treated empirically. The growth of sessile drop oscillations is linear at low air velocities and exponential at higher air velocities. This is explained by drawing analogies to drops experiencing a varying body force, and to wind driven capillarygravity waves on lakes, respectively. Liquid viscosity retards the growth of the waves, and has other important effects. [Preview Abstract] 
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