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 MH: Drops VII |
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Chair: Michael Renardy, Virginia Polytechnic Institute and State University Room: 101H |
Tuesday, November 24, 2009 8:00AM - 8:13AM |
MH.00001: Deformation of a hydrophobic ferrofluid droplet suspended in a viscous medium under uniform magnetic fields Yuriko Renardy, Shahriar Afkhami, Michael Renardy, Judy Riffle, Annette Tyler, Tim St. Pierre, Robert Woodward The effect of applied magnetic fields on the deformation of a biocompatible hydrophobic ferrofluid drop suspended in a viscous medium is investigated numerically and compared with experimental data. At high magnetic fields, experimental drop shapes deviate from numerical results when a constant surface tension value is used. One hypothesis for the difference is the dependence of interfacial tension on the magnetic field in the experimental data. This idea is investigated computationally by varying the interfacial tension as a function of the applied magnetic field, and by comparing the drop shapes with experimental data until matched. [Preview Abstract] |
Tuesday, November 24, 2009 8:13AM - 8:26AM |
MH.00002: Motion and deformation of a hydrophobic ferrofluid droplet in a viscous medium under non-uniform magnetic fields Shahriar Afkhami, Yuriko Renardy, Michael Renardy, Tim St. Pierre, Judy S. Riffle Recent interest in ferrofluids has been motived by biomedical and pharmaceutical applications. We numerically investigate dynamics of a hydrophobic ferrofluid droplet placed in a viscous medium under non-uniform magnetic fields. The drop deforms in response to the applied non-uniform magnetic field, and this in turn affects the motion of the ferrofluid droplet. Droplet properties such as interfacial tension, viscosity, magnetic permeabilty as well as its size and shape can be optimized for the efficient manipulation of the motion of drop through a viscous medium. By computationally measuring the migration velocity of ferrofluid droplets, it is possible to determine the ferrofluid ``magnetophoretic mobility'', which is an important characteristic for the feasibility of biomedical applications. [Preview Abstract] |
Tuesday, November 24, 2009 8:26AM - 8:39AM |
MH.00003: Infrared visualization of flow motion inside a sessile drop under evaporation David Brutin, Fabrice Rigollet, Christophe Le Niliot Drop evaporation is a simple phenomena but still unclear concerning the evaporation mechanisms. A common agreement of the scientific community based on experimental and numerical work evidence that most of the evaporation occurs at the triple line; however, the rate of evaporation is still predicted empirically due to the lack of knowledge on the convection which develops inside the drops under evaporation. The evaporation of sessile drops is more complicated than it appears due to the conduction coupling with the heating substrate, the convection and conduction inside the drop and the convection and diffusion with the vapour phase. The coupling of heat transfer in the three phases induces complicated cases to solve even for numerical simulations. In the present work, we present recent experimental results obtained using infrared thermography (infrared camera coupled with a microscopic lens of 10 $\mu$m of resolution) to visualize flow motion inside sessile drops under evaporation. The wavelength range (3-5 $\mu$m) is adapted to the observed fluid (99.9\% ethanol) since it is semi-transparent in that wavelength range. It is then possible to observe qualitatively inside the drop the convection cells appearance, evolution and disappearance. The relation between the convection cells and the heat transfer from the substrate to the drop is evidenced is this work. [Preview Abstract] |
Tuesday, November 24, 2009 8:39AM - 8:52AM |
MH.00004: Small-amplitude oscillations of a drop pinned at an azimuth Doraiswami Ramkrishna, Santhosh Ramalingam, Osman Basaran Natural modes of oscillation of an inviscid drop undergoing irrotational flow and constrained by a ring of negligible thickness at an azimuthal angle with respect to the center of the droplet are studied analytically and numerically. Similar to linear oscillations of a free drop first studied by Rayleigh, the analytical formulation of the oscillations of the constrained drop results in an eigenvalue problem but with one additional boundary condition, i.e. that accounting for zero perturbation along the contact point. A minimization method that converts the eigenvalue problem into a constrained optimization problem is used to solve for the eigenvalues of various modes of oscillation and the corresponding mode shapes. An extension of Green's function method used to analyze oscillations of a drop in contact with a spherical bowl [M. Strani and F. Sabetta, \textit{J. Fluid Mech.} \textbf{141}, 233 (1984)] is also employed to study the problem at hand. Results obtained from these two approaches are compared to those reported by Bostwick and Steen [\textit{Phys. Fluids} \textbf{21}, 032108 (2009)] and ones obtained from new simulations using the Galerkin/finite element method. [Preview Abstract] |
Tuesday, November 24, 2009 8:52AM - 9:05AM |
MH.00005: Trajectories of a pair of drops in steady shear at finite inertia: effects of viscosity ratio and positioning Rajesh Singh, Kausik Sarkar Two drops driven towards each other by shear, experience a new trajectory at finite inertia. Unlike in Stokes flow, where drops always slide past each other, here they turn back in a reversed trajectory due to a zone of reversed streamlines around the drops at finite inertia. The trajectory type depends on initial offset, Reynolds number, capillary number, as well as viscosity ratio. We investigate the transition from one type of trajectory to the other, and delineate the different zones in the parameter space. Drops pass each other at low and high capillary numbers, but reverse their motion at intermediate capillary numbers because of the increased drop inclination in the flow direction at increased capillary number. Above a critical viscosity ratio, drop trajectory transitions from reversed to passing. The critical viscosity ratio increases with Reynolds number at small capillary numbers, but shows a nonmonotonic behavior at higher capillary numbers. Increasing initial offset in the vorticity direction also leads to a transition from passing to reversed trajectory. [Preview Abstract] |
Tuesday, November 24, 2009 9:05AM - 9:18AM |
MH.00006: Calculation of Drag and Lift for a Deformable Droplet in a Shear Flow Youngho Suh, Changhoon Lee Significant efforts have recently been made to numerically investigate the drag and lift forces of a liquid droplet in a shear flow. The droplet deformation induced by interplay between surface tension and shear stress on the surface can affect the droplet behavior. In most previous studies, however, only the spherical droplet without deformation has been considered in the shear flow, and thus understanding of effects of droplet deformation on drag and lift characteristics lacks. In this study, the droplet behavior in the linear shear flow is numerically investigated by a level set method, which is improved by incorporating a sharp-interface modeling technique for accurately enforcing the matching conditions at the liquid-gas interface. Computations were carried out to investigate the deformation behavior of droplet caused by the linear shear flow with various shear rate, droplet size and flow velocity. Also, the effects of deformation of droplet on drag and lift forces acting on droplet are presented. In the computation, to determine the acting force on a droplet in shear flow field, the feedback forces which can maintain droplet position were adopted for efficient handling of deformation. [Preview Abstract] |
Tuesday, November 24, 2009 9:18AM - 9:31AM |
MH.00007: Numercial study of deformable droplet-pair subjected to sudden acceleration by an external flow Shaoping Quan, Jing Lou Numerical simulations of two deformable drops placed in tandem subjected to a sudden acceleration by a gaseous flow are performed by solving the integral form of the full Navier-Stokes equations using a finite volume/moving mesh interface tracking method. The interface is zero thickness and moves in a Lagrangian fashion. The unsteady interaction between the droplet-pair is studied by varying the minimum initial distance between the two droplets. The interaction on the shapes, the deformation factors, the drag coefficients, and the fluid fields are examined and compared to the single droplet. A mushroom shape is formed with a dimpled cap of the upstream drop and a bell shape of the downstream one for high Weber numbers and small initial separation distances. The drag coefficient of the downstream droplet is dramatically reduced, especially for the large Weber numbers, while drag force of the upstream drop is slightly decreased. It is found that when the spacing is less than zero, there is a sudden increase of drag coefficient for the downstream drop, while a sharp reduction for the upstream drop. For smaller Weber numbers, the two droplets experience oscillations, however, the oscillation modes are not the same. The two drops might coalescence for small separation distances. [Preview Abstract] |
Tuesday, November 24, 2009 9:31AM - 9:44AM |
MH.00008: Radiation torque on an absorptive spherical drop centered on an acoustic helicoidal Bessel beam Likun Zhang, Philip L. Marston Circularly polarized electromagnetic waves carry axial angular momentum and analysis shows that the axial radiation torque on an illuminated sphere is proportional to the power absorbed by the sphere [1]. Helicoidal acoustic beams also carry axial angular momentum and absorption of such a beam should also produce an axial radiation torque [2]. In the present work the acoustic radiation torque on solid spheres and spherical drops centered on acoustic helicoidal Bessel beams is examined. The torque is predicted to be proportional to the ratio of the absorbed power to the acoustic frequency. Depending on the beam helicity, the torque is parallel or anti-parallel to the beam axis. The analysis uses a relation between the scattering and the partial wave coefficients for a sphere in a helicoidal Bessel beam. Calculations suggest that beams with a low topological charge are more efficient for generating torques on solid spheres.\\[4pt] [1] P. L. Marston and J. H. Crichton, Phys. Rev. A. 30, 2508-2516 (1984).\\[0pt] [2] B. T. Hefner and P. L. Marston, J. Acoust. Soc. Am. 106, 3313-3316 (1999). [Preview Abstract] |
Tuesday, November 24, 2009 9:44AM - 9:57AM |
MH.00009: Radiation force on drops and bubbles in acoustic Bessel beams modeled using finite elements Philip L. Marston, David B. Thiessen, Likun Zhang Analysis of the scattering of sound by spheres centered on ordinary and helicoidal (higher-order) Bessel beams makes it possible to evaluate the acoustic radiation force on idealized drops and bubbles centered on the beam [1]. For potential applications it would be necessary to know if a small transverse displacement of the sphere from the beam's axis causes a radiation force that pushes the sphere toward (or away from) the axis of the beam. We applied 3D-finite elements to that problem. To trust FEM calculations of the radiation force with helicoidal beams it was first necessary to verify that analytical values for the axial force are recovered in the on-axis helicoidal case since only the zero-order beam had been previously studied with FEM. Cases have been identified where the force pushes a slightly off-set drop or bubble toward the axis. For some cases the effective potential method of Gorkov may be used to predict the transverse stability of small spheres.\\[4pt] [1] P. L. Marston, J. Acoust. Soc. Am. 125, 3539-3545 (2009). [Preview Abstract] |
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