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 A4: Drops I: Numerical Methods |
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Chair: Kausik Sarkar, University of Delaware Room: 307 |
Sunday, November 20, 2011 8:00AM - 8:13AM |
A4.00001: A new method for calculation of acting forces on a deformable droplet in shear flow Youngho Suh, Changhoon Lee A numerical method for calculating drag and lift acting on a deformable droplet in linear shear flow is presented. In this study, a level set approach is adopted to handle deformation and break-off of the interfaces. In order to determine the acting force on a droplet in shear flow field, we adopt feedback forces which can maintain the droplet at a fixed position with efficient handling of deformation. The presented method is applied for numerical simulation of spherical, deformed, and oscillating droplets in uniform flow, and the numerical results are favorably compared with the data reported in the literature [Dandy and Leal, JFM (1989)], [Feng and Beard, J. Atmos. Sci. (1991)]. The computation demonstrates that the shape of droplet deforms from sphere to oblate ellipsoid by increasing the Reynolds and Weber numbers. For large inertial effects at high Reynolds number, the droplet eventually breaks up into smaller droplets. Based on the numerical results, drag and lift forces acting on a droplet are observed to strongly depend on the deformation. Also, the present method is proven to be applicable to a three- dimensional deformation of droplet in the shear flow, which cannot be properly analyzed by the previous studies. [Preview Abstract] |
Sunday, November 20, 2011 8:13AM - 8:26AM |
A4.00002: Phase field model simulation of droplet deformation and breakup in wall bounded turbulence Luca Scarbolo, Dafne Molin, Alfredo Soldati Prediction of droplet breakup in turbulence is crucial in many industrial and environmental processes such as fluid mixing in stirred chemical reactors or fluid clusters dispersion in large scale oceanic currents. To this aim we analyze the deformation and breakup of a single droplet in turbulent channel flow. The fluids are considered incompressible, density-matched and viscosity-matched. We use a Phase Field Model (PFM) based on the Cahn-Hilliard/Navier-Stokes equations system. We simulated a wide range of Weber numbers (ratio between inertial forces and surface tension) spanning two orders of magnitude with a Reynolds number $Re=100$ based on the friction velocity and on the channel half height. We validate the approach by comparing specific droplet parameters such as the average droplet deformation and the droplet deformation in time, against available experiments. Turbulent flow statistics are also computed to examine the energy exchanges between the droplet and the surrounding fluid. [Preview Abstract] |
Sunday, November 20, 2011 8:26AM - 8:39AM |
A4.00003: On a phase-field model for a miscible drop in a spinning drop tensiometer Andrea Boghi, Anatoliy Vorobev We examine shape transformations of a solute droplet immersed into a solvent-filled and sealed capillary tube subject to fast rotations around its axis, i.e. the configuration of the spinning drop tensiometer. Despite the fact, that a droplet is miscible, its dissolution occurs rather slowly, and under rotations a droplet becomes elongated, which is used to measure the dynamic surface tension of the solute/solvent interface. The Boussinesq approximation [1] of the full (quasi- compressible) Cahn-Hilliard-Navier-Stokes is used as a theoretical model to capture the droplet evolution. We found that the behaviour of a miscible droplet contained in a closed enclosure is strongly different from an immiscible one. Miscible droplets in general are thermodynamically unstable and ultimately dissolve, large partially miscible droplets however may remain stable with the size determined by the total mass balance. In the limit of high Prandtl numbers, droplet's shape changes quickly (on a convective time scale), so that quasi- stable droplets are observed with only weak hydrodynamic flows present. Such states remain thermodynamically unstable: droplets lose their mass and the droplet's interface properties changes on a long diffusive time scale.\\[4pt] [1] A. Vorobev, PRE 82, 056312 (2010). [Preview Abstract] |
Sunday, November 20, 2011 8:39AM - 8:52AM |
A4.00004: Drops settling in sharp stratification with and without Marangoni effects Francois Blanchette, Avi Shapiro We present numerical simulations of drops settling in a layered ambient fluid. The ambient is made up of miscible fluids, with the top layer lighter than the lower one, representing fluid stratified through temperature or salinity variations. The surface tension between the ambient and the drop may be uniform or be smaller in the lower layer. Such a system is applicable to oil droplets settling or rising in the ocean. When surface tension is uniform, the drop slows down significantly as it encounters the transition region, due to entrained fluid from the upper layer, before accelerating again in the lower layer. When the lower surface tension is smaller, the drop suddenly accelerates through the transition region. We characterize these effects in terms of the sharpness of the transition, and the drop's Reynolds number. [Preview Abstract] |
Sunday, November 20, 2011 8:52AM - 9:05AM |
A4.00005: Scaling in the Transition from Selective Withdrawal to Viscous Entrainment Chris Pommer, Michael Harris, Osman Basaran In selective withdrawal, fluid is withdrawn through a tube that has its tip suspended a distance S above a flat interface separating two fluids. When the withdrawal rate Q is low, the interface forms a steady-state hump and only the upper fluid is withdrawn. When Q is increased (or S decreased), the interface undergoes a topological transition so that the lower fluid is entrained with the upper one, forming a steady-state spout. Here, this discontinuous transition is analyzed computationally when both fluids are incompressible and Newtonian. The numerical method employed is an implicit method of lines ALE algorithm which uses finite elements with elliptic mesh generation. The new approach neither starts with a priori idealizations, as has been the case with previous computations, nor is limited to length scales above that set by the wavelength of visible light as in any experimental study. In particular, it is shown that the critical withdrawal rate at which the aforementioned transition occurs scales with the nozzle separation raised to some power n. A study of the effect of the physical parameters of the system on the scaling behavior is also presented. [Preview Abstract] |
Sunday, November 20, 2011 9:05AM - 9:18AM |
A4.00006: Interactions between two unilamellar vesicles L. Gary Leal, Johann Walter Suspensions of lipid vesicles are widely used in industrial applications such as personal and household care products. Interactions between vesicles can cause them to adhere and aggregate, which may dramatically modify the rheology of the suspension. In this work, we study the interactions of two unilamellar vesicles in a head-on collision. The study takes into account hydrodynamic phenomena, electrostatic repulsion between charged vesicles, depletion attraction forces due to polymers in solution and the effect of the deformation of the vesicles. Numerical simulations are conducted using an axisymmetric model coupling boundary integrals for the motion of the fluids and finite elements for the membrane mechanics. The results are compared with a new analytical scaling theory. Contrary to drops, it is shown that the drainage time is reduced when the driving force bringing the vesicles together increases. This is due to the increasing tension in the membrane as the vesicles get closer, which leads to a higher pressure in the film. It is also shown that the vesicles' ability to deform can significantly enhance the adhesion between them. [Preview Abstract] |
Sunday, November 20, 2011 9:18AM - 9:31AM |
A4.00007: Strategies for Efficient Microfiltration of Oil-in-Water Emulsions Tohid Darvishzadeh, Nikolai Priezjev This study addresses the issue of the separation of oil droplets from water for oil spill mitigation and produced water treatment. The effective separation of oil-in-water dispersions involves high flux of water through a membrane and, at the same time, high rejection rate of oil droplets, while avoiding membrane fouling. In this study, the effects of transmembrane pressure and crossflow velocity on rejection of oil droplets by pores of different cross-section are investigated numerically by solving the Navier-Stokes equation. We found that in the absence of crossflow, the critical transmembrane pressure, which is required for the oil droplet entry into a circular pore of given surface hydrophobicity, agrees well with analytical predictions based on the Young-Laplace equation. With increasing crossflow velocity, the shape of the oil droplet residing at the pore entrance is elongated along the flow and the critical pressure increases. In the case of pores with an elliptical cross-section, the water flux through the membrane is enhanced, in agreement with simple analytical considerations. The results of the numerical simulations are used to outline strategies for the experimental design of porous filters for oil spill remediation and produced water treatment applications. [Preview Abstract] |
Sunday, November 20, 2011 9:31AM - 9:44AM |
A4.00008: Interfacial Effects on Droplet Dynamics in Poiseuille Flow Jonathan Schwalbe, Frederick Phelan Jr., Petia Vlahovska, Steven Hudson Many properties of emulsions arise from interfacial rheology, but a theoretical understanding of the effect of interfacial viscosities on droplet dynamics is lacking. Here we report such a theory, relating to isolated spherical drops in a Poiseuille flow. Stokes flow is assumed in the bulk phases, and a jump in hydrodynamic stress at the interface is balanced by Marangoni forces (linearized with respect to local deviations of interfacial surfactant concentration) and surface viscous forces according to the Boussinesq--Scriven constitutive law. Interfacial diffusion is also included. Our analysis predicts slip, cross-stream migration and droplet-circulation velocities. These results and the corresponding interfacial parameters are separable: e.g., cross-stream migration occurs only if gradients in surfactant concentration are present; slip velocity depends on viscosity contrast and dilatational properties, but not on shear Boussinesq number. This separability allows a new and advantageous means to measure surface viscous and elastic forces directly from the drop interface. Modeling of other geometries will also be discussed. [Preview Abstract] |
Sunday, November 20, 2011 9:44AM - 9:57AM |
A4.00009: Drops settling in a fluid with surface tension increasing with depth Avi Shapiro, Francois Blanchette We investigated numerically drops settling across layers of miscible fluids, representing oil droplets settling in a fluid stratified by temperature or salinity variations. The top layer is lighter than the lower one, while the drop itself is heavier than both layers. As the drop settles into the lower, its surface tension with the ambient fluid increases, which generates significant Marangoni effects. If the surface tension difference is small, the drop is delayed as it settles into the lower layer. Above a critical surface tension difference, the drop may be altogether prevented from crossing into the lower layer. We determine the conditions under which a drop may remain suspended at the transition region, and study the mixing generated by suspended drops. [Preview Abstract] |
Sunday, November 20, 2011 9:57AM - 10:10AM |
A4.00010: A model for droplet condensational growth in a turbulent, axisymmetric jet Ryan Keedy, Alberto Aliseda Droplet growth at the edge of clouds is strongly influenced by the non-linear saturation field produced by mixing of warm, wet air inside the cloud with cold, dry air outside. This, together with the high intermittency of the turbulent at these geological scales, leads to uncertainty in the modeling of this process. We use experiments in a turbulent, axisymmetric jet to study this problem and develop a model. Although the distribution of a passive scalar in a turbulent jet is a classic problem, with a well-established solution, little attention has been devoted to heterogeneous nucleation, condensational growth and evaporation within a turbulent mixing layer where local supersaturation values may exceed unity. By leveraging the well-characterized self-similar behavior of a scalar (temperature, humidity) within a turbulent jet, we use a stochastic model for the instantaneous values from the statistics of the distribution to determine the super-saturation profile. Taking into account the high intermittency of the supersaturation field allows us to predict the droplet size at various stages of the flow. A Phase Doppler Particle Analyzer (PDPA) is used to collect statistics of velocity statistics, droplet growth and frequency that are used to inform the development and validation of the model. [Preview Abstract] |
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