Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session D4: Drops II |
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Chair: Osman Basaran, Purdue University Room: 23C |
Sunday, November 18, 2012 2:15PM - 2:28PM |
D4.00001: Collision and coalescence of liquid drops in a dynamically active ambient fluid Krishnaraj Sambath, Hariprasad Subramani, Osman Basaran The fluid dynamics of the collision and coalescence of liquid drops has intrigued scientists and engineers for more than a century owing to its ubiquitousness in nature, e.g. raindrop coalescence, and industry, e.g. breaking of emulsions in the oil and gas industry. The complexity of the underlying dynamics, e.g. occurrence of hydrodynamic singularities, has required study of the problem at different scales -- macroscopic, mesoscopic and molecular -- using stochastic and deterministic methods. In this work, we adopt a multiscale, deterministic method to simulate the approach, collision, and eventual coalescence of two drops where the drops as well as the ambient fluid are incompressible, Newtonian fluids. The free boundary problem governing the dynamics consists of the Navier-Stokes system and associated initial and boundary conditions that have been augmented to account for the effects of disjoining pressure as the separation between the drops becomes of the order of a few hundred nanometers. This free boundary problem is solved by a Galerkin finite element-based algorithm. The approach and results to be reported build on earlier work by Leal and coworkers, and are used to identify conditions conducive for coalescence in terms of flow and fluid properties. [Preview Abstract] |
Sunday, November 18, 2012 2:28PM - 2:41PM |
D4.00002: PIV-Analysis of collapsing toroidal droplets Ekapop Pairam, Eric Berger, Alberto Fernandez-Nieves Toroidal droplets are unstable and always undergo a transformation into spherical droplets driven by surface tension. They either break ala Rayleigh-Plateau if the torus is thin or grow fatter to become a single spherical droplet if the torus is fat. We analyze the velocity field inside and outside the toroidal droplet as it transforms into spherical droplets using the particle image velocimetry (PIV) method and compare with recent theoretical calculations for this process. [Preview Abstract] |
Sunday, November 18, 2012 2:41PM - 2:54PM |
D4.00003: Droplet collisions in a liquid Gosse Oldenziel, Ren\'e Delfos, Gerrit Elsinga, Jerry Westerweel The collision of two equally sized fluid droplets in a continouous phase consisting of a second liquid is investigated. The outcome of the collision, i.e. coalescence or bouncing depends, for two given fluids, on the relative velocity of the droplets just before impact, and the mis-alignment of the collision $\Delta x$, nondimensionialized in a Weber number, $We = \rho_{d} U_{rel}^2 d_{ave}/\sigma$ and the alignment parameter $B = \Delta x/d_{ave}$. We studied nearly head-on collisons by launching the droplets from two opposing capillaries. High speed dual-axis shadowgraphy is used to reconstruct the 3D-droplet trajectories. We found that if the Weber number exceeds a critical value, the droplets will coalesce; for lower values they bounce off again. For silicon oil droplets with a dynamic viscosity $4.6$ times that of the surrounding phase (water) the critical Weber number is found to be $We \approx 22.5$. For all bouncing droplets, the contact time was measured and found to be approximately equal to the theoretical droplet oscillation frequency period. Current work aims at investigating the influence of external continuous phase turbulence on the outcome of the collisions by placing the two-capillary system in between two counterrotating discs (``von K\'{a}rm\'{a}n flow''). [Preview Abstract] |
Sunday, November 18, 2012 2:54PM - 3:07PM |
D4.00004: Simulations of Droplet Coalescence in Simple Shear Flow Orest Shardt, Jos Derksen, Sushanta Mitra We present highly-resolved simulations of droplet coalescence in a shear flow. In general, droplet coalescence is difficult to simulate due to the wide range of relevant length scales: the diameter of a droplet may be $10^4$ times larger than the minimum thickness of the film between a pair of droplets. In a shear flow, droplets coalesce unless a critical capillary number is exceeded. We found that this critical capillary number is about 20 times higher in simulations than in experiments when the domain size is at the scale of previous work. We use the binary-liquid free-energy lattice Boltzmann method. In this diffuse-interface model, the interface is characterized by a tension, thickness, and diffusivity. Using the parallel computational power of graphics processing units, we simulate sufficiently large domains to determine the dependence of the critical capillary number (Ca) on the diameter ($D$) of the droplets (relative to the interface thickness). The exponent in this scaling law depends strongly on the interface diffusivity. A new region in the Ca vs $D$ map for the outcome of a simulated droplet collision was identified. We also study geometric effects. Due to the high resolutions that we simulate, we obtain critical capillary numbers that approach experimental values. [Preview Abstract] |
Sunday, November 18, 2012 3:07PM - 3:20PM |
D4.00005: Wettability effects on droplet coalescence Percival Graham, Dennis De Pauw, Ali Dolatabadi Droplet impingement has been studied since 1895, with the works of A.M. Worthington. Throughout the past century, a variety of interesting phenomena have been uncovered. These include the bouncing of droplets off of each other or liquid pools, intricate droplet splashing mechanics, and droplets bouncing off of superhydrophobic surfaces; to name a few. In addition to intricate phenomena, droplet dynamics are relevant to many engineering applications, such as painting, spray coating ink-jet printing, and ice accumulation. These fields all involve interactions between droplets; therefore, studying droplet coalescence would benefit them greatly. The works presented include the coalescence of droplets with different impact conditions, various offsets, and at different wettabilities. Surface wettabilities studied are hydrophilic, hydrophobic and superhydrophobic. Fascinating phenomena observed include, bouncing of the impinging droplet off of the sessile droplet, sliding of the impinging droplet along the sessile droplet, and induced detachment on the sessile droplet on superhydrophobic surfaces. In order to capture the maximum spreading of the merged droplets, models related to coalescence of droplets in air and maximum spreading of a single droplet are combined to yield a new model to predict the maximum spreading of head-on droplet impact. Based on the free surface, and accuracy of the analytical model, droplet impact could be viewed as a mix of droplet coalescence in a gaseous media and droplet impact on a dry surface. [Preview Abstract] |
Sunday, November 18, 2012 3:20PM - 3:33PM |
D4.00006: Self-Propelled Jumping Drops on Leidenfrost Surfaces: Experiments and Simulations Fangjie Liu, Giovanni Ghigliotti, James J. Feng, Chuan-Hua Chen Coalescing drops spontaneously jump on a variety of biological and synthetic superhydrophobic surfaces, with potential applications in self-cleaning materials and self-sustained condensers. To investigate the mechanism of the self-propelled jumping drops, a Leidenfrost collider was constructed on which drops floating on a vapor layer were guided to merge and subsequently jump on a heated substrate. Above a threshold drop diameter, we experimentally observed a constant energy conversion efficiency, which is the ratio of the kinetic energy of the merged drop to the surface energy released upon coalescence. This trend matched with prior reports of jumping condensate drops on a superhydrophobic surface. The capillary-inertial scaling of the jumping process was confirmed with a phase-field simulation of two equally-sized spherical drops coalescing on a flat surface with a contact angle of 180$^{\circ}$. The numerical simulation revealed the role of viscous dissipation, leading to reduced energy conversion efficiency when the Ohnesorge number based on the drop diameter approaches unity. [Preview Abstract] |
Sunday, November 18, 2012 3:33PM - 3:46PM |
D4.00007: Symmetric and Asymmetric Coalescence of Drops on a Substrate Federico Hernandez-Sanchez, Luuk Lubbers, Antonin Eddi, Jacco Snoeijer The coalescence of viscous drops on a substrate is studied experimentally and theoretically. As a result, a universal shape of the bridge between the drops was found. The dynamics of the bridge is accurately described by similarity solutions of the one-dimensional lubrication equation. Such solutions were found for equal and unequal contact angles of the two drops, and characterized by the ratio of contact angles. Our theory predicts a bridge that grows linearly in time and stresses the strong dependence on the contact angles. Without any adjustable parameters, we find quantitative agreement with all experimental observations. The results reveal the importance of asymmetry on the coalescence process. [Preview Abstract] |
Sunday, November 18, 2012 3:46PM - 3:59PM |
D4.00008: Spontaneous penetration of a non-wetting drop into an exposed pore Pengtao Yue, Yuriko Renardy We consider the penetration process of a liquid drop approaching an exposed pore along the axis of symmetry, which is intended to model the penetration of non-wetting drops into a porous medium. Inertia and gravity are neglected at the current stage. Different from the penetration into a capillary tube in literature, the drop may spread on the outer surface of the porous medium. Based the on the mechanical equilibrium states, we find the critical drop radius, below which the drop penetration is spontaneous. We further identify five penetration regimes based on the drop radius and the static contact angle, all of which are exemplified by phase-field simulations. The free energy as a function of penetration depth reveals only two stable equilibrium states --- the drop either enters the pore completely (maximum penetration) or stays at the pore inlet (zero penetration). For a non-penetrating drop radius, the free energy has a local maximum which constitutes an energy barrier that prevents spontaneous penetration. Finally, we modify the Lucas-Washburn equation to describe the dynamic process of penetration, which turns out to greatly overestimate the penetration rate due to the neglect of dissipation from moving contact lines and flows outside the pore. [Preview Abstract] |
Sunday, November 18, 2012 3:59PM - 4:12PM |
D4.00009: Drop Impingement on Highly Wetting Porous Thin Films: Theoretical Justification for the Washburn-Reynolds Number Cullen Buie, Young Soo Joung Recently we've introduced a dimensionless parameter named the Washburn-Reynolds number (Re$_{w})$. The Washburn-Reynolds number predicts drop impingement modes on highly wetting porous thin films. Physically, the Washburn-Reynolds number (Re$_{w})$ can be interpreted as the ratio between the inertia of the impinging droplet and capillary transport in the porous thin film. In this talk we outline the theoretical considerations that lead to the Washburn-Reynolds number. To estimate droplet spreading after impact, we've devised an energy conservation expression employing a capillary potential energy term. This term leads to another dimensionless parameter denoted the capillary Weber number (We$_{c})$, which is the ratio of the kinetic energy of the droplet to the capillary energy of the surface. The energy equation can be simplified as a function of the Weber number (We) and the dimensionless spreading speed constant (C$_{cap}^{\ast })$ in high and low We$_{c}$ limits, respectively. Re$_{w}$ is obtained from the log scale geometric average of We and C$_{cap}^{\ast }$. Our theoretical analysis and experimental results verify that Re$_{w}$ is useful to predict impingement modes on highly wetting porous films for a wide range of impact velocities and fluid properties. [Preview Abstract] |
Sunday, November 18, 2012 4:12PM - 4:25PM |
D4.00010: Fluid dynamics following flow shut-off in bottle filling Sumeet Thete, Santosh Appathurai, Haijing Gao, Osman Basaran Bottle filling is ubiquitous in industry. Examples include filling of bottles with shampoos and cleaners, engine oil and pharmaceuticals. In these examples, fluid flows out of a nozzle to fill bottles in an assembly line. Once the required volume of fluid has flowed out of the nozzle, the flow is shut off. However, an evolving fluid thread or string may remain suspended from the nozzle following flow shut-off and persist. This stringing phenomenon can be detrimental to a bottle filling operation because it can adversely affect line speed and filling accuracy by causing uncertainty in fill volume, product loss and undesirable marring of the bottles' exterior surfaces. The dynamics of stringing are studied numerically primarily by using the 1D, slender-jet approximation of the flow equations. A novel feature entails development and use of a new boundary condition downstream of the nozzle exit to expedite the computations. While the emphasis is on stringing of Newtonian fluids and use of 1D approximations, results will also be presented for situations where (a) the fluids are non-Newtonian and (b) the full set of equations are solved without invoking the 1D approximation. Phase diagrams will be presented that identify conditions for which stringing can be problematic. [Preview Abstract] |
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