Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session Q02: Drops: General I |
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Chair: Dominique Legendre, Toulouse Fluid Mechanics Institute Room: 2B |
Tuesday, November 26, 2019 7:45AM - 7:58AM |
Q02.00001: Velocity Oscillations of a Walking Droplet Sam Turton, Matthew Durey, John Bush Couder \emph{et al.} (2005) demonstrated that a droplet bouncing on the surface of a vertically oscillating bath may destabilize to a walking state characterized by rectilinear motion across the bath surface at a constant speed. When a walking droplet is perturbed, there is experimental (Wind-Willassen \emph{et al.} (2013)) and theoretical (Bacot \emph{et al.} (2019)) evidence suggesting that its velocity may return to its free walking speed via over- or underdamped oscillations. By revisiting the stroboscopic pilot-wave model of Oza \emph{et al.} (2013), we demonstrate that linear stability analysis of the walking state predicts velocity oscillations over a lengthscale that becomes commensurate with the Faraday wavelength as the vibrational acceleration approaches the Faraday threshold. Furthermore, we demonstrate that this model predicts that the walking state destabilizes via a subcritical Hopf bifurcation, where the associated unstable limit cycle consists of periodic velocity oscillations, also on a scale comparable to the Faraday wavelength. This behavior conditions the droplet's histogram to develop a coherent structure on the scale of the Faraday wavelength, and so provides new insight into the emergence of quantum-like statistics from pilot-wave hydrodynamics. [Preview Abstract] |
Tuesday, November 26, 2019 7:58AM - 8:11AM |
Q02.00002: Experiments on Droplet Deformation and Lag in a Low Reynolds Number Flow David Bigio, Aditya N. Sangli, Margaret Lo, Artiom Kostiouk, Amir Riaz In low Reynolds number multiphase flows, existence of a velocity gradient in the bulk flow imposes viscous stresses on a deformable interface. Here we study the effect of a bulk flow of Castor oil, through a converging channel, on a suspended Silicone oil droplet \mbox{(radius $\sim$ 2 mm)}. We apply Lubrication theory to study the bulk flow and approximate the single phase flow profile, which agrees well with experimental determination of the flow velocity. Suspending Silicone oil droplets into the flow, we study the effect of a constant extensional rate on the droplet imposed by the bulk flow. The degree of droplet deformation depends on the initial Capillary number and heuristic deductions of the critical Capillary number are made. Experimental observations also indicate a lag in the droplet advection velocity compared to the bulk flow at the same point and we present a physical mechanism to explain the observation. [Preview Abstract] |
Tuesday, November 26, 2019 8:11AM - 8:24AM |
Q02.00003: Direct Numerical Simulations of Droplet Deformation in Low Reynolds Number Extensional Flows Aditya N. Sangli, Bernard Chang, David Bigio, Amir Riaz We study the effect of stagnant and non-stagnant extensional flows on a suspended immiscible droplet using direct numerical simulations. We use projection method to solve the governing equations of motion, and the deformable interface is treated using level set method. This scheme is used to simulate the behavior of a droplet in a hyperbolic flow as a low Reynolds number numerical analogue of the classic four-roll mill experiments. Results indicate that the critical Capillary number of the droplet increases with reduction in Reynolds number and approaches results from the four-roll mill study which approximated a Stokesian flow. To study non-stagnant extensional flows, we simulate the motion of a Silicone oil droplet \mbox{(radius $\sim$ 2 mm)} in a Castor oil matrix through a hyperbolic converging channel. Streamwise stretching of the droplet was observed and plots of drop draw ratio vs time and position of the droplet in the flow are validated with experimental results. [Preview Abstract] |
Tuesday, November 26, 2019 8:24AM - 8:37AM |
Q02.00004: The resonance of water balloons and water drops Chun-Ti Chang, Paul Steen What happens if a sessile drop is covered with a membrane and mechanically oscillated? In this study, we examine the resonance behaviors of water balloons, and we compare them to those of drops. It turns out that balloons and drops exhibit a variety of similar dynamical behaviors: families of corresponding modes, similar scalings for onset thresholds and almost identical dispersion relations. However, balloons and drops may synchronize differently with the forcing. In this talk, we shall carefully examine different aspects of the resonance of balloons and drops. Ultimate, we shall identify the extent to which one can understand the dynamics of balloons in terms of that of drops. [Preview Abstract] |
Tuesday, November 26, 2019 8:37AM - 8:50AM |
Q02.00005: On the Basset-Boussinesq history force of a fluid sphere Dominique Legendre We consider the Basset-Boussinesq (history) force experienced by a spherical drop. The kernel of the Basset-Boussinesq force has not been determined so far when internal circulation of the fluid occurs. We first characterize the slip at a fluid sphere interface. Under both steady and unsteady conditions, the corresponding slip length is remarkably uniform along the fluid sphere interface and is directly related to the viscosity ratio. Combining the analytical expression of the Basset-Boussinesq kernel obtained for a solid sphere with interface slip and the obtained description of the slip at the fluid-fluid interface, we were able to describe for the first time the Basset-Boussinesq history force acting on a spherical drop. This expression is valid whatever the viscosity ratio from bubbles to viscous drops. [Preview Abstract] |
Tuesday, November 26, 2019 8:50AM - 9:03AM |
Q02.00006: Hydrodynamics of a hollow water droplet falling in air Mounika Balla, Manoj Tripathi, Kirti Sahu We study the hydrodynamics of a compound/hollow water droplet falling in air by conducting three-dimensional numerical simulations of the Navier-Stokes and the continuity equations using a finite volume based volume-of-fluid method. The various physical parameters influencing the dynamics are the thickness of the hollow droplet, inertia and surface tension at the air-water interface. It is found that the droplet exhibits shape oscillations. The oscillations of the inner interface (inner air bubble) of the hollow droplet is periodic with a time period about half of that of a normal droplet. The deformation of the outer interface of the hollow droplet is aperiodic and breaks up when the deformation is more. Increasing the thickness of the hollow droplet decreases the amplitude of oscillations of both the inner and outer interfaces. As expected, the oscillations decay with time at low inertia. As the thickness of the hollow droplet decreases a ‘spike’ like structure appears at the bottom of the hollow droplet. This instability is enhanced as the surface tension and the ratio of the viscous force to the gravitational force are decreased. The velocity contours are used to explain the behaviour observed in the present study. [Preview Abstract] |
Tuesday, November 26, 2019 9:03AM - 9:16AM |
Q02.00007: Force analysis acting on the moving droplet in air-flow Yewon Kim, Hyungmin Park, Alidad Amirfazli Movement of a water droplet over a surface due to a shearing airflow was studied in a wind tunnel. Water droplets (5-20 $\mu $l) were placed on PET (hydrophilic) and PTFE (hydrophobic) surfaces; airflow velocities up to 25 m/s and accelerations between 4.4-10 m/s$^{\mathrm{2}}$ were used. The Reynolds number is under 3,400 based on the free-stream air velocity ($U_{\infty })$ and the height of the droplet ($h)$. High-speed cameras from top and side views were used to evaluate the droplet velocity, acceleration, and contact angle hysteresis. Droplets start to move at different air velocities depending on the droplet volume, flow acceleration, and surface wettability. Also, droplets show different acceleration pattern for different experimental case. For example, when flow acceleration is 4.4 m/s$^{\mathrm{2}}$, 5$\mu $l droplet on the PTFE surface start to move at lower free-stream velocity with lower droplet acceleration compared to those on the PET surface. To understand the behavior of droplets, we constructed a model by considering the drag, adhesion, and viscous forces acting on the moving droplet. We would discuss the relation between the droplet behavior and airflow state (velocity and acceleration) and validate our force balance model for the droplet. [Preview Abstract] |
Tuesday, November 26, 2019 9:16AM - 9:29AM |
Q02.00008: Droplet condensation patterns: universality or non-universality? Laura Stricker, Juergen Vollmer, Robert Style, Eric Dufresne When a flux of supersaturated vapour gets into contact with a solid substrate, a condensation process can originate, leading to the formation of droplets patterns on the substrate (``breath figures''). The interest for breath figures is both practical and theoretical. We present here an experimental study of three-dimensional breath figures forming on a two-dimensional substrate. By making use of scaling concepts, we indentify a series of characteristic exponents, such as the so-called polydispersity exponent, characterizing the droplet size distribution. We proof the internal consistency of the results and we compare them to the predictions of the classical theory. According to such a theory, the polydispersity exponent should be a universal number, depending only on the dimensionality of the system. However, more recent theoretical studies claimed that the polydispersity exponent should heavily depend on the micrometric details of the condensation process (e.g. contact angle and critical nucleation radius of the droplets). We investigate the issue and we try to provide an answer, based on the experimental data. [Preview Abstract] |
Tuesday, November 26, 2019 9:29AM - 9:42AM |
Q02.00009: Ultrasonically-Enhanced Condensation by Induced Interfacial Droplet Ejection Thomas Boziuk, Marc Smith, Ari Glezer Ultrasonic (MHz range) actuation at the liquid-vapor interface of vapor flowing over a slow moving sub-cooled liquid layer exploits the differences in acoustic impedance to form a train of droplet that are ejected into the vapor. The increased interfacial surface area of the ejected droplets result in increased heat transfer between the vapor and the liquid and a significant increase in condensation without inducing a significant increase in upstream pressure. The enlarged droplets drop back into the subcooled liquid stream under gravity. A two-stream liquid-vapor experimental setup was designed to assess the effects of the acoustic actuation on the formation and ejection of the subcooled liquid droplets and the enhanced condensation over several combinations of relative flow rates and liquid subcooling, the observable increases in the sensible heat of the liquid stream as well as increased rate of mass transfer from the vapor to liquid stream. The evolution of the droplet-laden vapor within a mixing volume is visualized using high-speed imaging and is used to investigate the effects of the residence time of the droplets within the vapor volume and possible applications to acoustically-driven heat exchangers. [Preview Abstract] |
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