Bulletin of the American Physical Society
76th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2023; Washington, DC
Session T03: Drops: Coalescence II |
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Chair: Daniel Orejon, University of Edinburgh Room: Ballroom C |
Monday, November 20, 2023 4:25PM - 4:38PM |
T03.00001: Confined Coalescence Unveils New Regimes of Frictional Fluid Mechanics Justin C Burton, Haicen Yue, Daniel M Sussman, Tabitha C Watson, Nandish Vora Droplet coalescence is essential in a host of biological and industrial processes involving complex systems as diverse as cellular aggregates, colloidal suspensions, and polymeric liquids. Classical solutions for the time evolution of coalescing clusters are typically based on tractable limiting physics, such as analytical solutions to the Stokes equation, and discrepancies between experiments and these classical solutions can indicate relevant physical effects governing the behavior of different systems. By combining computational and theoretical analyses, we show that there is an unexplored family of ``dry hydrodynamic'' or ``frictional'' coalescence processes: those governed by highly dissipative coupling to the environment. This leads to new scaling laws characterizing droplet coalescence, as well as new time-invariant parameterizations of the shape evolution of the coalescing system. We demonstrate these effects via particle-based simulations and with both continuum and boundary-integral solutions to hydrodynamic equations, which we then understand in the context of a generalized Navier-Stokes-like equation. Our theoretical description of highly frictional coalescence mathematically maps onto Darcy flow in the presence of surface tension effects, and preliminary experiments show excellent agreement with particle-based simulations, opening up exciting avenues of research in applying well-studied fluid dynamical techniques to a broad range of novel systems. |
Monday, November 20, 2023 4:38PM - 4:51PM |
T03.00002: Modelling droplet coalescence on a tilted superhydrophilic cylindrical wire Souradip Chattopadhyay, Leyun Feng, Kyoo-Chul K Park, Hangjie Ji Transporting droplets along cylindrical wires is an emerging focus area with various practical applications such as fog collection and filtration. Recent experiments by Feng et al. (2022) have revealed a wealth of new droplet coalescence dynamics on a superhydrophilic cylindrical wire, illustrating the need for more advanced theory. In this study, we present a mathematical model using lubrication theory and weighted residual modeling techniques for a thin liquid film flowing on a tilted superhydrophilic cylinder. This model incorporates key physical factors such as gravity, low-to-moderate inertia effects, viscous dissipation, surface tension, and disjoining pressure. This model explains the observed phenomenon of directional self-propelled transport during droplet coalescence, where the large droplet moves towards the small one. Moreover, we identify two distinct coalescence modes that result in either droplet oscillations or quasi-static droplet collapses. Stability analysis and numerical simulation agree well with the experimental observations. |
Monday, November 20, 2023 4:51PM - 5:04PM |
T03.00003: Inertial coalescence with a little viscosity John R Lister, Edward Beaty We consider analytically the inertial regime of coalescence of two fluid drops, when inertial forces balance surface tension, at early times when the drops are joined by a small fluid bridge of radius rb propto (gamma a/ rho)^{1/4} t^{1/2}. This regime applies when Oh ≡ mu/(rho gamma a)^{1/2} << rb/a << 1. Remarkably, despite the small viscosity (Oh<<1), viscosity has a leading-order effect! Momentum created by surface tension at the edge of the fluid bridge is left behind in a thin viscous wake as the bridge grows. Fluid is entrained into the wake, driving an inertial flow on the scale of the fluid bridge. This flow opens up the gap between the drops, thus reducing the driving capillary pressure and resulting in an O(1) decrease in the rate of coalescence. Our matched asymptotic solution for the flow shows excellent qualitative agreement with previous results by Anthony et al. (2020) for the streamlines and gap profile in full Navier-Stokes simulations for Oh=0.001. |
Monday, November 20, 2023 5:04PM - 5:17PM |
T03.00004: Hydrodynamic Behavior of Droplet Pair Collision in Confined Shear Flow, and the Role of Physical and Geometric Parameters. S M Abdullah Al Mamun, Samaneh Farokhirad Gaining a comprehensive understanding of the dynamics involved in the collision of droplets under confined shear flow holds great significance for a diverse array of industrial processes and natural phenomena. The interplay between physical parameters and system geometry exerts a substantial influence on the stability and various attributes of the droplets, including their deformation, trajectory, and final state. We investigate computationally the mutual influence of the density ratio (60 to 800), viscosity ratio (24 to 60), initial offset, and confinement on the coalescence behavior of droplet pairs within a confined shear flow. The free-energy-based lattice Boltzmann method was employed, aiming to identify new regimes beyond the scope of earlier studies. The findings highlight the pivotal role played by density ratios and viscosity ratios in generating inertia and viscous interaction forces, which have profound implications for the resulting coalescence consequences. Meanwhile, the confinement imposed by walls and the initial vertical offset of droplets are shown to be critical in either promoting or suppressing different collision modes. In continuation, we have expanded the simulation to include compound droplets, where one droplet encapsulates another, serving as a model for core-shell structures. This has also yielded some enlightening preliminary results. The findings are expected to offer novel insights into the collision dynamics of droplet pairs and their underlying conditions. |
Monday, November 20, 2023 5:17PM - 5:30PM |
T03.00005: The role of interfacial viscosity and Marangoni stresses on droplet coalescence Vivek Narsimhan, Natasha Singh We perform boundary-integral simulations to explore the role of surface viscosity on the coalescence of two equal-sized droplets. We assume an insoluble surfactant monolayer, and numerically solve the droplet shape and surfactant surface coverage during a head-on collision by solving the Stokes equations inside and outside the droplet and a convection-diffusion equation at the drop surface. The surfactant obeys a Langmuir adsorption isotherm, and exhibits a 2D surface viscosity obeying the Boussinesq-Scriven constitutive relationship. We observe that the surface viscosity significantly delays coalescence and that the film drainage time depends only on the sum of the surface dilatational viscosity and surface shear viscosity. We provide explanations to these effects using lubrication theory, and provide scaling analyses for the drainage time versus capillary number. Lastly, we find that the mechanism of coalescence stabilization is very different for Marangoni effects compared to surface viscous effects. Whereas Marangoni effects delay drainage by increasing the dimpling of the thin film, surface viscosity delays drainage by widening the film and flattening it. We show thin film profiles for different combinations of Marangoni and surface viscous effects and discuss its consequences for different classes of surfactants. |
Monday, November 20, 2023 5:30PM - 5:43PM |
T03.00006: Coalescence regime during impingement of a liquid drop on a liquid pool Manas Ranjan R Behera, Hiranya Deka, Bishakh Bhattacharya, Gautam Biswas The coalescence of a drop is a common occurrence in both nature and technology, from rain formation to the production of food emulsion. However, studying the dynamics of the coalescence process of a drop is challenging due to the small time and length scales involved. Here, we investigate the coalescence dynamics of a liquid drop on a deep liquid pool at the air-liquid interface. The regime map of partial coalescence and complete coalescence phenomena is presented in terms of the pertinent governing parameters. Some key parameters are investigated in detail to analyze the dynamic behavior of the partial coalescence phenomenon quantitatively in terms of the drop tip height, kinetics of the neck radius, diameter ratio of the secondary drop to the primary drop, and the pinch-off time. |
Monday, November 20, 2023 5:43PM - 5:56PM |
T03.00007: Mechanistic model and experiments of dispersed liquid-liquid pipe flows. Charitos Anastasiou, Fria A Hossein, Panagiota Angeli The transportation and separation of dispersed liquid-liquid pipe flows are significant in the energy and chemical industries. However, accurately predicting their evolution remains challenging due to lack of data and the inherent complexity of the underlying mechanisms. This work aims to improve understanding and to provide a predictive model via experimental studies supported by Model based Design of Experiments (MbDoE) methodologies. |
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