Computation of the rise or fall of a drop through a suspending liquid with no mass transfer: Axisymmetric, transitional and complex regimes
type: CreativeWork
description: We investigate the buoyant motion of a liquid drop through a suspending liquid for three different liquid-liquid pairs and different drop sizes, covering a range of parameter space including axisymmetric, transitional and complex regimes, in cases for which there is no mass transfer between the drop and suspending liquid. We also investigate the accuracy of different numerical techniques for solving immiscible two-phase problems. In a number of free-surface flows, computations using an interface-fitted finite-element approach can lead to spurious velocities. Here, we use an Arbitrary Lagrangian-Eulerian (ALE) moving-mesh approach to investigate this using four test problems for which analytic solutions are available. An interface-fitted technique based on a stabilized Galerkin finite-element method is applied to the four test problems. We investigate Laplace’s equilibrium for a two-dimensional circular interface, an oscillating inviscid two-dimensional circular interface, damped capillary waves. We also consider relaxation to Laplace’s equilibrium for a spherical interface, neglecting mesh and interface motion. Two different approaches to account for interfacial tension are demonstrated for the spherical interface: one using differential geometry arguments and the other using a higher-order least-squares fit to the interface. We show that these approaches have approximately the same convergence rate and accuracy when used with second-order interpolation of velocity and pressure, with the least-squares fitting approach being significantly more accurate when linear interpolation is used. Application of artificial interfacial shear stress, including interfacial viscosity used to mitigate spurious velocities, is demonstrated and the oscillating inviscid circular interface case is shown to effectively dampen spurious velocities without adversely affecting the solution if the amount of damping is judiciously chosen. The first investigation of a buoyant drop is for the n-b…
abstract: We investigate the buoyant motion of a liquid drop through a suspending liquid for three different liquid-liquid pairs and different drop sizes, covering a range of parameter space including axisymmetric, transitional and complex regimes, in cases for which there is no mass transfer between the drop and suspending liquid. We also investigate the accuracy of different numerical techniques for solving immiscible two-phase problems. In a number of free-surface flows, computations using an interface-fitted finite-element approach can lead to spurious velocities. Here, we use an Arbitrary Lagrangian-Eulerian (ALE) moving-mesh approach to investigate this using four test problems for which analytic solutions are available. An interface-fitted technique based on a stabilized Galerkin finite-element method is applied to the four test problems. We investigate Laplace’s equilibrium for a two-dimensional circular interface, an oscillating inviscid two-dimensional circular interface, damped capillary waves. We also consider relaxation to Laplace’s equilibrium for a spherical interface, neglecting mesh and interface motion. Two different approaches to account for interfacial tension are demonstrated for the spherical interface: one using differential geometry arguments and the other using a higher-order least-squares fit to the interface. We show that these approaches have approximately the same convergence rate and accuracy when used with second-order interpolation of velocity and pressure, with the least-squares fitting approach being significantly more accurate when linear interpolation is used. Application of artificial interfacial shear stress, including interfacial viscosity used to mitigate spurious velocities, is demonstrated and the oscillating inviscid circular interface case is shown to effectively dampen spurious velocities without adversely affecting the solution if the amount of damping is judiciously chosen. The first investigation of a buoyant drop is for the n-b…
author: Steytler, Louis L.
language: en
keywords: Arbitrary Lagrangian-Eulerian method, Multiphase flow, Two-phase flow, Moving mesh, Interface-fitted mesh, Adaptive mesh refinement, Volume-of-fluid Method, Terminal velocity, Wake instability, Helical wake, Drop rotation, Liquid-liquid interfaces, Drop shape oscillations, Carbon dioxide drops, Subsea carbon sequestration, Surface tension, Butanol-water drops, Nitrobenzene drops, Multiple long-time solutions, Drop trajectories
date published: 2021-03-05T21:45:21Z
date modified: 2026-07-22T22:24:50Z
provider: University of Illinois - Urbana-Champaign
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Illinois at Urbana-Champaign

PropertyValue
property ID: Handle
value: http://hdl.handle.net/2142/109577