398 research outputs found
The Flow Induced by the Coalescence of Two Initially Stationary Drops
The coalescence of two initially stationary drops of different size is investigated by solving the unsteady, axisymmetric Navier-Stokes equations numerically, using a Front-Tracking/Finite Difference method. Initially, the drops are put next to each other and the film between them ruptured. Due to surface tension forces, the drops coalesce rapidly and the fluid from the small drop is injected into the larger one. For low nondimensional viscosity, or Ohnesorge number, little mixing takes place and the small drop fluid forms a blob near the point where the drops touched initially. For low Ohnesorge number, on the other hand, the small drop forms a jet that penetrates far into the large drop. The penetration depth also depends on the size of the drops and shows that for a given fluid of sufficiently low viscosity, there is a maximum penetration depth for intermediate size ratios
An experimental and computational study of bouncing and deformation in droplet collision
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76090/1/AIAA-1997-129-419.pd
Numerical simulations of drop collisions
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76145/1/AIAA-1994-835-900.pd
Head‐on collision of drops—A numerical investigation
The head‐on collision of equal sized drops is studied by full numerical simulations. The Navier–Stokes equations are solved for the fluid motion both inside and outside the drops using a front tracking/finite difference technique. The drops are accelerated toward each other by a body force that is turned off before the drops collide. When the drops collide, the fluid between them is pushed outward leaving a thin layer bounded by the drop surface. This layer gets progressively thinner as the drops continue to deform, and in several of our calculations we artificially remove this double layer at prescribed times, thus modeling rupture. If no rupture takes place, the drops always rebound, but if the film is ruptured the drops may coalesce permanently or coalesce temporarily and then split again. Although the numerically predicted boundaries between permanent and temporary coalescence are found to be consistent with experimental observations, the exact location of these boundaries in parameter space is found to depend on the time of rupture. © 1996 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71337/2/PHFLE6-8-1-29-1.pd
Head-on collision of drops: A numerical investigation
The head-on collision of equal sized drops is studied by full numerical simulations. The Navier-Stokes equations are solved for fluid motion both inside and outside the drops using a front tracking/finite difference technique. The drops are accelerated toward each other by a body force that is turned off before the drops collide. When the drops collide, the fluid between them is pushed outward leaving a thin later bounded by the drop surface. This layer gets progressively thinner as the drops continue to deform and in several of the calculations this double layer is artificially removed once it is thin enough, thus modeling rupture. If no rupture takes place, the drops always rebound, but if the film is ruptured the drops may coalesce permanently or coalesce temporarily and then split again
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Direct numerical simulations of fluid flow, heat transfer and phase changes
Direct numerical simulations of fluid flow, heat transfer, and phase changes are presented. The simulations are made possible by a recently developed finite difference/front tracking method based on the one-field formulation of the governing equations where a single set of conservation equations is written for all the phases involved. The conservation equations are solved on a fixed rectangular grid, but the phase boundaries are kept sharp by tracking them explicitly by a moving grid of lower dimension. The method is discussed and applications to boiling heat transfer and the solidification of drops colliding with a wall are shown
A phase-field model of Hele-Shaw flows in the high viscosity contrast regime
A one-sided phase-field model is proposed to study the dynamics of unstable
interfaces of Hele-Shaw flows in the high viscosity contrast regime. The
corresponding macroscopic equations are obtained by means of an asymptotic
expansion from the phase-field model. Numerical integrations of the phase-field
model in a rectangular Hele-Shaw cell reproduce finger competition with the
final evolution to a steady state finger the width of which goes to one half of
the channel width as the velocity increases
Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study
We study the singular effects of vanishingly small surface tension on the
dynamics of finger competition in the Saffman-Taylor problem, using the
asymptotic techniques described in [S. Tanveer, Phil. Trans. R. Soc. Lond. A
343, 155 (1993)]and [M. Siegel, and S. Tanveer, Phys. Rev. Lett. 76, 419
(1996)] as well as direct numerical computation, following the numerical scheme
of [T. Hou, J. Lowengrub, and M. Shelley,J. Comp. Phys. 114, 312 (1994)]. We
demonstrate the dramatic effects of small surface tension on the late time
evolution of two-finger configurations with respect to exact (non-singular)
zero surface tension solutions. The effect is present even when the relevant
zero surface tension solution has asymptotic behavior consistent with selection
theory.Such singular effects therefore cannot be traced back to steady state
selection theory, and imply a drastic global change in the structure of
phase-space flow. They can be interpreted in the framework of a recently
introduced dynamical solvability scenario according to which surface tension
unfolds the structually unstable flow, restoring the hyperbolicity of
multifinger fixed points.Comment: 16 pages, 15 figures, submitted to Phys. Rev
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