Two-dimensional numerical investigation on the dynamics of ligament formation by Faraday instability

•The interface is traced by the coupled-level-set and volume-of-fluid method.•We analyze the detailed pressure and velocity fields obtained by simulation.•Nonlinearity causes a maximum pressure location formed at the crest root.•A freed ligament is formed above the maximum pressure location. Ligamen...

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Published inInternational journal of multiphase flow Vol. 60; pp. 64 - 75
Main Authors Li, Yikai, Umemura, Akira
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier Ltd 01.04.2014
Elsevier
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Online AccessGet full text
ISSN0301-9322
1879-3533
DOI10.1016/j.ijmultiphaseflow.2013.12.002

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Abstract •The interface is traced by the coupled-level-set and volume-of-fluid method.•We analyze the detailed pressure and velocity fields obtained by simulation.•Nonlinearity causes a maximum pressure location formed at the crest root.•A freed ligament is formed above the maximum pressure location. Ligament formation from the surface of a horizontal liquid layer subject to a vertical vibration (Faraday instability) is a crucial part of the atomization process because it is the transition phase for droplet generation. Based on the numerical solutions of the two-dimensional incompressible Euler equations for a prototype Faraday instability flow, we explored physically how a liquid ligament that is dynamically free from the vibrating liquid layer and behaves like a jet can be produced. According to linear theory, the suction of liquid from the trough portion to the crest portion creates an amplified crest. The amplified crest is always pulled back to the liquid layer in linear theory, no matter how largely the surface deforms; thus, a dynamically freed ligament never forms. However, under nonlinear conditions produced by large surface deformation, the impinging liquid flow from the trough portion enhances the pressure at the high crest (ligament) root. This pressure enhancement has two major effects. First, it reduces the amount of liquid sucked from the trough portion, which abates the increase in the crest height compared with that associated with linear theory. Second, it forms a local maximum pressure at the crest root; in this case, the ligament above this location becomes dynamically free from the motion of the bottom substrate in the laboratory reference frame. Liquid elements continuously enter the dynamically freed liquid region, producing a slender ligament from the liquid layer.
AbstractList Ligament formation from the surface of a horizontal liquid layer subject to a vertical vibration (Faraday instability) is a crucial part of the atomization process because it is the transition phase for droplet generation. Based on the numerical solutions of the two-dimensional incompressible Euler equations for a prototype Faraday instability flow, we explored physically how a liquid ligament that is dynamically free from the vibrating liquid layer and behaves like a jet can be produced. According to linear theory, the suction of liquid from the trough portion to the crest portion creates an amplified crest. The amplified crest is always pulled back to the liquid layer in linear theory, no matter how largely the surface deforms; thus, a dynamically freed ligament never forms. However, under nonlinear conditions produced by large surface deformation, the impinging liquid flow from the trough portion enhances the pressure at the high crest (ligament) root. This pressure enhancement has two major effects. First, it reduces the amount of liquid sucked from the trough portion, which abates the increase in the crest height compared with that associated with linear theory. Second, it forms a local maximum pressure at the crest root; in this case, the ligament above this location becomes dynamically free from the motion of the bottom substrate in the laboratory reference frame. Liquid elements continuously enter the dynamically freed liquid region, producing a slender ligament from the liquid layer.
•The interface is traced by the coupled-level-set and volume-of-fluid method.•We analyze the detailed pressure and velocity fields obtained by simulation.•Nonlinearity causes a maximum pressure location formed at the crest root.•A freed ligament is formed above the maximum pressure location. Ligament formation from the surface of a horizontal liquid layer subject to a vertical vibration (Faraday instability) is a crucial part of the atomization process because it is the transition phase for droplet generation. Based on the numerical solutions of the two-dimensional incompressible Euler equations for a prototype Faraday instability flow, we explored physically how a liquid ligament that is dynamically free from the vibrating liquid layer and behaves like a jet can be produced. According to linear theory, the suction of liquid from the trough portion to the crest portion creates an amplified crest. The amplified crest is always pulled back to the liquid layer in linear theory, no matter how largely the surface deforms; thus, a dynamically freed ligament never forms. However, under nonlinear conditions produced by large surface deformation, the impinging liquid flow from the trough portion enhances the pressure at the high crest (ligament) root. This pressure enhancement has two major effects. First, it reduces the amount of liquid sucked from the trough portion, which abates the increase in the crest height compared with that associated with linear theory. Second, it forms a local maximum pressure at the crest root; in this case, the ligament above this location becomes dynamically free from the motion of the bottom substrate in the laboratory reference frame. Liquid elements continuously enter the dynamically freed liquid region, producing a slender ligament from the liquid layer.
Author Umemura, Akira
Li, Yikai
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Keywords Ligament
CLSVOF
Faraday instability
Nonlinear effect
Gas liquid interface
Digital simulation
Periodic oscillation
Boundary conditions
Surface waves
Two-phase flow
Modelling
Atomization
Non linear effect
Liquid spraying
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Snippet •The interface is traced by the coupled-level-set and volume-of-fluid method.•We analyze the detailed pressure and velocity fields obtained by...
Ligament formation from the surface of a horizontal liquid layer subject to a vertical vibration (Faraday instability) is a crucial part of the atomization...
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StartPage 64
SubjectTerms Amplification
CLSVOF
Droplets
Exact sciences and technology
Faraday instability
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Hydrodynamic waves
Instability
Ligament
Ligaments
Liquids
Multiphase and particle-laden flows
Nonhomogeneous flows
Nonlinear effect
Physics
Roots
Stability
Two dimensional
Title Two-dimensional numerical investigation on the dynamics of ligament formation by Faraday instability
URI https://dx.doi.org/10.1016/j.ijmultiphaseflow.2013.12.002
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