We report an experimental and theoretical study of the collapse time of a gas bubble injected into an otherwise stagnant liquid under quasi-static conditions and for a wide range of liquid viscosities. The experiments were performed by injecting a constant flow rate of air through a needle with inner radius a into several water/glycerine mixtures, providing a viscosity range of 20 cP ≲ μ ≲ 1500 cP. By analyzing the temporal evolution of the neck radius, R0(t), the collapse time has been extracted for three different stages during the collapse process, namely, Ri/a = 0.6, 0.4, and 0.2, being Ri = R0(t = 0) the initial neck radius. The collapse time is shown to monotonically increase with both Ri/a and with the Ohnesorge number, , where ρ and σ represent the liquid density and the surface tension coefficient, respectively. The theoretical approach is based on the cylindrical Rayleigh-Plesset equation for the radial liquid flow around the neck, which is the appropriate leading-order representation of the collapse dynamics, thanks to the slenderness condition R0(t) r1(t) ≪ 1, where r1(t) is half the axial curvature of the interface evaluated at the neck. The Rayleigh-Plesset equation can be integrated numerically to obtain the collapse time, τcol, which is made dimensionless using the capillary time, . We present a novel scaling law for τcol as a function of Ri/a and Oh that closely follows the experimental data for the entire range of both parameters, and provide analytical expressions in the inviscid and Stokes regimes, i.e., and τcol(Oh → ∞) → 2Oh, respectively, where C is a constant of order unity that increases with Ri/a.
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April 2016
Research Article|
April 06 2016
The necking time of gas bubbles in liquids of arbitrary viscosity
R. Bolaños-Jiménez
;
R. Bolaños-Jiménez
a)
1Área de Mecánica de Fluidos, Departamento de Ingeniería Mecánica y Minera,
Universidad de Jaén
, Campus de las Lagunillas, 23071 Jaén, Spain
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A. Sevilla
;
A. Sevilla
b)
2Área de Mecánica de Fluidos, Departamento de Ingeniería Térmica y de Fluidos,
Universidad Carlos III de Madrid
, 28911 Leganés, Spain
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C. Martínez-Bazán
C. Martínez-Bazán
c)
1Área de Mecánica de Fluidos, Departamento de Ingeniería Mecánica y Minera,
Universidad de Jaén
, Campus de las Lagunillas, 23071 Jaén, Spain
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a)
Electronic mail: rbolanos@ujaen.es
b)
Electronic mail: asevilla@ing.uc3m.es
c)
Electronic mail: cmbazan@ujaen.es
Physics of Fluids 28, 042105 (2016)
Article history
Received:
January 10 2016
Accepted:
March 17 2016
Citation
R. Bolaños-Jiménez, A. Sevilla, C. Martínez-Bazán; The necking time of gas bubbles in liquids of arbitrary viscosity. Physics of Fluids 1 April 2016; 28 (4): 042105. https://doi.org/10.1063/1.4944973
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