Publication Date:
2016-04-07
Description:
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, R 0 ( t ), the collapse time has been extracted for three different stages during the collapse process, namely, R i / a = 0.6, 0.4, and 0.2, being R i = R 0 ( t = 0) the initial neck radius. The collapse time is shown to monotonically increase with both R i / a and with the Ohnesorge number, Oh = μ / ρ σ R i , 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 R 0 ( t ) r 1 ( t ) ≪ 1, where r 1 ( 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, τ col , which is made dimensionless using the capillary time, t σ = ρ R i 3 / σ . We present a novel scaling law for τ col as a function of R i / 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., τ col ( Oh → 0 ) → 2 ln C and τ col ( Oh → ∞) → 2 Oh , respectively, where C is a constant of order unity that increases with R i / a .
Print ISSN:
1070-6631
Electronic ISSN:
1089-7666
Topics:
Physics
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