The necking time of gas bubbles in liquids of arbitrary viscosity Articles uri icon

publication date

  • April 2016

issue

  • 4

volume

  • 28

international standard serial number (ISSN)

  • 1070-6631

electronic international standard serial number (EISSN)

  • 1089-7666

abstract

  • 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 less than or similar to mu less than or similar to 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 = mu/root rho sigma R-i, where rho and sigma 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, tau(col), which is made dimensionless using the capillary time, t(sigma) = root rho R-i(3)/sigma. We present a novel scaling law for tau(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., tau(col)(Oh -> 0) -> root 2 lnC and tau(col)(Oh -> infinity) -> 2Oh, respectively, where C is a constant of order unity that increases with R-i/a. (C) 2016 AIP Publishing LLC.

keywords

  • viscous-liquid; inviscid liquid; orifice; coalescence; injection