Bubble pressure requirements to control the bubbling process in forced co-axial air-water jets Articles uri icon

publication date

  • December 2020

start page

  • 1

end page

  • 14


  • 133

International Standard Serial Number (ISSN)

  • 0301-9322

Electronic International Standard Serial Number (EISSN)

  • 1879-3533


  • We analyse the controlled generation of bubbles of a given size at a determined bubbling rate in a co flowing water stream forcing the gas flow. The temporal evolution of the bubble size, R(t), the air flow
    rate, Qa(t), and the pressure evolution inside the bubble, pb(t), during the bubbling process are reported.
    To that aim, the temporal evolution of the bubble shape and the pressure inside the air feeding chamber,
    pc(t), where a harmonic perturbation is induced using a loudspeaker, are obtained from high-speed im ages synchronized with pressure measurements. A model is developed to describe the unsteady motion
    of the gas stream along the injection needle, coupled with the Rayleigh-Plesset equation for the growing
    bubble, allowing us to obtain pb(t). Thus, the minimum pressure amplitudes required inside the forming
    bubble to control their size and bubbling frequency are provided as a function of the gas flow rate, the
    liquid velocity, uw, and the forcing frequency, ff. Two different behaviors have been observed, depending
    on the liquid-to-gas velocity ratio, = uw/ua. For small enough values of , the critical pressure ampli tude is given by ps ∼ ρa c ua St3
    f , associated to a rapid pressure increase taking place during an interval of
    time of the order of the acoustic time. However, for larger values of , ps ∼ ρ u2
    w St3
    f −1/5 We−1/4. Here
    ρ and ρa are the liquid and gas densities respectively, c the speed of sound in air and Stf = ffro/uw and
    We = ρu2
    wro/σ the Strouhal and Weber numbers, where ro denotes the outer radius of the injector.


  • Industrial Engineering


  • bubble formation; bubble pressure; bubbling frequency