Bolaños Jimenez, RocioSevilla Santiago, AlejandroMartínez Bazán, C.2022-09-132022-09-132016-06-01Bolaños-Jiménez, R., Sevilla, A. & Martínez-Bazán, C. (2016, junio). Modeling of the bubbling process in a planar co-flow configuration. International Journal of Multiphase Flow, 82, 86-92.0301-9322https://hdl.handle.net/10016/35683This work presents an analytical model developed to describe the bubbling regime resulting from the injection of an air sheet of thickness 2H(o) with a mean velocity u(a) between two water streams of thickness H-w - H-o, moving at a uniform velocity u(w). Based on previous experimental and numerical characterizations of this flow, the gas stream is modeled as a two-dimensional sheet divided into three different parts in the streamwise direction: a neck that moves downstream at the water velocity, a gas ligament attached to the injector upstream of the neck, and a forming bubble downstream of the neck, whose uniform dimensionless half-thicknesses are eta(n)(tau), eta(l)(tau), eta(b)(tau) respectively, and the corresponding pressures are given by Pi(n)(tau), Pi(l)(tau), and Pi(b)(tau) Pi(n)(tau). Lengths are made dimensionless with H-o, and pressures with rho(a)u(a)(2) where rho(a) is the air density.7eng© 2016 Elsevier Ltd. All rights reservedAtribución-NoComercial-SinDerivadas 3.0 EspañaBubble formationCo-flow configurationTheorerical modelingAir-water sheetsMicrobubblesGenerationAbsoluteGrowthNozzleJetsresearch articleIngeniería Mecánicahttps://doi.org/10.1016/j.ijmultiphaseflow.2016.02.010open access8692International Journal of Multiphase Flow82AR/0000018675