This 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. In a reference frame moving with the water velocity, and imposing a negative pressure caused by the sudden expansion of the air stream at the outlet of the injector, a set of algebraic-differential equations are deduced, that can be numerically integrated to obtain the temporal evolution of the interface positions and gas pressures, as well as of the gas flow rate through the neck. The model shows a good agreement with previous experimental and numerical results for a given value of the initial velocity of the collapsing neck, determined by an iterative method that matches the bubbling time with that given by Gutierrez-Montes et al. (2013), tau(c)(b) = 9.1 Lambda root(rho(w)/rho(a))(h - 1)/[We (beta - beta(2))]. Here Lambda = u(w)/u(a) is the water-to-air velocity ratio, We = rho(w)u(w)(2)H(o)/sigma the Weber number, h = H-w/H-o the water-to-air thickness ratio and (1 - beta) = (H-o - H-i)/H-o the dimensionless wall thickness of the air injector. (C) 2016 Elsevier Ltd. All rights reserved.