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We present an experimental and numerical study of the periodic breakup of an air sheet surrounded by two co-flowing water streams. For a fixed liquid-to-gas thickness ratio, h = h(w)/h(a) similar or equal to 5.27, we explore the dependence of the bubbling regime on the two main governing parameters, namely the Weber number, We = rho(w)u(w)(2)h(a)/sigma, and the velocity ratio, Lambda = u(w)/u(a), where u(w) and u(a) are the mean water and air velocities at the exit slit, respectively, and h(a) and h(w) are the half-thicknesses of the air and water sheets at the outlet. The bubble formation frequencies obtained experimentally are in good quantitative agreement with the results of numerical computations performed with the volume-of-fluid technique. The analysis of the results obtained allows a detailed characterization of the dynamics of the bubble formation process in planar co-flows. In particular, using the pressure fluctuations in the gas stream and the time evolution of the bubble interface, both obtained from the numerical simulations, the bubbling process is described through a two-stage mechanism governed by distinct physical phenomena: the first stage is characterized by the formation of a neck that moves downstream at the liquid velocity, and it collapses towards the symmetry plane during the second stage. A simple scaling law is proposed for the bubbling frequency, that shows a good agreement with our experimental and numerical results.