The interfacial area per unit volume is one of the key parameters in bubbly flow. Momentum, mass and energy transfer occur through the interface between the phases. The functionality of two phase reactors with bubbly flow depends mainly on these three transfer processes. Thus, the design process of a reactor requires the prediction of interfacial area density. In the present work a simple equation for the interfacial area density is derived from the population balance, taking into account the events of coalescence and bubble break-up for each bubble fraction. The system of partial integro-differential equations is simplified. Since the integrals in these equations complicate a numerical treatment. This reduces the balance to one single partial differential equation. An approximate analytical solution is given. If the resulting equation is applied to large gas fluxes, the instability of the coalescence process causes large bubbles and gas plugs to develop. From the instability the volume fraction of the large bubbles and gas plugs may be predicted. Additives may hinder the coalescence process. Experiments show that coalescence hindrance changes the coalescence kernel only by a factor. Calculations are done for bubble columns and vertical pipe flow.