We present a model for volcanic eruptions in open-conduit condition based on the transport of batches of magma driven by the accumulation of bubbles. The viscosity of the surrounding magma counteracts gravity; however, the primary upward force acting on these bodies is driven by gas vesicles which accumulate beneath the denser bodies. Few simple and realistic assumptions lead to our theoretical model, based on the Brownian motion of colder and denser bodies embedded in a less dense and hotter magma, that can fit very well the erupted volumes distribution obtained from on field observations. Further validation is provided by extensive simulations which include all the main theoretical ingredients and, at the same time, provide additional insights on the functioning of volcanoes. Overall, the model provides a good representation of the Strombolian eruptive style. In fact, it was developed to address the apparent paradox of observing denser erupted materials embedded within a less dense magmatic medium. Furthermore, the model successfully reproduces the eruption volume distributions across various eruptive styles, suggesting that a mechanism such as coalescence underpins a more generalized framework for volcanic activity.