The recent volcanic crisis of 2010 Eyjafjallajökull eruption (Iceland) has demonstrated the widespread impact that even small-moderate explosive volcanic eruptions can have on our society. As a matter of fact the long range prediction of volcanic ash is still affected by our poor understanding of size-selective sedimentation processes, e.g. particle aggregation. Main objectives of this thesis include to: i) develop a robust mathematical framework to theoretically describe ash aggregation, based on field, theoretical and experimental constraints. This new theoretical framework, named the Generalized Fixed Pivot Technique (GFPT), can be applied in different contexts and disciplines; ii) better characterize the physics of ash aggregation, providing a coherent formalization. This resulted in a new parameterization of crucial physical processes, such as the collision rate and the sticking efficiency of collisional processes; and iii) improve the description of large clasts sedimentation in order to better characterize the plume height of volcanic eruptions.