Fouling in gas turbines is caused by airborne contaminants which, under certain conditions, adhere to aerodynamic surfaces upon impact. The growth of solid deposits causes geometric modifications of the blades in terms of both mean shape and roughness level. The consequences of particle deposition range from performance deterioration to life reduction to complete loss of power. Due to the importance of the phenomenon, several methods to model particle sticking have been proposed in literature. Most models are based on the idea of a sticking probability, defined as the likelihood a particle has to stick to a surface upon impact. Other models investigate the phenomenon from a deterministic point of view by calculating the energy available before and after the impact. The nature of the materials encountered within this environment does not lend itself to a very precise characterization, consequently, it is difficult to establish the limits of validity of sticking models based on field data or even laboratory scale experiments. As a result, predicting the growth of solid deposits in gas turbines is still a task fraught with difficulty. In this work, two non-dimensional parameters are defined to describe the interaction between incident particles and a substrate, with particular reference to sticking behavior in a gas turbine. In the first part of the work, historical experimental data on particle adhesion under gas turbine-like conditions are analyzed by means of relevant dimensional quantities (e.g. particle viscosity, surface tension, and kinetic energy). After a dimensional analysis, the data then are classified using non-dimensional groups and a universal threshold for the transition from erosion to deposition and from fragmentation to splashing based on particle properties and impact conditions is identified. The relation between particle kinetic energy/surface energy and the particle temperature normalized by the softening temperature represents the original non-dimensional groups able to represent a basis of a promising adhesion criterion. (C) 2019 Elsevier Ltd. All rights reserved.