In most of the literature, the hydrocyclone is viewed as a black box in which only global variables are present and where the equations are obtained by curve fitting. Recently some work has appeared where the Navier Stokes equations are solved numerically in the hydrocyclone geometry. However, in all of these works the air core surface, which has an important influence on the hydrocyclone dynamical behaviour, is modelled as being a cylindrical surface of fixed radius. In this work, we model the surface of the air core as a free-boundary which has to satisfy a jump condition, the Young-Laplace equation, relating the physics to the geometry. Based on this model, we are able to explain, qualitatively, some phenomena that have puzzled research workers in the field for many years, and can show, through the air core behaviour, the influence of material parameters on the performance of the hydrocyclone.