Self-similar fields are observed in flows when there is no time or length scale imposed. The self-similar behavior of flows allows for a description of the velocity field as a function of one self-similar coordinate only. Further to many single-phase flows, there is evidence for self-similar behavior of both the liquid and the gas phase in spray flows also. In most works on self-similar sprays, the liquid and the gas were injected simultaneously, often resulting in a small slip velocity between the two phases. The dynamics of these sprays can be modeled analogous to single-phase jets, accounting for variable fluid density.

In the present work we experimentally investigate the dynamics of sprays from consumer spray cans for body and textile care in order to predict the transport and drying behaviors of the spray drops. The aim is to assess health risks from nanoparticle-laden sprays. In the sprays investigated, only liquid is ejected into quiescent ambient air, resulting in large slip velocities between the liquid and the gas phase. Hence, solely momentum transfer between the two phases induces the motion of the gas phase. Phase-Doppler measurements reveal the evolution of the spray drop and gas flow fields to be modelled. Three sprays at different liquid Weber and Ohnesorge numbers are considered.

We show that, for all the sprays investigated, the gas flow fields exhibit self-similar behavior close to the well-known single-phase jet, but with different axial scaling of the self-similar variables, since the momentum flow rate increases downstream, while it is constant for single-phase jets. In order to model the gas flow we transform the equations of motion from boundary layer theory into a self-similar form, accounting for momentum transfer between the gas and the liquid phases in the flow at constant pressure. The self-similar ansatz introduced yields a self-similar solution for the gas flow fields of the sprays investigated. A priori unknown coefficients of the ansatz are determined with the help of the Phase-Doppler data. The self-similar solution obtained for the gas flow field shows excellent agreement with the experimental results.