Modelling of sprays: simple solutions of complex problems

Some new approaches to the solution of complex problems, focused on spray modelling, using relatively simple mathematical tools are briefly summarised. The following problems are considered: modelling of spray drying with pharmaceutical applications, modelling of heating and evaporation of suspended droplets with applications to water sprays for fire suppression, modelling of micro-explosions with automotive applications, and parameterisations of slow invariant manifolds with applications to spray ignition modelling. The modelling of spray drying is based on the assumption that the array of small suspended solid particles inside droplets can be treated as a non-evaporating liquid component. The modelling of the effect of a support rod on droplet heating and evaporation is based on the assumption that this heat is homogeneously distributed inside the whole volume of a droplet. In the modelling of a puffing/micro-explosion it is assumed that a water sub-droplet is located exactly at the centre of a fuel droplet and the temperature at the surface of the fuel droplet is fixed. In the presentation of slow invariant manifolds in parametric form these manifolds are found using asymptotic expansions. (paper)