Fluid mechanics calculations in physics of droplets I: Theoretical hydrodynamic formalism for the formation and condensation of spherical drops

It is proposed here a hydrodynamic formalism in order to obtain an approximate numerical solution to the Navier–Stokes equations. This formalism consists in the interpolation of the properties of the system of particles. The Smoothed Particle Hydrodynamics formalism (SPH) is employed when the system exhibits big deformation and large velocities because it is mesh-free in nature. In this study, it is simulated for the first time the condensation and formation of a spherical van der Waals drop by means of particles in three-dimensional space with the SPH formalism. When the drop is formed, starting from a gas box, the distribution of density implies that there are zones where the mass of gas is converted to a liquid state, but out of the droplet radius, some particles remain in the gas form.