Rarefaction effects in head-on collision of two near-critical droplets

Abstract

The head-on collision of two droplets near the critical point is investigated based on the Boltzmann-BGK equation. Gauss–Hermite quadratures with different degree of precision are used to solve the kinetic equation, so that the solutions truncated at the Navier–Stokes order and non-continuum (i.e., rarefied fluid dynamics) solutions can be compared. When the kinetic equation is solved with adequate accuracy, prominent variations of the vertical velocity (the collision is in the horizontal direction), the viscous stress components, and droplet morphology are observed during the formation of liquid bridge, which demonstrates the importance of the rarefaction effects and the failure of the Navier–Stokes equation. The rarefaction effects change the topology of streamlines near the droplet surface, suppress the high-magnitude vorticity concentration inside the interdroplet region, and promote the vorticity diffusion around outer droplet surface. Two physical mechanisms responsible for the local energy conversion between the free and kinetic energies are identified, namely, the total pressure-dilatation coupling effect and the interaction between the density gradient and strain rate tensor. An energy conversion analysis is performed to show that the rarefaction effects can enhance the conversion from free energy to kinetic energy and facilitate the discharge of the gas interval along the vertical direction, thereby boosting droplet coalescence. Furthermore, the magnitude and the spatial oscillation frequency of the Lamb vector divergence inside the gas interval are shown to be suppressed by the rarefaction effects. It is found that the dynamic process in the gas interval is closely associated with the interaction between the adjacent positive and negative regions of the Lamb vector divergence.