Rarefaction effects in head-on collision of two identical droplets

TL;DR

This study investigates how rarefaction effects influence the head-on collision dynamics of identical droplets, revealing significant deviations from continuum models and identifying mechanisms that enhance droplet coalescence.

Contribution

It demonstrates the importance of rarefaction effects in droplet collisions using kinetic theory, highlighting their impact on flow topology, vorticity, and energy conversion mechanisms.

Findings

Rarefaction effects alter streamline topology near droplets.

They suppress high vorticity concentration inside the interdroplet region.

Rarefaction enhances energy transfer from free to kinetic energy, promoting coalescence.

Abstract

The head-on collision of two identical droplets is investigated based on the BGK-Boltzmann equation. Gauss-Hermite quadratures with different degree of precision are used to solve the kinetic equation, so that the continuum (solution truncated at the Navier-Stokes order) and non-continuum (rarefied gas 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 interdroplet gas film along the vertical direction, thereby boosting droplet coalescence.