  We study the dynamics of a liquid droplet inside a gas over a large range of
the Knudsen numbers. The moving liquid droplet is modeled by the incompressible
Navier-Stokes equations, the surrounding rarefied gas by the Boltzmann
equation. The interface boundary conditions between the gas and liquid phases
are derived. The incompressible Navier-Stokes equations are solved by a
meshfree Lagrangian particle method called Finite Pointset Method (FPM), and
the Boltzmann equation by a DSMC type of particle method. To validiate the
coupled solutions of the Boltzmann and the incompressible Navier-Stokes
equations we have further solved the compressible and the incompressible
Navier-Stokes equations in the gas and liquid phases, respectively. In the
latter case both the compressible and the incompressible Navier-Stokes
equations are also solved by the FPM. In the continuum regime the coupled
solutions obtained from the Boltzmann and the incompressible Navier-Stokes
equations match with the solutions obtained from the compressible and the
incompressible Navier-Stokes equations. In this paper, we presented solutions
in one-dimensional physical space.
