We have developed hybrid numerical simulation codes to investigate the dynamics of nanobubbles. The idea is based on a combination of a molecular dynamics (MD) technique and a continuum dynamics with the CIP method. The MD technique enables us to examine rapid change of the bubble surface and the inside region of nanobubbles at molecular scale. The CIP method enables us to trace the mass and energy transfer processes far from the bubble surface at continuum scale. In the hybrid simulation, the simulation cell is divided into two parts. The inner region containing a bubble (or bubbles) consists of sufficiently large number of particles and is treated with the MD method. The outer region is treated with a computational fluid dynamics (CFD) scheme. The boundary between the inner and outer regions is movable and driven with the pressure difference between the two regions. To deal with the moving boundary, we adopt the CIP scheme. Two different codes have been developed, i.e., one-dimensional CFD with assuming a spherical symmetry, and full three-dimensional CFD. Examples will be given in the paper to demonstrate each code. The first example is the oscillating dynamics of a spherical bubble with one-dimensional CFD. The bubble is initially located at the center of the MD region with no translational motion. The outer (continuum) region is treated one dimensionally, with the assumption of spherical symmetry. Under the equilibrium condition, where there is no pressure difference between the two regions, we give a sudden pressure increase in the continuum region far from the bubble. The spherical pressure wave propagates through the continuum region, and the pressure difference drives the boundary to shrink the MD region. As the MD region shrinks, the bubble inside the region starts to collapse. The collapsed bubble bounces back. We have analyzed the oscillation dynamics under several different conditions, such as different initial pressures and the state of gas inside the bubble. The second one is the deformation of a non-spherical bubble. For that purpose, the continuum region is treated with full three-dimensional CIP scheme. Furthermore, we use the level set method in order to capture the interfaces (boundary) between the MD region and the continuum region.

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