Early stage of bubble spreading in a viscous ambient liquid

We investigate numerically the spreading dynamics of a bubble coming into contact with a smooth solid substrate in a viscous liquid. The substrate is partially wettable, and the singularity of the moving contact line is relieved by adopting the Navier-slip model. The Stokes equations are solved by employing a boundary element method coupled with adaptive mesh refinement. This allows us to realize sufficiently small slip lengths down to $O(10^{-5})$ in dimensionless form, which is crucial to resolve the local interface structures at the early stage of spreading. The results show that the early-stage spreading of the bubble is always characterized by the growth and propulsion of a dewetting liquid rim close to the contact line, while the macroscopic interface remains unchanged. The evolution of the contact line and the morphology of the rim depends on the wettability and the slip length, and a parametric investigation is performed. Based on mass conservation, a relation between the rim size and the spreading radius is established. We also propose an analytical prediction of the temporal variation in the contact line radius at the early stage of spreading, which is found to follow a logarithmically corrected linear relation rather than a pure power law. Moreover, the early stages of bubble spreading are qualitatively similar for two-dimensional and axisymmetric configurations.