Single-bubble cavitation in quiescent and sheared liquids

The bubble cavitation problem in quiescent and sheared liquids is investigated using a third-order isothermal lattice Boltzmann (LB) model that describes a two-dimensional ($2D$) fluid obeying the van der Waals equation of state. The LB model has 16 off-lattice velocities and is based on the Gauss-Hermite quadrature method. The evolution equations for the distribution functions in this model are solved using the corner transport upwind numerical scheme on large square lattices (up to $4096 \times 4096$ nodes). In a quiescent liquid, the computer simulation results are in good agreement to the $2D$ Rayleigh-Plesset equation. In a sheared liquid, we investigated the evolution of the total bubble area, the bubble deformation and the bubble tilt angle, for various values of the shear rate. A linear relation between the dimensionless deformation coefficient $D$ and the capillary number $Ca$ is found at small $Ca$ but with a different factor than in equilibrium liquids. A non-linear regime is observed for $Ca \gtrsim 0.3$.