simulate a fluid within a solid sphere we take the simple approach of defining all grid cells whose centers lie within the solid region as solid. Then Dirichlet (no-slip) boundary conditions for the velocity and Neumann conditions for the pressure are applied to those cell faces as in the projection method. On a Cartesian grid this necessarily creates a stair-stepped solid/fluid boundary; however it is found that the method works well in practice since the discrete momentum flux is conserved and is simpler than and equivalent to other approaches which impose a near-wall force to ensure a no-slip condition at the solid [@Trygg2011]. See [@shin2017solver] for further details.

Physical parameters of the fluids {#sec:phys_par}
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Our numerical code can treat inner and outer spherical domains of any size containing fluids of any density $\rho$, viscosity $\nu$, and surface tension $\sigma$, leading potentially to a large number of non-dimensional parameters, in addition to those describing the forcing amplitude $a$ and frequency $\omega$. We have chosen to limit the parameter space as follows.

The density and viscosity ratios that we have chosen are typical of oil droplets in air. The inner and outer densities are $\rho_d=940$ kg/m$^3$ and $\rho_{\rm out}=1.205$ kg/m$^3$, leading 