(444b) Shape Evolution of Miscible Drops with Arbitrary Viscosity Ratio: Lagrangian-Eulerian Swarms of Stokeslets and Subgrid Resolution
In this talk we present a Lagrangian/Eulerian hybrid method based on a swarm of Stokeslets that accurately tracks complex shape evolutions. The case of unit viscosity ratio is interesting in its determination of intricate local structures by global hydrodynamic interactions, These are efficiently treated with a particle-mesh (PM) scheme in which cell-cell interactions are computed in O(N log N) operations.
The new element presented here is a subgrid-accurate scheme for treating different viscosities of the drop versus bath. A particle-particle / particle-mesh (P3M) scheme is combined with iterative treatment of piecewise constant viscosity (and discontinuities at the interfaces) as an effective body force. Computer simulations will be compared with drop visualization experiments using a high-speed camera.
The particulate character of the method opens an avenue for tracking strain histories and thereby extending the treatment to viscoelastic drops as well.