(444b) Shape Evolution of Miscible Drops with Arbitrary Viscosity Ratio: Lagrangian-Eulerian Swarms of Stokeslets and Subgrid Resolution

Gravity/buoyancy driven motion, deformation, coalescence and breakup of miscible drops is central to geophysical flows of mantle plumes, and also enables an emerging, patented technology of fluid-phase self-assembly of drug delivery particles (toroidal-spiral particles or TSP) by competitive-kinetics. Essentially unchecked by (negligible) interfacial forces, viscous effects lead to evolution of extremely intricate drop shapes and their interfaces, which can frustrate Eulerian-volumetric and boundary-element methods.

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.