1. Chaotic Mixing in Microdroplets
Roman Grigoriev, School of Physics, Georgia Institute of Technology
The fundamental difficulty of mixing fluids at small scale is a major obstacle to the success of many planned applications of microfluidics/ microreaction technologies. This project explores basic mechanisms of introducing chaotic advection to enhance mixing in steady and time-dependent volume-preserving Stokes flows.
Our studies of weakly chaotic (near-integrable) flows have shown that the mechanism leading to mixing in both types of flows is similar and can be described by the slow drift of the adiabatic invariants resulting from the crossings of singular surfaces (separatrices for steady and resonant surfaces for time-periodic flows) by the flow streamlines.
We have developed a computational procedure allowing one to:
- Determine the types of weak perturbations that are most effective in
destroying the transport barriers of integrable flows
- Compute the shape of the domains where mixing does (or does not)
occur
- Obtain an estimate of the mixing rate inside the mixed domain
These developments allow identification of several fundamental principles that should be followed in designing flows with good mixing properties and should provide guidance for engineers developing the next generation of microfluidic devices.
Volume of the unmixed domain as a function of the curvature of the temperature field driving a steady thermocapillary flow inside a droplet
Width of the unmixed domain as a function of the modulation frequency for a magneto-hydrodynamically driven cellular flow in a rectangular microchannel