On localized mixing in action–action–angle flows

• We studied mixing in multiscale-flows.
• We illustrated the method of partial averaging near resonances.
• We computed the size of the localized domain of chaotic advection.
• We estimated the rate of mixing.

Tailored mixing inside individual droplets could be useful to ensure that reactions within microscopic discrete fluid volumes, which are used as microreactors in “digital microfluidic” applications, take place in a controlled fashion. We consider a translating spherical liquid drop to which we impose a time periodic rigid-body rotation. Such a rotation induces mixing via chaotic advection in a narrow area inside the drop. We show that chaotic advection is caused by the resonance destruction of adiabatic invariants and derive an analytical description for the size of the mixing region.