  The design of strategies to generate efficient mixing is crucial for a
variety of applications, particularly digital microfluidic devices that use
small "discrete" fluid volumes (droplets) as fluid carriers and microreactors.
In recent work, we have presented an approach for the generation and control of
mixing inside a translating spherical droplet. This was accomplished by
considering Stokes' flow within a droplet proceeding downstream to which we
have superimposed time dependent (sinusoidal) rotation. The mixing obtained is
the result of the stretching and folding of material lines which increase
exponentially the surface contact between reagents. The mixing strategy relies
on the generation of resonances between the steady and the unsteady part of the
flow, which is achieved by tuning the parameters of the periodic rotation. Such
resonances, in our system, offer the possibility of controlling both the
location and the size of the mixing region within the droplet, which may be
useful to manufacture inhomogeneous particles (such as Janus particles). While
the period and amplitude of the periodic rotation play a major role, it is
shown here by using a triangular function that the particular shape of the
rotation (as a function of time) has a minor influence. This finding
demonstrates the robustness of the proposed mixing strategy, a crucial point
for its experimental realization.
