Periodic forcing of nonlinear oscillators generates a rich and complex variety of behaviors, ranging from regular to chaotic behavior. In this work we seek to control, i.e., either suppress or generate, the chaotic behavior of a classical reference e
xample in books or introductory articles, the Duffing oscillator. For this purpose, we propose an elegant strategy consisting of simply adjusting the shape of the time-dependent forcing. The efficiency of the proposed strategy is shown analytically, numerically and experimentally. In addition due to its simplicity and low cost such a work could easily be turned into an excellent teaching tool.
The ability to generate complete, or almost complete, chaotic mixing is of great interest in numerous applications, particularly for microfluidics. For this purpose, we propose a strategy that allows us to quickly target the parameter values at which
complete mixing occurs. The technique is applied to a time periodic, two-dimensional electro-osmotic flow with spatially and temporally varying Helmoltz-Smoluchowski slip boundary conditions. The strategy consists of following the linear stability of some key periodic pathlines in parameter space (i.e., amplitude and frequency of the forcing), particularly through the bifurcation points at which such pathlines become unstable.
The use of microscopic discrete fluid volumes (i.e., droplets) as microreactors for digital microfluidic applications often requires mixing enhancement and control within droplets. In this work, we consider a translating spherical liquid droplet to w
hich we impose a time periodic rigid-body rotation which we model using the superposition of a Hill vortex and an unsteady rigid body rotation. This perturbation in the form of a rotation not only creates a three-dimensional chaotic mixing region, which operates through the stretching and folding of material lines, but also offers the possibility of controlling both the size and the location of the mixing. Such a control is achieved by judiciously adjusting the three parameters that characterize the rotation, i.e., the rotation amplitude, frequency and orientation of the rotation. As the size of the mixing region is increased, complete mixing within the drop is obtained.
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 pr
esented 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.
