Lagrangian transport structures for three-dimensional and time-dependent fluid flows are of great interest in numerous applications, particularly for geophysical or oceanic flows. In such flows, chaotic transport and mixing can play important environ
mental and ecological roles, for examples in pollution spills or plankton migration. In such flows, where simulations or observations are typically available only over a short time, understanding the difference between short-time and long-time transport structures is critical. In this paper, we use a set of classical (i.e. Poincare section, Lyapunov exponent) and alternative (i.e. finite time Lyapunov exponent, Lagrangian coherent structures) tools from dynamical systems theory that analyze chaotic transport both qualitatively and quantitatively. With this set of tools we are able to reveal, identify and highlight differences between short- and long-time transport structures inside a flow composed of a primary horizontal contra-rotating vortex chain, small lateral oscillations and a weak Ekman pumping. The difference is mainly the existence of regular or extremely slowly developing chaotic regions that are only present at short time.
The mayfly nymph breathes under water through an oscillating array of wing-shaped tracheal gills. As the nymph grows, the kinematics of these gills change abruptly from rowing to flapping. The classical fluid dynamics approach to consider the mayfly
nymph as a pumping device fails in giving clear reasons to this switch. In order to understand the whys and the hows of this switch between the two distinct kinematics, we analyze the problem under a Lagrangian viewpoint. We consider that a good Lagrangian transport that distributes and spreads water and dissolved oxygen well between and around the gills is the main goal of the gill motion. Using this Lagrangian approach we are able to provide the reason behind the switch from rowing to flapping that the mayfly nymph experiences as it grows. More precisely, recent and powerful tools from this Lagrangian approach are applied to in-sillico mayfly nymph experiments, where body shape, as well as, gill shapes, structures and kinematics are matched to those from in-vivo. In this letter, we show both qualitatively and quantitatively how the change of kinematics enables a better attraction, stirring and confinement of water charged of dissolved oxygen inside the gills area. From the computational velocity field we reveal attracting barriers to transport, i.e. attracting Lagrangian coherent structures, that form the transport skeleton between and around the gills. In addition, we quantify how well the fluid particles and consequently dissolved oxgen is spread and stirred inside the gills area.
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.
Enhancing and controlling chaotic advection or chaotic mixing within liquid droplets is crucial for a variety of applications including digital microfluidic devices which use microscopic ``discrete fluid volumes (droplets) as microreactors. In this w
ork, we consider the Stokes flow of a translating spherical liquid droplet which we perturb by imposing a time-periodic rigid-body rotation. Using the tools of dynamical systems, we have shown in previous work that the rotation not only leads to one or more three-dimensional chaotic mixing regions, in which mixing occurs through the stretching and folding of material lines, but also offers the possibility of controlling both the size and the location of chaotic mixing within the drop. Such a control was achieved through appropriate tuning of the amplitude and frequency of the rotation in order to use resonances between the natural frequencies of the system and those of the external forcing. In this paper, we study the influence of the orientation of the rotation axis on the chaotic mixing zones as a third parameter, as well as propose an experimental set up to implement the techniques discussed.
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.
