Quasiadiabatic description of nonlinear particle dynamics in typical magnetotail configurations

International audienceIn the present paper we discuss the motion of charged particles in three different regions of the Earth magnetotail: in the region with magnetic field reversal and in the vicinities of neutral line of X- and O-types. The presence of small parameters (ratio of characteristic length scales in and perpendicular to the equatorial plane and the smallness of the electric field) allows us to introduce a hierarchy of motions and use methods of perturbation theory. We propose a parameter that plays the role of a measure of mixing in the system

Controlling Mixing Inside a Droplet by Time Dependent Rigid-body Rotation

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 which 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.Comment: 6 pages, 6 figure

Using Resonances to Control Chaotic Mixing within a Translating and Rotating Droplet

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 work, 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.Comment: 15 pages, 6 figure

On passage through resonances in volume-preserving systems

Resonance processes are common phenomena in multiscale (slow-fast) systems. In the present paper we consider capture into resonance and scattering on resonance in 3-D volume-preserving slow-fast systems. We propose a general theory of those processes and apply it to a class of viscous Taylor-Couette flows between two counter-rotating cylinders. We describe the phenomena during a single passage through resonance and show that multiple passages lead to the chaotic advection and mixing. We calculate the width of the mixing domain and estimate a characteristic time of mixing. We show that the resulting mixing can be described using a diffusion equation with a diffusion coefficient depending on the averaged effect of the passages through resonances.Comment: 23 pages and 9 Figure

Tuning Mixing within a Droplet for Digital Microfluidics

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.Comment: 17 pages,6 figures. to appear Mechanics Research Communication

The fcc-bcc crystallographic orientation relationship in AlxCoCrFeNi high-entropy alloys

This paper concentrates on the crystallographic-orientation relationship between the various phases in the Al-Co-Cr-Fe-Ni high-entropy alloys. Two types of orientation relationships of bcc phases (some with ordered B2 structures) and fcc matrix were observed in Al0.5CoCrFeNi and Al0.7CoCrFeNi alloys at room temperature: (1 -1 0)(bcc)//(200)(fcc), [CM](bcc)//[001](fcc), (b) (1 -1 1)B2//(2 - 2 0)(fcc), [011]B2//[11 root 2](fcc). (C) 2016 Elsevier B.V. All rights reserved.</p