46,974 research outputs found

    Pairwise interactions in inertially-driven one-dimensional microfluidic crystals

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    In microfluidic devices, inertia drives particles to focus on a finite number of inertial focusing streamlines. Particles on the same streamline interact to form one-dimensional microfluidic crystals (or "particle trains"). Here we develop an asymptotic theory to describe the pairwise interactions underlying the formation of a 1D crystal. Surprisingly, we show that particles assemble into stable equilibria, analogous to the motion of a damped spring. Although previously it has been assumed that particle spacings scale with particle diameters, we show that the equilibrium spacing of particles depends on the distance between the inertial focusing streamline and the nearest channel wall, and therefore can be controlled by tuning the particle radius.Comment: 15 pages, 9 figure

    Vortex sheets and diffeomorphism groupoids

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    In 1966 V.Arnold suggested a group-theoretic approach to ideal hydrodynamics in which the motion of an inviscid incompressible fluid is described as the geodesic flow of the right-invariant L2L^2-metric on the group of volume-preserving diffeomorphisms of the flow domain. Here we propose geodesic, group-theoretic, and Hamiltonian frameworks to include fluid flows with vortex sheets. It turns out that the corresponding dynamics is related to a certain groupoid of pairs of volume-preserving diffeomorphisms with common interface. We also develop a general framework for Euler-Arnold equations for geodesics on groupoids equipped with one-sided invariant metrics.Comment: Final version accepted to Advances in Mathematics; 46 pages, 6 figure
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