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Register a new userLevy Walks and Path Chaos in the Dispersal of Elongated Structures Moving across Cellular Vortical Flows
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In cellular vortical flows, namely arrays of counter-rotating vortices, short but flexible filaments can show simple random walks through their stretch-coil interactions with flow stagnation points. Here, we study the dynamics of semi-rigid filaments long enough to broadly sample the vortical field. Using simulation, we find a surprising variety of long-time transport behavior -- random walks, ballistic transport, and trapping -- depending upon the filaments relative length and effective flexibility. Moreover, we find that filaments execute Levy walks whose diffusion exponents generally decrease with increasing filament length, until transitioning to Brownian walks. Lyapunov exponents likewise increase with length. Even completely rigid filaments, whose dynamics is finite-dimensional, show a surprising variety of transport states and chaos. Fast filament dispersal is related to an underlying geometry of ``conveyor belts. Evidence for these various transport states are found in experiments using arrays of counter-rotating rollers, immersed in a fluid and transporting a flexible ribbon.
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We study the flow of elongated grains (wooden pegs of length $L$=20 mm with circular cross section of diameter $d_c$=6 and 8 mm) from a silo with a rotating bottom and a circular orifice of diameter $D$. In the small orifice range ($D/d<5$) clogs are mostly broken by the rotating base, and the flow is intermittent with avalanches and temporary clogs. Here $dequiv(frac{3}{2}d_c^2L)^{1/3}$ is the effective grain diameter. Unlike for spherical grains, for rods the flow rate $W$ clearly deviates from the power law dependence $Wpropto (D-kd)^{2.5}$ at lower orifice sizes in the intermittent regime, where $W$ is measured in between temporary clogs only. Instead, below about $D/d<3$ an exponential dependence $Wpropto e^{kappa D}$ is detected. Here $k$ and $kappa$ are constants of order unity. Even more importantly, rotating the silo base leads to a strong -- more than 50% -- decrease of the flow rate, which otherwise does not depend significantly on the value of $omega$ in the continuous flow regime. In the intermittent regime, $W(omega)$ appears to follow a non-monotonic trend, although with considerable noise. A simple picture, in terms of the switching from funnel flow to mass flow and the alignment of the pegs due to rotation, is proposed to explain the observed difference between spherical and elongated grains. We also observe shear induced orientational ordering of the pegs at the bottom such that their long axes in average are oriented at a small angle $langlethetarangle approx 15^circ$ to the motion of the bottom.
Despite decades of research, the modeling of moving contact lines has remained a formidable challenge in fluid dynamics whose resolution will impact numerous industrial, biological, and daily life applications. On the one hand, molecular dynamics (MD) simulation has the ability to provide unique insight into the microscopic details that determine the dynamic behavior of the contact line, which is not possible with either continuum-scale simulations or experiments. On the other hand, continuum-based models provide a link to the macroscopic description of the system. In this Feature Article, we explore the complex range of physical factors, including the presence of surfactants, which governs the contact line motion through MD simulations. We also discuss links between continuum- and molecular-scale modeling and highlight the opportunities for future developments in this area.
Surface roughness becomes relevant if typical length scales of the system are comparable to the scale of the variations as it is the case in microfluidic setups. Here, an apparent boundary slip is often detected which can have its origin in the assumption of perfectly smooth boundaries. We investigate the problem by means of lattice Boltzmann (LB) simulations and introduce an ``effective no-slip plane at an intermediate position between peaks and valleys of the surface. Our simulations show good agreement with analytical results for sinusoidal boundaries, but can be extended to arbitrary geometries and experimentally obtained surface data. We find that the detected apparent slip is independent of the detailed boundary shape, but only given by the distribution of surface heights. Further, we show that the slip diverges as the amplitude of the roughness increases.
Circular milling, a stunning manifestation of collective motion, is found across the natural world, from fish shoals to army ants. It has been observed recently that the plant-animal worm $Symsagittifera~roscoffensis$ exhibits circular milling behaviour, both in shallow pools at the beach and in Petri dishes in the laboratory. Here we investigate this phenomenon, through experiment and theory, from a fluid dynamical viewpoint, focusing on the effect that an established circular mill has on the surrounding fluid. Unlike systems such as confined bacterial suspensions and collections of molecular motors and filaments that exhibit spontaneous circulatory behaviour, and which are modelled as force dipoles, the front-back symmetry of individual worms precludes a stresslet contribution. Instead, singularities such as source dipoles and Stokes quadrupoles are expected to dominate. A series of models is analyzed to understand the contributions of these singularities to the azimuthal flow fields generated by a mill, in light of the particular boundary conditions that hold for flow in a Petri dish. A model that treats a circular mill as a rigid rotating disc that generates a Stokes flow is shown to capture basic experimental results well, and gives insights into the emergence and stability of multiple mill systems.
Aims. We show how the build-up of magnetic gradients in the Suns corona may be inferred directly from photospheric velocity data. This enables computation of magnetic connectivity measures such as the squashing factor without recourse to magnetic field extrapolation. Methods.Assuming an ideal evolution in the corona, and an initially uniform magnetic field, the subsequent field line mapping is computed by integrating trajectories of the (time-dependent) horizontal photospheric velocity field. The method is applied to a 12 hour high-resolution sequence of photospheric flows derived from Hinode/SOT magnetograms. Results. We find the generation of a network of quasi-separatrix layers in the magnetic field, which correspond to Lagrangian coherent structures in the photospheric velocity. The visual pattern of these structures arises primarily from the diverging part of the photospheric flow, hiding the effect of the rotational flow component: this is demonstrated by a simple analytical model of photospheric convection. We separate the diverging and rotational components from the observed flow and show qualitative agreement with purely diverging and rotational models respectively. Increasing the flow speeds in the model suggests that our observational results are likely to give a lower bound for the rate at which magnetic gradients are built up by real photospheric flows. Finally, we construct a hypothetical magnetic field with the inferred topology, that can be used for future investigations of reconnection and energy release.
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