3,719 research outputs found

    On the control and suppression of the Rayleigh-Taylor instability using electric fields

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    It is shown theoretically that an electric field can be used to control and suppress the classical Rayleigh-Taylor instability found in stratified flows when a heavy fluid lies above lighter fluid. Dielectric fluids of arbitrary viscosities and densities are considered and a theory is presented to show that a horizontal electric field (acting in the plane of the undisturbed liquid-liquid surface), causes growth rates and critical stability wavenumbers to be reduced thus shifting the instability to longer wavelengths. This facilitates complete stabilization in a given finite domain above a critical value of the electric field strength. Direct numerical simulations based on the Navier-Stokes equations coupled to the electrostatic fields are carried out and the linear theory is used to critically evaluate the codes before computing into the fully nonlinear stage. Excellent agreement is found between theory and simulations, both in unstable cases that compare growth rates and in stable cases that compare frequencies of oscillation and damping rates. Computations in the fully nonlinear regime supporting finger formation and roll-up show that a weak electric field slows down finger growth and that there exists a critical value of the field strength, for a given system, above which complete stabilization can take place. The effectiveness of the stabilization is lost if the initial amplitude is large enough or if the field is switched on too late. We also present a numerical experiment that utilizes a simple on-off protocol for the electric field to produce sustained time periodic interfacial oscillations. It is suggested that such phenomena can be useful in inducing mixing. A physical centimeter-sized model consisting of stratified water and olive oil layers is shown to be within the realm of the stabilization mechanism for field strengths that are approximately 2 × 104  V/m

    Instability and dripping of electrified liquid films flowing down inverted substrates

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    We consider the gravity-driven flow of a perfect dielectric, viscous, thin liquid film, wetting a flat substrate inclined at a nonzero angle to the horizontal. The dynamics of the thin film is influenced by an electric field which is set up parallel to the substrate surface—this nonlocal physical mechanism has a linearly stabilizing effect on the interfacial dynamics. Our particular interest is in fluid films that are hanging from the underside of the substrate; these films may drip depending on physical parameters, and we investigate whether a sufficiently strong electric field can suppress such nonlinear phenomena. For a non-electrified flow, it was observed by Brun et al. [Phys. Fluids 27, 084107 (2015)] that the thresholds of linear absolute instability and dripping are reasonably close. In the present study, we incorporate an electric field and analyze the absolute and convective instabilities of a hierarchy of reduced-order models to predict the dripping limit in parameter space. The spatial stability results for the reduced-order models are verified by performing an impulse-response analysis with direct numerical simulations (DNS) of the Navier–Stokes equations coupled to the appropriate electrical equations. Guided by the results of the linear theory, we perform DNS on extended domains with inflow and outflow conditions (mimicking an experimental setup) to investigate the dripping limit for both non-electrified and electrified liquid films. For the latter, we find that the absolute instability threshold provides an order-of-magnitude estimate for the electric-field strength required to suppress dripping; the linear theory may thus be used to determine the feasibility of dripping suppression given a set of geometrical, fluid, and electrical parameters

    Tayler instability of toroidal magnetic fields in MHD Taylor-Couette flows

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    The nonaxisymmetric 'kink-type' Tayler instability (TI) of toroidal magnetic fields is studied for conducting incompressible fluids of uniform density between two infinitely long cylinders rotating around the same axis. It is shown that for resting cylinders the critical Hartmann number for the unstable modes does not depend on Pm. By rigid rotation the instability is suppressed where the critical ratio of the rotation velocity and the Alfven velocity of the field (only) slightly depends on the magnetic Prandtl number Pm. For Pm=1 the rotational quenching of TI takes its maximum. Rotation laws with negative shear (i.e. d\Omega/dR<0) strongly destabilize the toroidal field if the rotation is not too fast. For sufficiently high Reynolds numbers of rotation the suppression of the nonaxisymmetric magnetic instability always dominates. The angular momentum transport of the instability is anticorrelated with the shear so that an eddy viscosity can be defined which proves to be positive. For negative shear the Maxwell stress of the perturbations remarkably contributes to the angular momentum transport. We have also shown the possibility of laboratory TI experiments with a wide-gap container filled with fluid metals like sodium or gallium. Even the effect of the rotational stabilization can be reproduced in the laboratory with electric currents of only a few kAmp.Comment: 9 pages, 11 figures, sub

    Electrically driven convection in a thin annular film undergoing circular Couette flow

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    We investigate the linear stability of a thin, suspended, annular film of conducting fluid with a voltage difference applied between its inner and outer edges. For a sufficiently large voltage, such a film is unstable to radially-driven electroconvection due to charges which develop on its free surfaces. The film can also be subjected to a Couette shear by rotating its inner edge. This combination is experimentally realized using films of smectic A liquid crystals. In the absence of shear, the convective flow consists of a stationary, azimuthally one-dimensional pattern of symmetric, counter-rotating vortex pairs. When Couette flow is applied, an azimuthally traveling pattern results. When viewed in a co-rotating frame, the traveling pattern consists of pairs of asymmetric vortices. We calculate the neutral stability boundary for arbitrary radius ratio α\alpha and Reynolds number Re{{\cal R} e} of the shear flow, and obtain the critical control parameter Rc(α,Re){\cal R}_c (\alpha, {{\cal R} e}) and the critical azimuthal mode number mc(α,Re){m_c (\alpha, {{\cal R} e})}. The Couette flow suppresses the onset of electroconvection, so that Rc(α,Re)>Rc(α,0){\cal R}_c (\alpha, {{\cal R} e}) > {\cal R}_c (\alpha,0). The calculated suppression is compared with experiments performed at α=0.56\alpha = 0.56 and 0≤Re≤0.220 \leq {{\cal R} e} \leq 0.22 .Comment: 17 pages, 2 column with 9 included eps figures. See also http://mobydick.physics.utoronto.c

    Electrohydrodynamically induced mixing in immiscible multilayer flows

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    In the present study we investigate electrostatic stabilization mechanisms acting on stratified fluids. Electric fields have been shown to control and even suppress the Rayleigh-Taylor instability when a heavy fluid lies above lighter fluid. From a different perspective, similar techniques can also be used to generate interfacial dynamics in otherwise stable systems. We aim to identify active control protocols in confined geometries that induce time dependent flows in small scale devices without having moving parts. This effect has numerous applications, ranging from mixing phenomena to electric lithography. Two-dimensional computations are carried out and several such protocols are described. We present computational fluid dynamics videos with different underlying mixing strategies, which show promising results.Comment: Video submission for the gallery of fluid motion, as part of the APS DFD 2013 conferenc
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