Effect of static deformation and external forces on the oscillations of levitated droplets

Suryanarayana, P. V. R.; Bayazıtoğlu, Yıldız

doi:10.1063/1.857974

Cited by 56 publications

(21 citation statements)

References 8 publications

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“…Firstly, levitated drops may be significantly aspherical and the oscillations amplitudes not necessarily small, whereas the classical theories describing the oscillation frequencies (Rayleigh 1945) and damping rates (Lamb 1993;Chandrasekhar 1981;Reid 1960) assume small-amplitude oscillations about an ideally spherical equilibrium shape. Corrections due to the drop asphericity have been calculated by Cummings & Blackburn (1991) and Suryanarayana & Bayazitoglu (1991). Bratz & Egry (1995) find the same order correction to the damping rate resulting also from AC-magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Oscillations of weakly viscous conducting liquid drops in a strong magnetic field

Priede

2011

J. Fluid Mech.

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We analyse small-amplitude oscillations of a weakly viscous electrically conducting liquid drop in a strong uniform DC magnetic field. An asymptotic solution is obtained showing that the magnetic field does not affect the shape eigenmodes, which remain the spherical harmonics as in the non-magnetic case. Strong magnetic field, however, constrains the liquid flow associated with the oscillations and, thus, reduces the oscillation frequencies by increasing effective inertia of the liquid. In such a field, liquid oscillates in a twodimensional (2D) way as solid columns aligned with the field. Two types of oscillations are possible: longitudinal and transversal to the field. Such oscillations are weakly damped by a strong magnetic field -the stronger the field, the weaker the damping, except for the axisymmetric transversal and inherently 2D modes. The former are overdamped because of being incompatible with the incompressibility constraint, whereas the latter are not affected at all because of being naturally invariant along the field. Since the magnetic damping for all other modes decreases inversely with the square of the field strength, viscous damping may become important in a sufficiently strong magnetic field. The viscous damping is found analytically by a simple energy dissipation approach which is shown for the longitudinal modes to be equivalent to a much more complicated eigenvalue perturbation technique. This study provides a theoretical basis for the development of new measurement methods of surface tension, viscosity and the electrical conductivity of liquid metals using the oscillating drop technique in a strong superimposed DC magnetic field.

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Section: Introductionmentioning

confidence: 99%

Oscillations of weakly viscous conducting liquid drops in a strong magnetic field

Priede

2011

J. Fluid Mech.

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“…In this case the flow is linear and potential, the Rayleigh capillary oscillation frequencies are known analytically 6,7) :…”

Section: Solutions In Absence Of Gravitymentioning

confidence: 99%

“…The ideal fluid oscillations of the droplets under such conditions using the small amplitude linear theory were investigated in Refs. 6,7), and the transient decay of the viscous droplet oscillation in Ref. 8).…”

Section: Introductionmentioning

confidence: 99%

Modelling Electromagnetically Levitated Liquid Droplet Oscillations

Bojarevics

Pericleous

2003

ISIJ International

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This work comprises accurate computational analysis of levitated liquid droplet oscillations in AC and DC magnetic fields. The AC magnetic field interacting with the induced electric current within the liquid metal droplet generates intense fluid flow and the coupled free surface oscillations. The pseudo-spectral technique is used to solve the turbulent fluid flow equations for the continuously dynamically transformed axisymmetric fluid volume. The volume electromagnetic force distribution is updated with the shape and position change. We start with the ideal fluid test case for undamped Rayleigh frequency oscillations in the absence of gravity, and then add the viscous and the DC magnetic field damping. The oscillation frequency spectra are further analysed for droplets levitated against gravity in AC and DC magnetic fields at various combinations. In the extreme case electrically poorly conducting, diamagnetic droplet (water) levitation dynamics are simulated. Applications are aimed at pure electromagnetic material processing techniques and the material properties measurements in uncontaminated conditions. KEY WORDS: electromagnetic material processing; magnetic levitation; free surface dynamics; turbulent fluid flow.results demonstrate the correspondence to analytical Rayleigh frequencies without numerical damping in the case of an ideal fluid droplet. For the case of realistic AC field levitation with normal gravity the internal fluid flow is turbulent, and an appropriate model for the time dependent turbulence is applied to obtain the oscillation frequencies in this complex nonlinear case. For the electrically conducting droplet both DC and AC magnetic fields exert a damping effect included in the numerical model. Finally, diamagnetic water droplet levitation is simulated in a high gradient DC magnetic field. The predicted oscillations are strongly affected by the droplet surface motion within the steep gradient force field. Mathematical Model Momentum and Temperature EquationsThe present modelling approach is based on the turbulent momentum and heat transfer equations for an incompressible fluid:where v is the velocity vector, p -the pressure, r -the density, n e ϭn T ϩn (summ of turbulent and laminar viscosity) is the effective viscosity which is variable in time and position, f is the electromagnetic force, g -the gravity vector, T -the temperature, a e ϭa T ϩa (summ of turbulent and laminar) is the effective thermal diffusivity, C p -the specific heat, C p * -the solid fraction modified specific heat function which accounts for latent heat effects (see Ref. 19)) for details), and | J| 2 /s is the Joule heat. The momentum Eq. (1) contains the nonlinear term in the convective (in difference to the rotational) form which, according to our tests, gives greater stability for the long time development problems. We will consider the flow representation for an axisymmetric fluid droplet in the spherical co-ordinates (R, q, f). The momentum and the continuity Eqs. (1), (2) in the absence of the azimuthal velocit...

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“…Viscosity-related corrections are addressed by Suryanarayana and Bayazitoglu [3], and gravity and magnetic field-related corrections are treated by Cummings and Blackburn [4]. Instead of full-scale numerical calculations for the freely oscillating drop presented in this paper, Meradji et al [5] recently used a Galerkin/finite element technique along with the spine method for interfacial deformations to solve for the fluid flow inside a drop under zero gravity.…”

Section: Theory: Oscillating Droplets In Electromagnetic Levitationmentioning

confidence: 97%

Surface Oscillations of an Electromagnetically Levitated Droplet

et al. 2005

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The natural oscillation frequency of freely suspended liquid droplets can be related to the surface tension of the material, and the decay of oscillations to the liquid viscosity. However, the fluid flow inside the droplet must be laminar to measure viscosity with existing correlations; otherwise the damping of the oscillations is dominated by turbulent dissipation. Because no experimental method has yet been developed to visualize flow in electromagnetically levitated oscillating metal droplets, mathematical modeling can assist in predicting whether or not turbulence occurs, and under what processing conditions. In this paper, three mathematical models of the flow: (1) assuming laminar conditions, (2) using the k − ε turbulence model, and (3) using the RNG turbulence model, respectively, are compared and contrasted to determine the physical characteristics of the flow. It is concluded that the RNG model is the best suited for describing this problem when the interior flow is turbulent. The goal of the presented work was to characterize internal flow in an oscillating droplet of liquid metal, and to verify the accuracy of the characterization by comparing calculated surface tension and viscosity values to available experimental results.

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Effect of static deformation and external forces on the oscillations of levitated droplets

Cited by 56 publications

References 8 publications

Oscillations of weakly viscous conducting liquid drops in a strong magnetic field

Oscillations of weakly viscous conducting liquid drops in a strong magnetic field

Modelling Electromagnetically Levitated Liquid Droplet Oscillations

Surface Oscillations of an Electromagnetically Levitated Droplet

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