The oscillations of a viscous liquid drop

Reid, W. H.

doi:10.1090/qam/114449

Cited by 146 publications

(72 citation statements)

References 2 publications

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“…In the reality, experimental measurements may be affected by several side-effects. 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).…”

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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“…Recent work includes analysis by Tsamopoulos and Brown (1983) and computations by Patzek, Benner, Basaran and Scriven (1991). The decay of linear oscillations due to viscosity was analyzed in an approximate way by Lamb (1932) in the limit of small viscosity and a more detailed analysis was later carried out by Reid (1960), Miller and Scriven (1968) and others. Numerical investigations of viscous effects can be found in Foote (1973) who used the Marker And Cell (MAC) method to solve the full Navier Stokes equations, and Mansure and Lundgren (1988) who used a boundary integral method, modified to account for small viscous dissipation in an approximate way.…”

Section: Introductionmentioning

confidence: 99%

Head-on collision of drops—A numerical investigation

1996

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The head-on collision of equal sized drops is studied by full numerical simulations. The Navier-Stokes equations are solved for the fluid motion both inside and outside the drops using a front tracking/finite difference technique. The drops are accelerated toward each other by a body force that is turned off before the drops collide. When the drops collide, the fluid between them is pushed outward leaving a thin layer bounded by the drop surface. This layer gets progressively thinner as the drops continue to deform and in several of our calculations we artificially remove this double layer once it is thin enough, thus modeling rupture. If no rupture takes place, the drops always rebound, but if the film is ruptured the drops may coalesce permanently or coalesce temporarily and then split again.

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“…Theoretical investigations on oscillations of viscous droplets have been performed by various authors. Reid (1960) considered aperiodically damped oscillating droplets. Prosperetti (1977Prosperetti ( , 1980 gives results for the damping constant and for the frequency of small amplitude oscillations.…”

Section: Introductionmentioning

confidence: 99%

An experimental method for the investigation of droplet oscillations in a gaseous medium

Brenn

Frohn

1993

Experiments in Fluids

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An experimental method for the investigation of droplet oscillations in a gaseous medium is presented. The droplets are produced using vibrating orifice droplet generators. Experiments are carried out with droplets in the diameter range from 91 lam to 288 pm using propanol-2, water, and n-hexadecane; the gaseous host medium is air. Oscillatory motions of the fundamental mode n=2 and of the first higher order mode n = 3 occur during the disintegration of the liquid jet produced by the droplet generator. The periodical production of the droplets allows the observation and evaluation of each phase of the motion under quasi-steady conditions. Surface energies are determined from the droplet shapes on photos. The periods of the oscillations are found to be very close to the prediction of the linear theory.

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The oscillations of a viscous liquid drop

Cited by 146 publications

References 2 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

Head-on collision of drops—A numerical investigation

An experimental method for the investigation of droplet oscillations in a gaseous medium

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