P. V. R. Suryanarayana

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

The oscillations of an aspherical droplet subjected to different external forces are considered. For an arbitrary shape deformation, it is shown that the frequency spectrum splits into (2l−1) peaks for a mode l oscillation, and the splitting of the frequency spectrum is calculated for mode 2, 3, and 4 oscillations. The deformation is then treated as a consequence of a general external force, and the frequency split is obtained in terms of the external force parameters. Droplets levitated by acoustic, electromagnetic, and combined acoustic‐electromagnetic forces are considered in particular, and it is shown that the effects of asphericity adequately explain the splitting of the frequency spectrum observed commonly in experiments. The interpretation of spectra with regard to accurate surface tension measurement using the oscillations of levitated droplets is discussed, and the results applied to some previous experimental results. It is shown that the accuracy of surface tension measurements can improve if ...

Surface tension and viscosity from damped free oscillations of viscous droplets

Damped oscillations of a viscous droplet in vacuum or in an inert gas of negligible density are considered. The dependence of the complex decay factor on the properties of the liquid is investigated for the first time, and numerical results are compared with earlier studies for special cases. A new method is developed to determine both surface tension and viscosity from a single experiment in which the damping rate and frequency of oscillations are measured. The procedure to determine surface tension and viscosity from oscillating levitated liquids is outlined, and results are presented for various modes of shape oscillations.

Determination of surface tension from the shape oscillations of an electromagnetically levitated droplet

In the fundamental (l=2) mode, the frequency spectrum of a magnetically levitated inviscid droplet exhibits three distinct peaks. If the modes that correspond to each of these peaks is known, the surface tension of the droplet may be calculated. In experiments that make use of this principle, there is no unambiguous method of assigning mode numbers to these peaks. The dynamics of the oscillating droplet depend on the magnetic pressure on the droplet surface. Consequently, the order of the peaks in the l=2 mode oscillations is determined by the magnetic pressure distribution. In this paper, the magnetic pressure distribution on the surface of the droplet is calculated as a function of the parameters that govern the external magnetic field. The frequencies of the droplet oscillation and its static shape deformation are also expressed in terms of these same parameters. The frequencies of oscillation are used to determine the surface tension of the liquid droplet. Finally, the magnetic pressure distribution o...

High temperature thermal diffusivity determination procedure for solids and liquids

A new method for measuring the thermal diffusivity of materials at high temperatures is presented. The method is applicable to solids on Earth, and to liquids in the reduced gravity environment of space. It is especially suited to levitated liquid metals at elevated temperatures where thermal diffusivity data is not available. The method is applied in two parts, such that lumped analysis is valid in the first part, and Fouriers law of conduction is valid in the second. In both parts, the spherical specimen is assumed to have been heated to a desired temperature and cooled. An inverse conduction problem is then formulated and solved using Laplace transformation techniques. Using this solution, sample sizes, and experimentally obtained surface temperature history, the thermal diffusivity is determined by minimizing a function that satisifies the heat balance at the surface. Minimization is performed using a modified quasilinearization algorithm. Accuracy is very sensitive to error in the temperature data and increases with better curve fits to the temperature data. An error analysis is also performed, and the effect of errors in the various parameters on the evaluated thermal diffusivity is determined. An experimental study for solids on Earth is suggested, before development for implementation in space.

Transient Radiative Heat Transfer From a Sphere Surrounded by a Participating Medium

Transient radiative cooling of a solid or liquid sphere in space, surrounded by a radiatively participating vapor cloud, is considered. A quasi-steady assumption is applied to the radiation transfer in the medium, with the unsteadiness being retained at the inner spherical boundary. The problem is solved by applying the third-order (P3 ) spherical harmonics approximation to the radiative transfer equation for the participating cloud, and a finite difference scheme for transient conduction in the sphere. In general, the presence of a participating medium decreases the cooling rate of the sphere, and cooling curves are presented to show this effect. Effective emissivity of the surface in the presence of a surrounding medium is evaluated, and an approximate explicit equation is given.

Dynamics of oscillating viscous droplets immersed in viscous media

SummaryDamped oscillations of a viscous droplet immersed in a viscous medium are considered in detail. The characteristic equation is solved numerically for arbitrary, finite fluid properties. The cylinder functions in the characteristic equation are solved using an accurate continued fraction algorithm, and the complex decay factor is searched using a minimization scheme. Oscillation frequency and damping rate results are presented for the fundamental mode, for various cases of practical interest (liquid-gas, and liquid-liquid systems), and the effect of the external medium properties are discussed. Results are compared to exact solutions for limiting cases, and to existing experimental data for both the fundamental and higher order modes. It is shown that the theoretical frequency prediction matches well with the experimental observation. Damping rate predictions, however, underestimate experimental observation in some cases, and this is thought to be due to surface impurities. The application of these results to the measurement of surface tension and viscosity of liquid droplets from single-droplet levitation experiments is also discussed.

Electromagnetic Levitation with Acoustic Modulation for Property Measurement

Nomenclature a = characteristic length of levitated material, m B,B = magnetic flux density, Wb/m2 cp = specific heat of levitated material (J/kg K) E = ohmic heating rate, W g ,g = gravitational acceleration 7 = moment of inertia, / = 2/5 ma2 /,/ = induced eddy current density (A/m2), /= 1/juV xB k = wave number of sound waves in the medium K = radius of curvature of deformed droplet, m m = mass of droplet, kg P = pressure, N/m2 Pm = mean magnetic pressure on the droplet surface, N/m2 Ps = pressure amplitude of acoustic standing wave P2o = quadrupole radial projection of acoustic radiation pressure