An investigation of the internal flow field for a drop at the antinode of a standing wave has been carried out. The main difference from the solid sphere case is the inclusion of the shear stress and velocity continuity conditions at the liquid-gas interface. To the leading order of calculation, the internal flow field was found to be quite weak. Also, this order being fully time dependent has a zero mean flow. At the next higher order, steady internal flows are predicted and, as in the case of a solid sphere, there is a recirculating layer consisting of closed streamlines near the surface. In the case of a liquid drop, however, the behavior of this recirculating Stokes layer is quite interesting. It is predicted that the layer ceases to have recirculation when [formula: see text], where [symbol: see text] is the liquid viscosity, mu is the exterior gas-phase viscosity, and M is the dimensionless frequency parameter for the gas phase, defined by M = i omega a2 rho/mu, with a being the drop radius. Thorough experimental confirmation of this interesting new development needs to be conducted. Although it seems to agree with many experiments with levitated drops where no recirculating layer has been clearly observed, a new set of experiments for specifically testing this interesting development need to be carried out.
This analysis consists of the development of the fluid flow about a spherical particle placed at the velocity node of a standing wave. High-frequency acoustic fields are being used to levitate particles in Earth gravity, and to stabilize particles in low-gravity situations. While a standing wave in an infinite medium may be purely oscillatory with no net flow components, the interaction with particles or solid walls leads to nonlinear effects that create a net steady component of the flow. In the present development, the perturbation method is employed to derive the flow field for the situation when a spherical particle is positioned at the velocity node. As found in an earlier analysis ͓Riley, Q. J. Mech. Appl. Math 19, 461 ͑1966͔͒ applicable to a solid sphere at the velocity antinode, there is a thin shear-wave region adjacent to the spherical boundary. However, this thin Stokes layer does not cover the entire sphere in the same manner as in the previous case. In the polar regions flow reversal takes place but the Stokes layer opens to the surrounding field. On an equatorial belt region there are closed streamlines.
To study the spectrum of magnesium plasma, the escape factors and transition probabilities of two resonance absorption lines that making up the MgⅡ280nm line are discussed theoretically, for both Gaussian profile and Lorentzian profile. The oscillator strength, the number density of the absorbing atoms in the ground state, and the optical depth in the line center are discussed also. The results we calculated are in good agreement with the exerimental results, and some useful conclusions are drawn. This calculation will be significant in the research of plasma spectrum of magnesium plasma.
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