Dynamics of a clamped drop under translational vibrations

Alabuzhev, A. A.; Pyankova, Marina A.

doi:10.7242/1999-6691/2023.16.1.6

Cited by 2 publications

(3 citation statements)

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“…Substituting the expressions and using the boundary condition for the pulsating deviation of the surface and the equation for the pulsating pressure (20), we obtain:…”

Section: The Averaged Motion Problemmentioning

confidence: 99%

“…On the other hand, from the condition on the free surface of the drop for the velocity potential of pulsating motion (20), it follows that…”

Section: Variational Principle For Compressible Dropmentioning

confidence: 99%

“…In [18] the influence of the properties of the plate surface on the oscillations of the cramped drop is studied. The forced oscillations of a drop clamped between different surfaces is discussed in [19] for normal vibration and in [20] for translational vibration.…”

Section: Introductionmentioning

confidence: 99%

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The Shape of a Compressible Drop on a Vibrating Solid Plate

Ivantsov,

Lyubimova,

Khilko

et al. 2023

Mathematics

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The influence of high-frequency vibrations on the shape of a compressible drop placed on an oscillating solid substrate is studied in this paper. Due to the significant difference in characteristic temporal scales, the average and pulsating motions of the drop can be considered separately. For nearly hemispherical drop, the solution to the problem of pulsating motion is found in the form of series in Legendre polynomials. Frequencies of natural sound oscillations of hemispherical axisymmetric drop are obtained. Resonances of the acoustic mode of drop oscillations are found. The problem of forced oscillations of hemispherical drop in the limit of weakly compressible liquid is considered. It is found that drop oscillation amplitude grows with vibration intensity according to quadratic law, which is consistent with the solution of the pulsation problem for finite compressibility assumption. A variational principle for calculation of average drop shape is formulated based on minimization of energy functional for the case, so the compressibility of the liquid should be taken into account. It is shown that the functional (the sum of the kinetic and potential energies of the pulsating flow, the kinetic energy of the averaged flow, and the surface tension energy of the drop) decreases and reaches a minimum value at quasi-equilibrium state, in which the average shape of the drop becomes static. The influence of vibrations on the drop shape is studied for small values of the vibrational parameter. The surface of the drop in the absence of vibrations is assumed to be hemispherical. Calculations showed that under vibrations, drop height decreases, while the area of the base increases.

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“…Substituting the expressions and using the boundary condition for the pulsating deviation of the surface and the equation for the pulsating pressure (20), we obtain:…”

Section: The Averaged Motion Problemmentioning

confidence: 99%

“…On the other hand, from the condition on the free surface of the drop for the velocity potential of pulsating motion (20), it follows that…”

Section: Variational Principle For Compressible Dropmentioning

confidence: 99%