Effect of Charge Relaxation Effect on Electromagnetic Radiation Intensity of Oscillating Viscous Liquid Drop

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Resumo

Theoretical asymptotic methods have shown that the electric charge relaxation effect affects the physical characteristics of the electromagnetic radiation of the oscillating charged droplet. Analytical expressions are obtained for frequencies, decrements of attenuation of capillary oscillations of droplets due to viscous attenuation and energy losses on radiation. It has been shown that the frequencies of electromagnetic radiation of cloud droplets, realized in the ranges of hundreds of kilohertz and megahertz units, decrease with an increase in the radius and charge parameter of the emitting droplet, as well as attenuation decrements associated with radiation. Intensity of emission of electromagnetic waves decreases with decrease of electrical conductivity and mobility of charges in liquid.

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Sobre autores

A. Grigoryev

Ishlinsky Institute for Problems in Mechanics of the RAS

Autor responsável pela correspondência
Email: grigorai@mail.ru
Rússia, Moscow

N. Kolbneva

Demidov Yaroslavl State University

Email: kolbneva-nata@yandex.ru
Rússia, Yaroslavl

S. Shiryaeva

Demidov Yaroslavl State University

Email: shir@uniyar.ac.ru
Rússia, Yaroslavl

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2. Fig. 1. Dependence of the natural frequency of capillary oscillations of a viscous charged cloud droplet: a: on its radius R; curves 1-4 correspond to values W = 0.1, 2, 3, 3.9; b: on the value of the Rayleigh parameter W; curves 1-4 correspond to values R = 5, 10, 15, 20 μm. The calculations were carried out using formula (5.2) at n = 2, σ = 73 dyne/cm, ρ = 1 g/cm3, ν = 0.01 cm2/s, ε1 = 80, γ = 1 - 106 SGSE, b = 300 SGSE.

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3. Fig. 2. Dependence of the decrement of attenuation of capillary oscillations of a viscous cloud droplet with charge Q = 2 - 10-5 SGSE (~ 0.06Qkr at R = 3 μm and ~ 0.002Qkr at R = 30 µm) from: a: radius R (a) curves 1-4 correspond to values ν = 0.01, 0.03, 0.05, 0.1 cm2/s; b: kinematic viscosity coefficient ν, curves 1-4 correspond to values R = 5, 10, 15, 20 µm. Calculations were carried out by formula (5.14) at the same values of parameters as in Fig. 1.

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4. Fig. 3. Dependence of Mn (t) amplitudes of different modes of perturbation of the equilibrium shape of a viscous cloud droplet with charge Q = 2 - 10-5 SGSE (~ 0.06Qkr at R = 3 μm and ~ 0.03Qkr at R = 5 μm) on time t. a - n = 2, b - n = 5. Curves 1-3 correspond to values R = 3, 4, 5 μm. Calculations were carried out by formula (5.16) at the same values of parameters as in Fig. 1.

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5. Fig. 4. Dependence of the decrement of attenuation of capillary oscillations of a drop of radius R = 5 μm with charge Q = 2 - 10-5 SGSE (~ 0.03Qkr) on the mode number n. The calculations were carried out by formula (5.14) at the same values of parameters as in Fig. 1.

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6. Fig. 5. Temporal evolution of the amplitude M2 (t) of the main mode of the n = 2 perturbation of the equilibrium shape of a drop of radius R = 5 μm with charge Q = 2 - 10-5 SGSE (~ 0.03Qcr), corresponding to the charge-relaxation aperiodic motion of the liquid. Calculations were carried out by formula (5.17) at the same values of parameters as in Fig. 1.

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7. Fig. 6. Dependence of the magnitude of the capillary oscillation attenuation decrement correction associated with the emission of electromagnetic waves of a drop of radius R = 10 μm and charge Q = 2 - 10-5 SGSE (~ 0.01Qcr) on the specific conductivity γ. Calculations were carried out by formula (5.15) at the same parameter values as in Fig. 1.

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8. Fig. 7. Dependence of the magnitude of the capillary oscillation attenuation decrement correction associated with the emission of electromagnetic waves of a drop of radius R = 10 μm and charge Q = 2 - 10-5 SGSE (~ 0.01Qcr) on the charge carrier mobility b. Calculations were carried out by formula (5.15) at the same values of parameters as in Fig. 1.

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9. Fig. 8. Dependence of the correction of the decrement of the capillary oscillation attenuation decrement associated with the emission of electromagnetic waves of a charged cloud droplet on the value of the Rayleigh parameter W. a - ε1 = 80, b - ε1 = ∞, c - ε1 = 0; curves 1-3 correspond to the values of R = 26, 28, 30 μm. The calculations were carried out by formula (5.15) at the same values of parameters as in Fig. 1.

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10. Fig. 9. Dependence of the intensity of electromagnetic radiation I of a charged drop of an ideally conducting liquid on the Rayleigh parameter W (a) and radius R (b). a: Curves 1-3 correspond to values R = 26, 28, 30 µm. b: Curves 1-3 correspond to values W = 2, 2.5, 3. Calculations were performed using formula (5.4) at n = 2, σ = 73 dyne/cm, ρ = 1 g/cm3.

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11. Fig. 10. Dependence of the intensity of electromagnetic radiation I of a charged drop of an ideally conducting liquid on the Rayleigh parameter W, plotted according to [1].

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12. Fig. 11. Dependence of the electromagnetic radiation intensity I of a charged viscous drop of finite electrical conductivity on the Rayleigh parameter W (a) and radius R (b). The calculations were carried out at the same parameter values as in Fig. 1.

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