音圧による液滴の強制振動

概要

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Acoustically excited shape oscillations of drops are studied both experimentally and theoretically and are applied to the measurement of viscosity. When steady-state shape oscillations of drops hanging from tubes are excited by a modulated acoustic radiation pressure on the drop-air interface, the bottom of the drops are lifted to some height and oscillate around there. A mathematical model of the oscillation is given by a third order differential equation : 1/Ω_1 d^3Z_0/dT^3+d^2Z_0/dT^2+Ω_1 dZ_0/dT+Ω_0^2Z_0=F{1+cos(ΩT)}, Where Z_0 is the displacement of the bottom of the drop along the vertical axis. The right hand side is the acoustic driving force. When the phase of the response lags behing the driving force by 90°, the frequency is Ω_0,and when the phase sift is 180°, the frequency is Ω_1. Ω_0≨Ω_1. The phase sift changes from 0°to 270°. Both the resonant frequency and the damped oscillation frequency amount between Ω_0 and Ω_1. The ratio Ω_1/Ω_0 increases with the viscosity of the drop. When the phase sift is 90°, the viscosity of the drop increases with the ratio of the lift L_0 to the amplitude A_0 : L_0/A_0=Ω_1/Ω_0-Ω_0/Ω_1. The experimental results for drops having the contact radius equal to the height agreed well with the mathematical model.
東海大学の論文