"Rising bubbles, oscillation, stability, frequency"@en . . "Dumbbell model of bubble stability"@en . "3"^^ . . "6"^^ . "Dumbbell model of bubble stability"@en . . "[EFEACD4A14AE]" . . "Dumbbell model of bubble stability" . "Wichterle, Kamil" . . "38th International Conference of Slovak Society of Chemical" . "RIV/61989100:27360/12:86084799!RIV13-GA0-27360___" . . "Ruzicka, M. C." . . . "2011-05-23+02:00"^^ . . . . . "978-80-227-3503-2" . "Dumbbell model of bubble stability" . . "RIV/61989100:27360/12:86084799" . . . "132346" . "27360" . . "Bratislava" . . . "Dumbbell model has been suggested simulating rising larger ellipsoidal bubble in low- and medium-viscosity liquids by a couple of interconnected spherical bubbles. When the spherical bubbles are out of a horizontal alignment, the action of gravity and surface tension pumps some gas from the upper sphere to the lower one. As a consequence, the lower sphere rising is accelerated and upper is decelerated. Mathematical model of the process for small perturbations leads to the equation of relative motion in form of differential equation (\u03C1_L ( C)_M)/(%22delta%22\u03C1 g) (d^2 h)/(dt^2 )=2/u dh/dt+(d %22delta%22\u03C1 g)/(4 \u03C3) h where CM=0.5 is the virtual mass coefficient and d and u are sphere average diameter and velocity resp. According to this equation, any disturbance h is damped for small spheres, while the solution for larger spheres leads to a harmonic oscillation. Limits of stability can be expressed by the critical E\u00F6tv\u00F6s number, and frequency of oscillation of larger bubbles is f=%22radix%22((%22delta%22\u03C1 g^2 d)/(4 \u03C3 C_M )) These predictions have been confronted with our original experimental data for ellipsoidal bubbles and with the data taken from literature. Adequacy of the dumbbell model proves that the oscillation of bubbles is controlled primarily by surface forces, and the vortex shedding plays a secondary role."@en . "Slovensk\u00E1 technick\u00E1 univerzita v Bratislave" . "2"^^ . "Ve\u010De\u0159, Marek" . . "P(GA104/07/1110)" . "Tatransk\u00E9 Matliare" . "Dumbbell model has been suggested simulating rising larger ellipsoidal bubble in low- and medium-viscosity liquids by a couple of interconnected spherical bubbles. When the spherical bubbles are out of a horizontal alignment, the action of gravity and surface tension pumps some gas from the upper sphere to the lower one. As a consequence, the lower sphere rising is accelerated and upper is decelerated. Mathematical model of the process for small perturbations leads to the equation of relative motion in form of differential equation (\u03C1_L ( C)_M)/(%22delta%22\u03C1 g) (d^2 h)/(dt^2 )=2/u dh/dt+(d %22delta%22\u03C1 g)/(4 \u03C3) h where CM=0.5 is the virtual mass coefficient and d and u are sphere average diameter and velocity resp. According to this equation, any disturbance h is damped for small spheres, while the solution for larger spheres leads to a harmonic oscillation. Limits of stability can be expressed by the critical E\u00F6tv\u00F6s number, and frequency of oscillation of larger bubbles is f=%22radix%22((%22delta%22\u03C1 g^2 d)/(4 \u03C3 C_M )) These predictions have been confronted with our original experimental data for ellipsoidal bubbles and with the data taken from literature. Adequacy of the dumbbell model proves that the oscillation of bubbles is controlled primarily by surface forces, and the vortex shedding plays a secondary role." .