The nonlinear dynamics of self-organising bubble departures from twin nozzles in engine oils was analysed. Air bubbles were generated from twin brass nozzles with an inner diameter equal to 1 mm. The flow of bubbles in bubble chains was recorded using high-speed camera. The time series of air pressure oscillations and signal from laser-phototransistor identifying the presence of bubbles over the nozzles outlet were recorded simultaneously. The self-organising bubble departures were observed and their stability was analysed. It was found that self-organising bubble departures become unstable because of successive (during subsequent bubble departures) decrease of the mean air pressure in one of the nozzle air supply system. It was shown that instability of selforganising bubble departures leads to equalization of pressures in both nozzles air supply systems which causes that simultaneous bubble departures appear. In the present experiment, this process was repeated in a cyclic and chaotic way. It was shown that stable selforganising bubble departures are accompanied by periodic air pressure oscillations in one of the nozzles and chaotic air pressure oscillations in the second one. Keywords Bubble Á Bubble chain Á Self-organising bubble departures Á Nonlinear data analysis
The paper investigates the dynamics of bubble departures from a glass nozzle submerged in a tank filled with distilled water. Air pressure and liquid flow inside the nozzle are simultaneously recorded using a data acquisition system and a high speed camera. The recurrence plot and cross recurrence plot methods are used to identify the loss of synchronization between air pressure fluctuations and the depth of liquid flow inside the nozzle during chaotic bubble departures. We claim that the synchronization between pressure fluctuations and the depth of liquid penetration inside the nozzle is suppressed during chaotic bubble departures. The experimental results show agreement with the numerical findings. The results demonstrate that the non-linearities of processes occurring during liquid penetration inside the nozzle have a significant impact on the synchronization between the time histories of pressure and the corresponding depths of liquid penetration inside the nozzle.
The bubble departures from two neighbouring brass nozzles (with inner
diameter of 1.1 mm) in three liquids: distilled water, mineral and synthetic
engine oils were investigated. The numerical simulations were used for
reconstruction of liquid flow around the departing bubbles. Bubble movements
in liquid have been recorded using a high speed camera. The 2D bubble paths
have been reconstructed using: Laplacian of Gaussian filters, algorithm of
detection of local extremes of image brightness and Kalman filter. It was
shown that during alternative bubble departures bubble paths become
repeatable. The dimensionless number (similar to Strouhal number) was
proposed to describe oscillating liquid flow generated by departing bubbles
over the nozzle outlet. Such number was used for defining the hydrodynamic
criterion of alternative bubble departures.
The influence of small changes to water hardness on the nonlinear behaviour of liquid penetration into a capillary and the resulting air pressure fluctuations during air bubble formation are examined in this paper. Experiments were undertaken in which bubbles were generated both in water having a surface tensile force of σ = 72.2 mN/m and in an aqueous solution of calcium carbonate having a surface tensile force of σ = 75.4 mN/m, each contained in a glass capillary with an internal diameter of 1 mm. It is shown that both the maximum value of liquid penetration into the capillary and bubble growth time are affected by perturbations to the water hardness. The time it takes for the bubble to depart the capillary was estimated using the following nonlinear data analysis methods: time delay (τ), attractor reconstructions, correlation dimension (D), and largest Lyapunov exponent (λ). All estimates demonstrate that the pressure fluctuations in the c–c aqueous solutions and extent of liquid solution penetration into the capillary during the time between subsequent bubble departures behave chaotically. Furthermore, this work demonstrates that the dynamics of bubble formation along with the bubble waiting time are very sensitive to small perturbation in the physical properties of the liquid, and this sensitivity has a significant effect on the observed chaotic behaviour.
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