Chaotic Characteristics of Bubbles Rising with Coalescences in Pseudoplastic Fluid

Abstract The chaotic characteristics of bubbles rising with accompanying coalescences in pseudoplastic aqueous carboxymethylcellulose sodium (CMC) solution were studied by means of smoothed pseudo Wigner-Ville distribution and Wigner-Hough distribution. The temporal signal of bubble passage was measured utilizing a photoconductive data acquisition system. As bubble coalescence occurred, the smoothed pseudo Wigner-Ville distribution of the signal revealed that the signal could be divided into low-frequency and high-frequency ranges and the transition range according to the distribution feature of frequency domain, which reflected eddy motion of fluid, high frequency fluctuations of fluid velocity and other random components measured in the signal, and bubbles rising accompanied with coalescences, respectively. However, bubble coalescence occurred in the lower position and the frequency range of bubbles motion became wide under higher gas flowrate, while the frequency range of bubbles motion became narrow when the CMC concentration increased. The typical dynamics of bubbles motion, such as periodicity, bifurcation and chaos, could be easily found in terms of the Wigner-Hough distribution.