Chaotic behavior of in-line bubbles rising with coalescences in non-Newtonian fluids: A multiscale analysis

Abstract

International audienceThe nonlinear dynamics of in-line bubbles rising with coalescence in non-Newtonian Carboxymethylcellulose sodium (CMC) fluids was studied through the techniques such as the multiresolution signal decomposition and the chaotic time series analysis. The temporary signals of bubble passages collected by an optical sensing device at different heights were investigated by a 12-level wavelet decomposition and the scalewise characteristics of bubble motion were extracted and analyzed. The chaotic time series analysis distinguished the periodicity or the deterministic chaos of bubble motion successsfully. The calculation of Kolmogorov entropy proves that in the ranges of experimental heights and gas flowrates, the bubble rising dynamics becomes more chaotic with the increase of height, and reaches the maximum chaotic extent in a certain height, while with the further increase of height, the chaotic extent decreases slowly. With the increase of gas flowrate, at the lower height, the bubble rising dynamics changes from periodicity to deterministic chaos, and at the higher heights it reaches the maximum chaotic extent in a certain gas flowrate; however, for both cases, it has little change in the higher gas flowrates. Moreover, with the increase of CMC concentration, the bubble rising dynamics becomes less chaotic when the height is beyond a certain value

A Multiscale Approach for Modeling Bubbles Rising in Non-Newtonian Fluids

“…In order to understand the coalescence nature, the time delay embedding method of reconstructing the phase–space diagram was applied to time series data (bubble passage) recorded at different heights in the bubble column. The calculation of several parameters, the largest Lyapunov exponent, the correlation dimension, the power spectrum and the phase portraits, indicates that the coalescence between bubbles is chaotic. , Experimentally, the chaos’ appearance can also be described by the period-doubling sequences. It is worth noting that the variation of the correlation dimension with the embedding dimension shows that the chaos is deterministic with a limited number of degrees of freedom.…”

“…The calculation of several parameters, the largest Lyapunov exponent, the correlation dimension, the power spectrum and the phase portraits, indicates that the coalescence between bubbles is chaotic. 27,28 Experimentally, the chaos' appearance can also be described by the perioddoubling sequences. It is worth noting that the variation of the correlation dimension with the embedding dimension shows that the chaos is deterministic with a limited number of degrees of freedom.…”

“…These rules are based on the physical mechanisms understood at the mesoscopic level and could be hopefully expected to predict the interactions and coalescence between a great number of bubbles to come close to the industrial scale. In particular, the experimental results 27,28 show that the coalescence between bubbles rising in-line takes place easily in non-Newtonian fluids. The film drainage is mainly encountered in Newtonian fluids or for the lateral coalescence between bubbles in non-Newtonian fluids.…”

Bubbles in Non-Newtonian Fluids: A Multiscale Modeling

“…In order to understand the coalescence nature, the time delay embedding method of reconstructing the phasespace diagram was applied to time series data (bubble passage) recorded at different heights in the bubble column. The calculation of several parameters: the largest Lyapunov exponent, the correlation dimension, the power spectrum and the phase portraits, indicates that the coalescence between bubbles is chaotic (Li et al, 1997;Jiang et al, 2011). Experimentally, the chaos' appearance can also be described by the period-doubling sequences.…”

“…In particular, the experimental results (Li et al, 1997;Jiang et al, 2011) show that the coalescence between bubbles rising in-line takes place easily in non-Newtonian fluids. The film drainage is mainly encountered in Newtonian fluids or for the lateral coalescence between bubbles in non-Newtonian fluids.…”