56 † To whom correspondence should be addressed. E-mail: ygma@tju.edu.cn Korean J. Chem. Eng., 28(1), 56-63 (2011) DOI: 10.1007/s11814-010-0327-z INVITED REVIEW PAPER Chaotic behavior of in-line bubbles rising with coalescences in non-Newtonian fluids: A multiscale analysis Shaokun Jiang*, Youguang Ma* ,† , Wenyuan Fan*, Ke Yang*, and Huaizhi Li** *State Key Laboratory of Chemical Engineering, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China **Laboratoire des Sciences du Génie Chimique, Nancy-Université, CNRS, 1, rue Grandville, BP 451, 54001 Nancy cedex, France (Received 27 February 2010  accepted 19 May 2010) Abstract−The nonlinear dynamics of in-line bubbles rising with coalescence in non-Newtonian Carboxymethylcellu- lose 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. Key words: Bubble, Coalescence, Wavelet Decomposition, Chaos, Kolmogorov Entropy INTRODUCTION Gas-liquid two-phase flows involving non-Newtonian fluids are widely encountered in many industrial processes, such as gas-liquid contact, gas-liquid separation, gas absorption, and bubble column. Bubbles in non-Newtonian fluids display complicated behavior, especially the coalescence between rising bubbles. The interfacial area between phases is reduced and the liquid film at the gas/liquid interface desquamates and renews due to bubble coalescence, lead- ing to a significant impact on mass and heat transfer. Few studies on bubble coalescence in non-Newtonian fluids have been reported due to its complex nature. The rupture time of the thin film separating two bubbles in non-Newtonian fluids was meas- ured by a high speed camera [1]. The bubble coalescence in vis- coelastic fluids was visually observed by injecting two or three bub- bles of different volumes [2,3]. Afterwards, Li et al. [4] recorded the frequency signal of bubble passage at different heights in vis- coelastic fluids via an optical sensing device, and based on the time delay embedding method of reconstructing the phase-space diagram, the calculated results of the largest Lyapunov exponent, the corre- lation dimension and the phase portrait revealed that the bubble coa- lescence in viscoelastic fluids obeys a deterministic and chaotic mech- anism. Furthermore, a mathematical model was developed to de- scribe the complex nonlinear dynamics of bubble chains rising in viscoelastic fluids [5]. However, the fundamental mechanism on bubble coalescence in non-Newtonian fluid is still far from fully understood. In the present work, an optical sensing system was employed to acquire the temporary signals of bubble passages in a non-Newto- nian fluid at different heights. Due to the influence of particles in the fluid and the variation of the laser beam itself, the temporary signal of bubble passages, including the information of various motions, was quite complicated and needed to be analyzed using proper and efficient methods to distinguish the dynamics of rising bubbles. Re- cently, the multiresolution signal decomposition [6] has been widely applied to analyze pressure fluctuation signals with multiscale fea- tures and unsteady characteristics in fluidization and bubble col- umns in chemical engineering [7-12]. Another technique, the chaotic time series analysis, has also shown great advantages in studying the nonlinear dynamics of bubble columns [4,13,14]. In the present work, both the multiresolution signal decomposition and chaotic time series analysis were simultaneously employed to analyze the temporary signals of bubble passages in non-Newtonian fluids and then to characterize qualitatively and quantitatively the nonlinear dynamics of in-line bubbles rising with coalescences. EXPERIMENTAL 1. Collection of the Temporary Signal of Bubble Passages The experimental setup is shown in Fig. 1. A Plexiglas square tank with the size of 0.15×0.15×1.50 m was constructed. Nitrogen bubbles were continuously formed through an orifice of a diameter 1×10 −3 m, submerged in the liquid at the central bottom of the tank