Pergamon Int. J. Multiphase Flow Vol. 23, No. 4, pp. 713-723, 1997 © 1997 ElsevierScience Ltd. All rights reserved Printed in Great Britain Plh S0301-9322(97)00004-9 o301-9322/97 $17.00+ o.0o CHAOTIC BUBBLE COALESCENCE IN NON-NEWTONIAN FLUIDS H. Z. LP, Y. MOULINE ~, L. CHOPLIN ~ and N. MIDOUX 2 ~Centre de G6nie Chimique des Milieux Complexes, 2Laboratoire des Sciences du G6nie Chimique, CNRS-ENSIC-INPL, 1 rue Grandville, BP 451, 54001 Nancy Cedex, France (Received 25 August 1996; in revised form 5 February 1997) Abstract--This work aims at studying in-line bubble coalescence in non-Newtonian fluids. The visualisation and power spectrum of time series data, recorded via an optical sensing device, confirm that the bubble formation at the orifice is perfectly periodic under a constant gas flowrate. However, the separation interval between bubbles becomes irregular during rise, until, at a certain height above the orifice, the coalescence occurs. An original approach is elaborated by relating the rise of a chain of bubbles to consecutive shear deformations. A series of measurements on a rheometer proves for the first time that the bubble coalescence is mainly governed by the dynamical competition between the creation and relaxation of shear stresses. The time delay embedding method of reconstructing the phase-space diagram is applied to time series data 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, reveals that the coalescence between bubbles obeys a chaotic and deterministic mechanism. © 1997 Elsevier Science Ltd. Key Words: chaos, bubble, coalescence, interactions, non-Newtonian fluid 1. INTRODUCTION The behaviour of bubbles, especially their coalescence, in non-Newtonian fluids is of key importance in such diverse fields as polymer devolatilisation, composites processing, boiling, bubble column, fermentation, cavitation, plastic foam processing, bubble absorption, etc. However, basic knowledge is still missing concerning the coalescence of bubbles in both Newtonian and non-Newtonian fluids. Compared with the understanding of bubbles in Newtonian fluids, the study of the bubble behaviour in non-Newtonian fluids remains still in an elementary stage. Due to the inherent complex nature of bubble phenomena, a complete theoretical analysis is impossible at present. A somewhat simplified starting point in this field has been the study of bubbles formed from a single submerged orifice, which excludes mutual influence of bubbles formed in neighbouring orifices. Until now, little attention was paid to studies of bubble coalescence (Trambouze 1993). Nevertheless, the loss of interfacial area due to coalescence can be a serious matter in industrial gas-fluid installations. The final stage of coalescence is the rupture of the thin film of non-Newtonian fluid separating two bubbles, a matter that has received some attention (Acharya and Ulbrecht 1978; De Kee et al. 1990). However, an equally important problem, about which there is no information in the literature, is the governing mechanism by which bubbles draw together and coalesce. This is the topic for consideration in the present paper. 2. BASIC CONCEPTS: SOME DEFINITIONS Chaos theory is a newly developing discipline, we recommend the books by Berg6 et al. (1984), Schuster (1988) and Ott (1993) as good overviews. To facilitate the understanding, the basic definitions are given below without resorting to too much mathematics before presenting results. 713