Multiple steadily translating bubbles in a Hele-Shaw channel by Christopher C. Green, and Giovani L. Vasconcelos Proceedings A Volume 470(2163): March 8, 2014 ©2014 by The Royal Society

Schematic of a Hele-Shaw channel of width 2 containing an assembly of bubbles steadily translating with constant velocity U parallel to the x-axis. Christopher C. Green, and Giovani L. Vasconcelos Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

Schematic showing the flow domains in the w-plane (a) and in the τ-plane (b), representing the complex potentials in the laboratory and co-moving frames, respectively. Christopher C. Green, and Giovani L. Vasconcelos Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

The circular domain Dζ in the auxiliary complex ζ-plane. Christopher C. Green, and Giovani L. Vasconcelos Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

An example of two bubbles which are reflectionally symmetric about the channel centreline. Christopher C. Green, and Giovani L. Vasconcelos Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

An example of two bubbles in a general asymmetric configuration with a set of streamlines superposed in the frame co-travelling with the bubbles. Christopher C. Green, and Giovani L. Vasconcelos Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

An example of three bubbles in a general asymmetric configuration. Christopher C. Green, and Giovani L. Vasconcelos Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

An example of four bubbles in a general asymmetric configuration. Christopher C. Green, and Giovani L. Vasconcelos Proc. R. Soc. A 2014;470: ©2014 by The Royal Society