Velocity Profiles in Slowly Sheared Bubble Rafts

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Velocity Profiles in Slowly Sheared Bubble Rafts, John Lauridsen, Gregory Chanan, and Michael Dennin, PRL vol.93 018303 (2004) [1]

Keywords

Foam, Yield Stress, Jamming, Couette Viscometer

Original Abstract from Paper

"Measurements of average velocity profiles in a bubble raft subjected to slow, steady shear demonstrate the coexistence between a flowing state and a jammed state similar to that observed for three-dimensional foams and emulsions [P. Coussot , Phys. Rev. Lett. 88, 218301 (2002)]. For sufficiently slow shear, the flow is generated by nonlinear topological rearrangements. We report on the connection between this short-time motion of the bubbles and the long-time averages. We find that velocity profiles for individual rearrangement events fluctuate, but a smooth, average velocity is reached after averaging over only a relatively few events."

Soft Matter

This study looks at the jamming of a flow of bubble rafts in a Couette viscometer. The experiment consists of first forming a single layer of bubbles at a fluid-air interface by flowing nitrogen through a solution of 44% glycerine, 28% each of water and "miracle bubble" (presumable containing some surfactant). The single layer of bubbles permits the authors to speak of a bubble "raft" and treat this as a two dimensional problem. In the paper, the units of stress are appropriatly modified for 2D (ie. <math>[ \sigma ] = [ N/m ]</math>). The bubble rafts are located between the concentric cylinders that define the Couette cylinder. The outer cylinder is driven at a constant rotation rate, while the torque on the inner cylinder is measured via a torsion wire (this cylinder is passive - not driven). For a rigid body rotation, one expects an angular velocity profile <math>v_{\theta} = \Omega r</math> from simple classical mechanics. Thus, the authors non-dimensionalize the velocity of the bubbles by <math>v(r) = v_{\theta} / \Omega r</math>