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Two-dimensional flow of foam around a circular obstacle: local measurements of elasticity, plasticity and flow


We investigate the two-dimensional flow of a liquid foam around a circular obstacle by measuring all the local fields necessary to describe this flow: velocity, pressure, and bubble deformations and rearrangements. We show how our experimental set-up, a quasi-two-dimensional ‘liquid pool’ system, is adapted to the determination of these fields: the velocity and bubble deformations are easy to measure from two-dimensional movies, and the pressure can be measured by exploiting a specific feature of this system, a two-dimensional effective compressibility. To describe accurately neighbour swapping (so-called ‘T1’ processes), we propose a new, tensorial descriptor. All these quantities are evaluated via an averaging procedure that we justify by showing that the fluctuations of the fields are essentially Gaussian. The flow is extensively studied in a reference experimental case; the velocity presents an overshoot in the wake of the obstacle, and the pressure is maximum at the leading side and minimal at the trailing side. The study of the elastic deformations and of the velocity gradients shows that the transition between plug flow and yielded regions is smooth. Our tensorial description of T1s highlights their correlation both with the bubble deformations and the velocity gradients. A salient feature of the flow, notably for the velocity and T1 distribution, is a marked fore–aft asymmetry, the signature of the elastic behaviour of the foam. We show that the results do not change qualitatively when various control parameters (flow rate, bubble area, fluid fraction, bulk viscosity, obstacle size and boundary conditions) vary, identifying a robust quasi-static regime. These results are discussed in the framework of the foam rheology literature. A movie is available with the online version of the paper.

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M. Beaulne & E. Mitsoulis 1997 Creeping motion of a sphere in tubes filled with Herschel–Bulkley fluids. J. Non-Newtonian Fluid Mech. 72, 5571.

I. Cantat & R. Delannay 2003 Dynamical transition induced by large bubbles in two-dimensional foam flows. Phys. Rev. E 67, 031501.

I. Cantat , C. Poloni & R. Delannay 2006 Experimental evidence of flow destabilization in a two-dimensional bidisperse foam. Phys. Rev. \rm E 73, 011505.

S. Courty , B. Dollet , F. Elias , P. Heinig & F. Graner 2003 Two-dimensional shear modulus of a Langmuir foam. Europhys. Lett. 64, 709715.

B. Dollet , M. Aubouy & F. Graner 2005 aAnti-inertial lift in foams: A signature of the elasticity of complex fluids. Phys. Rev. Lett. 95, 168303.

B. Dollet , F. Elias , C. Quilliet , A. Huillier , M. Aubouy & F. Graner 2005 bTwo-dimensional flows of foam: Drag exerted on circular obstacles and dissipation. Colloids Surf. A 263, 101110.

M. Durand & H. A. Stone 2006 Relaxation time of the topological T1 process in a two-dimensional foam. Phys. Rev. Lett. 97, 226101.

A. D. Gopal & D. J. Durian 2003 Relaxing in foam. Phys. Rev. Lett. 91, 188303.

B. Gueslin , L. Talini , B. Herzhaft , Y. Peysson , C. Allain 2006 Flow induced by a sphere settling in an aging yield-stress fluid. Phys. Fluids 18, 103101.

O. G. Harlen 2002 The negative wake behind a sphere sedimenting through a viscoelastic fluid. J. Non-Newtonian Fluid Mech. 108, 411430.

É. Janiaud , D. Weaire & S. Hutzler 2006 Two-dimensional foam rheology with viscous drag. Phys. Rev. Lett. 97, 038302.

S. A. Khan & R. C. Armstrong 1986 Rheology of foams. I. Theory for dry foams. J. Non-Newtonian Fluid Mech. 22, 122.

T. G. Mason , J. Bibette & D. A. Weitz 1996 Yielding and flow of monodisperse emulsions. J. Colloid Interface Sci. 179, 439448.

G. Picard , A. Adjari , F. Lequeux & L. Bocquet 2004 Elastic consequences of a single plastic event: A step towards the microscopic modeling of the flow of yield stress fluid. Eur. Phys. J. \rm E 15, 371381.

H. M. Princen 1983 Rheology of foams and highly concentrated emulsions. I. Elastic properties and yield stress of a cylindrical model system. J. Colloid Interface Sci. 91, 160175.

H. M. Princen 1985 Rheology of foams and highly concentrated emulsions. II. Experimental study of the yield stress and wall effects for concentrated oil-in-water emulsions. J. Colloid. Interface. Sci. 105, 150171.

P. Sollich , F. Lequeux , Hébraud, P. & M. E. Cates 1997 Rheology of soft glassy materials. Phys. Rev. Lett. 78, 20202023.

Y. Wang , K. Krishan & M. Dennin 2006 Impact of boundaries on velocity profiles in bubble rafts. Phys. Rev. E 73, 031401.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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