Rheological properties of the soft-disk model of two-dimensional foams

Abstract

The soft-disk model previously developed and applied by Durian [D. J. Durian, Phys. Rev. Lett. 75, 4780 (1995)] is brought to bear on problems of foam rheology of longstanding and current interest, using two-dimensional systems. The questions at issue include the origin of the Herschel-Bulkley relation, normal stress effects (dilatancy), and localization in the presence of wall drag. We show that even a model that incorporates only linear viscous effects at the local level gives rise to nonlinear (power-law) dependence of the limit stress on strain rate. With wall drag, shear localization is found. Its nonexponential form and the variation of localization length with boundary velocity are well described by a continuum model in the spirit of Janiaud et al. [Phys. Rev. Lett. 97, 038302 (2006)]. Other results satisfactorily link localization to model parameters, and hence tie together continuum and local descriptions.

References in corpus (8)

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• Rate Dependence and Role of Disorder in Linearly Sheared Two-Dimensional Foams
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• Impact of boundaries on velocity profiles in bubble rafts
• Two dimensional foam rheology with viscous drag
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Cited by in corpus (16)

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• Model for the Scaling of Stresses and Fluctuations in Flows near Jamming
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• The Jamming Perspective on Wet Foams
• Rheology of dense suspensions of elastic capsules: normal stresses, yield stress, jamming and confinement effects
• Flow in linearly sheared two dimensional foams: from bubble to bulk scale
• Viscous forces and bulk viscoelasticity near jamming
• Jamming in sheared foams and emulsions, explained by critical instability of the films between neighboring bubbles and drops
• Local description of the two-dimensional flow of foam through a contraction
• 2D foams above the jamming transition: Deformation matters
• Mean-field granocentric approach in 2D & 3D polydisperse, frictionless packings
• Ratio of effective temperature to pressure controls the mobility of sheared hard spheres
• Spatial correlations in polydisperse, frictionless two-dimensional packings
• Attraction-induced jamming in the flow of foam through a channel
• Shear localisation with 2D Viscous Froth and its relation to the Continuum Model