The Viscous Froth Model: steady states and the high-velocity limit

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences (Impact Factor: 2.38). 01/2009; DOI: 10.1098/rspa.2009.0057
Source: OAI

ABSTRACT The steady-state solutions of the viscous froth model for foam dynamics are analysed and shown to be of finite extent or to asymptote to straight lines. In the high-velocity limit, the solutions consist of straight lines with isolated points of infinite curvature. This analysis is helpful in the interpretation of observations of anomalous features of mobile two-dimensional foams in channels. Further physical effects need to be adduced in order to fully account for these. Financial support from (D.W.) the European Space Agency (MAP AO-99-108: C14914/02/NL/SH, MAP AO-99-075: C14308/00/NL/SH) (G.M.), the Wales Institute of Mathematical and Computational Sciences and (S.J.C.) EPSRC (EP/D048397/1, EP/D071127/1) is gratefully acknowledged.

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    ABSTRACT: The 2D flow of a foam confined in a Hele-Shaw cell through a contraction is investigated. Its rheological features are quantified using image analysis, with measurements of the elastic stress, rate of plasticity, and velocity. The behavior of the velocity strongly differs at the contraction entrance, where the flow is purely convergent, and at the contraction exit, where a velocity undershoot and a re-focussing of the streamlines are unraveled. The yielded region, characterized by a significant rate of plasticity and a maximal stress amplitude, is concentrated close to the contraction. These qualitative generic trends do not vary significantly with the flow rate, bubble area and contraction geometry, which is characteristic of a robust quasistatic regime. Using surfactants with a high surface viscoelasticity, a marked dependence of the elastic stress on the velocity is exhibited. The results show that the rate of plasticity does not only depend on the local magnitude of the deformation rate, but also crucially on the orientation of both elastic stresses and deformation rate. It is also discussed how the viscous friction controls the departure from the quasistatic regime. Comment: submitted to J. Rheol; frst resubmission
    Journal of Rheology 07/2009; · 2.80 Impact Factor

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