The link between discrete and continuous modeling of liquid foam at the level of a single bubble

Bruce Gardiner, A. Tordesillas

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    8 Citations (Web of Science)


    In order to test the adaptability of a homogenization scheme originally developed for dry granular media, a micromechanical constitutive law, for three-dimensional monodisperse wet foam is developed. The advantage of the homogenization scheme is that it provides a link between the discrete bubble-scale microstructure and the continuum quantities of stress and deformation. Furthermore, the resulting constitutive law is in terms of physical material properties (e.g., fluid viscosity, surface tension, and bubble radius) rather than the more phenomenological parameters, such as power-law indices, etc. Hence, predictions of the continuum model can be, and are, compared directly to experiments and simulations. Many of the general features of foam behavior are reproduced, including small-strain elasticity, dependence on gas fraction, and Bingham plastic type deformation rate dependency. However, the current micromechanical continuum model substantially overestimates the static shear modulus and yield stress of foams in comparison to simulations and experiments. This discrepancy is due to the adoption of a mean-field assumption for the deformation in the current model. It is then argued that future micromechanical continuum models for foams cannot neglect the nonaffine motions associated with bubble rearrangements. Finally, for both foams and granular materials, our study indicates that the uniform deformation assumption is only valid near the critical packing of monodisperse spherical particles. (C) 2005 The Society of Rheology.
    Original languageEnglish
    Pages (from-to)819-838
    JournalJournal of Rheology
    Issue number4
    Publication statusPublished - 2005


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