We give an exact formula for the velocity profile of shear localisation in a 2D foam, represented by a continuum model that incorporates a Herschel-Bulkley constitutive relation and wall drag. A more approximate treatment provides a relation between the localisation length and the boundary velocity as a power law whose exponent is explicitly determined by the input parameters of the model. This is corroborated, and its conditions for validity are clarified, by the analysis of various expansions of the exact solution. The general consequences are consistent with the recent findings of Katgert and co-workers (G. Katgert, M. Mobius, and M. van Hecke, available from http://arxiv.org/abs/0711.4024 [cond-mat.soft].
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机译：我们给出了二维泡沫中剪切局部化速度分布的精确公式，该公式由包含Herschel-Bulkley本构关系和壁阻力的连续模型表示。更为近似的处理提供了定位长度与边界速度之间的关系，作为幂律，其幂由模型的输入参数明确确定。通过分析精确解的各种展开，可以证实这一点，并阐明其有效性条件。一般的后果与Katgert及其同事的最新发现一致（G. Katgert，M。Mobius和M. van Hecke，可从http://arxiv.org/abs/0711.4024 [cond-mat.soft]获得。 。
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