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An analytical framework for evaluating the cohesion effects of coalescence between capillary bridges

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Abstract

In this work, we analyse the physical consequences of capillary bridges coalescence between spherical particles agglomerates and more particularly the jump of the capillary force. By referring to Murase et al. (Adv Powder Technol 19(4):349–367, 2008) and Rynhart et al. (Res Lett Inf Math Sci 5:119–127, 2003) about bridges adhered to three particles, we analyse the effects of coalescense between three bridges with two grains and a bridge joining three grains. This monographic synthesis intends to explain analytically and geometrically the significant increase of the inter-particle force, a strengthening cohesion effect, experimentally observed, reported and still largely unelucidated to our knowledge in the literature.

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Notes

  1. The coefficient \(\sqrt{3}\) comes from the composition rule of the forces inclined of a \(\pi /3\) angle with respect to the vertical.

  2. Independent of the coordinate system that is chosen.

  3. This value corresponds to \(4\pi r \sin \pi /6\).

  4. Whose vertex is the center of the upper sphere and the other direction given by the vertical.

  5. Characterized by the well-known relations \(s=0\) and \(y_{\delta }^{*}=r\sin \delta \ \sin \left( \delta +\theta \right) \).

  6. By geometrical construction by dividing the major axis in three equal parts.

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Acknowledgments

The authors acknowledge J.P. Gras for allowing to reproduce at Sect. 2 experimental data from his Ph.D. Thesis and Prof. N.-P. Kruyt for personal discussions about this paper to improve the manuscript.

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  1. LaSIE, UMR-CNRS 7356, Université de La Rochelle, Avenue Michel Crépeau, 17042, La Rochelle Cedex 1, France

    Gérard Gagneux & Olivier Millet

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  1. Gérard Gagneux
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  2. Olivier Millet
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Correspondence to Olivier Millet.

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Gagneux, G., Millet, O. An analytical framework for evaluating the cohesion effects of coalescence between capillary bridges. Granular Matter 18, 16 (2016). https://doi.org/10.1007/s10035-016-0613-5

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