Elastic properties of a cellular dissipative structure

P. Brunet (), J.-M. Flesselles and L. Limat

The European Physical Journal B: Condensed Matter and Complex Systems, 2003, vol. 35, issue 4, 525-530

Abstract: Transition towards spatio-temporal chaos in one-dimensional interfacial patterns often involves two degrees of freedom: drift and out-of-phase oscillations of cells, respectively associated to parity breaking and vacillating-breathing secondary bifurcations. In this paper, the interaction between these two modes is investigated in the case of a single domain propagating along a circular array of liquid jets. As observed by Michalland and Rabaud for the printer’s instability [1], the velocity V g of a constant width domain is linked to the angular frequency $\omega$ of oscillations and to the spacing between columns $\lambda_0$ by the relationship $V_g=\alpha \lambda_0 \omega$ . We show by a simple geometrical argument that $\alpha$ should be close to $1/ \pi$ instead of the initial value $\alpha=1/2$ deduced from their analogy with phonons. This fact is in quantitative agreement with our data, with a slight deviation increasing with flow rate. Copyright Springer-Verlag Berlin/Heidelberg 2003

Date: 2003
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DOI: 10.1140/epjb/e2003-00306-1

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