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Self-organization of ascending bubbles ensemble

Self-organization of hydrogen bubbles generated by laser-treated areas of an aluminum plate etched in a basic aqueous solution of ammonia is studied experimentally and theoretically. A dynamics of establishment of stationary pattern of gas bubbles is experimentally is shown. In the theoretical model the velocity field of liquid flows around an ensemble of several bubbles is obtained. Modeling of the process of self-organization of gas bubbles is performed on the basis of continuum model of bubbles jet. Under certain assumptions, the pressure of diluted gas bubbles is described by equation similar to that for non-ideal gas that follows the van der Waals equation of state. The model predicts an alignment of gas bubbles along bisectors of the laser-treated area limited by a square, which is in good agreement with experimental observations. Further development of the model leads to the equation with negative diffusion coefficient that may be responsible for symmetry breakdown and pattern formation.