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We study in details the most generic 2,3 cusp singularity which gives rise to an elementary branching event. We also formulate the dispersive solution in algebro-geometrical terms as an evolution of Krichever-Boutroux complex curve.

In finite time, the flow develops cusplike singularities.

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We show that the ill-defined problem admits a weak dispersive solution when singularities give rise to a graph of shock waves propagating in the viscous fluid. The graph of shocks grows and branches. Velocity and pressure jump across the shock.

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We formulate a few simple physical principles which single out the dispersive solution and interpret shocks as lines of decompressed fluid. We also formulate the dispersive solution in algebro-geometrical terms as an evolution of Krichever-Boutroux complex curve.

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We study in details the most generic 2,3 cusp singularity which gives rise to an elementary branching event. This solution is self-similar and expressed in terms of elliptic functions.

However, the opacity of metals enforces the use of indirect imaging techniques with limited temporal or spatial resolution. In addition, accurate interface tracking requires tomography which further complicates the design of a high-temperature experimental setup. In this paper, an alternative approach is suggested that circumvents these two main restrictions.

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By injecting gas in a thin layer of liquid metal entrapped between two flat and closely spaced plates, bubbles in a Hele-Shaw flow regime are generated. The resulting quasi-2D multiphase flow phenomena can be fully captured from a single point of view and, when using a non-wetted transparent plate material, the bubbles can be observed directly.

The feasibility of this approach is demonstrated by observations on buoyancy-driven nitrogen Betting Starter Trading strateegia in liquid mercury in a vertical Hele-Shaw cell.

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By using a moving high-speed camera to make continuous close up recordings of individual bubbles, the position and geometry of these bubbles are quantified with a high resolution along their entire path.

After a thorough evaluation of the experimental accuracy, this information is used Betting Starter Trading strateegia a detailed analysis of the bubble expansion along the path. While the observed bubble growth is mainly caused by the hydrostatic pressure gradient, a careful assessment of the volume variations for smaller bubbles shows that an accurate bubble description should account for significant dynamic pressure variations that seem to be largely regime dependent.

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