Dam break of viscoplastic elliptical objects

TL;DR

This paper investigates the physical mechanisms and flow regimes involved in the gravity-driven spreading of viscoplastic elliptical objects modeled as Bingham fluids, using numerical simulations and theoretical analysis.

Contribution

It introduces a new variational multi-scale numerical approach to analyze viscoplastic spreading and identifies three distinct flow regimes influenced by initial geometry.

Findings

Identification of gravito-viscous, gravito-plastic, and mixed flow regimes.

Development of a collapse diagram linking spreading and collapse time.

Discovery of a collapse number parameter controlling regimes.

Abstract

In this note, we numerically and theoretically analyze the physical mechanisms controlling the gravity-induced spreading of viscoplastic elliptical metric objects on a sticky solid surface (without sliding). The two-dimensional collapsing objects are described as Bingham fluids. The numerical simulations are based on a variational multi-scale approach devoted to multiphase non-Newtonian fluid flows. The results are depicted by considering the spreading dynamics, energy budgets, and new scaling laws. They show that, under negligible inertial effects, the driving gravitational energy of the elliptical columns is dissipated through viscoplastic effects during the collapse, giving rise to three flow regimes: gravito-viscous, gravito-plastic, and mixed gravito-visco-plastic. These regimes are strongly affected by the initial aspect ratio of the collapsing column, which reveals the possibility of using morphology to control spreading. Finally, the results are summarized in a diagram linking the object's maximum spreading and the collapse time with different collapsing regimes through a single dimensionless parameter called collapse number.