Abstract
We report the dynamics of a viscoplastic (Bingham) torus suspended in an unbounded Newtonian medium. In this study, the immiscible ambient fluid is subjected to an axisymmetric compressional (biaxial-extensional) flow. Numerical simulations applying the boundary integral formulation to the Stokes flow are performed for the torus drop having initially a circular cross section. The quasi-stationary dynamic simulation reveals that depending on the initial conditions and the capillary number (Ca), the Bingham number (Bn), and the viscosity ratio (λ), three different scenarios of the drop evolution are obtained for a range of viscosity ratio and Bingham number: collapsing toward the axis of symmetry, expanding infinitely, and having a stationary toroidal shape.
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