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.

中文翻译：

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压缩斯托克斯流中的粘塑性环形下降

我们报告了悬浮在无界牛顿介质中的粘塑性（宾厄姆）圆环的动力学。在这项研究中，不混溶的环境流体受到轴对称压缩（双轴拉伸）流动的影响。将边界积分公式应用于斯托克斯流的数值模拟是针对最初具有圆形横截面的环面液滴进行的。准稳态动力学模拟表明，根据初始条件和毛细管数 ( Ca )、宾汉数 ( Bn ) 和粘度比 ( λ )，可以在一定范围的粘度下获得三种不同的液滴演化场景比和宾汉数：向对称轴坍缩，无限膨胀，并具有静止的环形。