The deformation and breakup of viscoelastic drops in simple shear flows of Newtonian liquids are studied numerically. Our three-dimensional numerical scheme, extended from our previous two-dimensional algorithm, employs a diffusive-interface lattice Boltzmann method together with a lattice advection–diffusion scheme, the former to model the macroscopic hydrodynamic equations for multiphase fluids and the latter to describe the polymer dynamics modeled by the Oldroyd-B constitutive model. A block-structured adaptive mesh refinement technique is implemented to reduce the computational cost. The multiphase model is validated by a simulation of Newtonian drop deformation and breakup under an unconfined steady shear, while the coupled algorithm is validated by simulating viscoelastic drop deformation in the shear flow of a Newtonian matrix. The results agree with the available numerical and experimental results from the literature. We quantify the drop response by changing the polymer relaxation time λ and the concentration of the polymer c. The viscoelasticity in the drop phase suppresses the drop deformation, and the steady-state drop deformation parameter D exhibits a non-monotonic behavior with the increase in Deborah number De (increase in λ) at a fixed capillary number Ca. This is explained by the two distribution modes of the polymeric elastic stresses that depend on the polymer relaxation time. As the concentration of the polymer c increases, the degree of suppression of deformation becomes stronger and the transient result of D displays an overshoot. The critical capillary number for unconfined drop breakup increases due to the inhibitive effects of viscoelasticity. Different distribution modes of elastic stresses are reported for different De.

中文翻译：

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粘弹性液滴在简单剪切流中变形和破碎的格子 Boltzmann 模型

数值研究了牛顿流体简单剪切流中粘弹性液滴的变形和破碎。我们的三维数值方案从我们之前的二维算法扩展而来，采用扩散界面格子玻尔兹曼方法和格子平流扩散方案，前者模拟多相流体的宏观流体动力学方程，后者描述由 Oldroyd-B 本构模型建模的聚合物动力学。实施块结构自适应网格细化技术以降低计算成本。多相模型通过模拟无侧限稳定剪切下的牛顿液滴变形和破碎来验证，而耦合算法通过模拟牛顿矩阵剪切流中的粘弹性液滴变形来验证。结果与文献中可用的数值和实验结果一致。我们通过改变聚合物弛豫时间 λ 和聚合物 c 的浓度来量化下降响应。液滴相中的粘弹性抑制液滴变形，稳态液滴变形参数 D 在固定毛细管数 Ca 下随着德博拉数 De 的增加（λ 增加）表现出非单调行为。这是由取决于聚合物松弛时间的聚合物弹性应力的两种分布模式来解释的。随着聚合物c浓度的增加，对变形的抑制程度变强，D的瞬态结果显示出超调。由于粘弹性的抑制作用，无侧限液滴破碎的临界毛细管数增加。