Stabilization of purely elastic instabilities in cross-slot geometries
Stabilization of purely elastic instabilities in cross-slot geometries
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DOI：
10.1017/jfm.2021.473
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发表时间：
2021-07-07
影响因子：
3.7
通讯作者：
Poole, Robert J.
中科院分区：
文献类型：
--
作者：
Davoodi, Mahdi;Houston, Gemma;Poole, Robert J.
在这项工作中，牛顿和/或粘弹性流体在一个“十字槽”的几何形状的两相流的实验和数值研究在蠕变流动的限制。一系列的微流控实验-使用牛顿流体-已经进行了不同的横截面纵横比，以支持我们的数值模拟。数值模拟依赖于流体体积法，并利用对数构象制剂结合简化的粘弹-Thien和坦纳模型。从中央十字的下游，一旦流动已成为充分发展，我们还估计分析的厚度，每个流体层的二维和三维的情况下。除了为我们的数值求解器提供基准测试外，这些分析结果还提供了对粘度比作用的深入了解。从每个入口臂注入两种具有不同弹性特性的流体被证明是一种有效的方法，以稳定在交叉槽几何形状中观察到的纯弹性不稳定性，基于具有较大弛豫时间的流体的特性。我们的研究结果表明，界面张力也可以发挥重要的作用，在自由驻点附近（即在中心十字）的两种流体的界面的形状。通过减小界面张力，两种流体的界面变得弯曲，并且这可以因此改变该区域中流线的曲率，这进而可以修改纯弹性流动转变。因此，增加界面张力被证明有一个稳定的效果，对相关的稳定破胶纯弹性不稳定。然而，在高值的粘度比，一个新的时间依赖的纯弹性不稳定性出现最有可能是由于在这些条件下观察到的流线曲率的变化。即使当两种流体都是牛顿流体时，在二维极限之外，也会出现弱不稳定性，使得在深度（中性）方向上的流体界面不再保持平坦。
In this work, two-phase flows of Newtonian and/or viscoelastic fluids in a 'cross-slot' geometry are investigated both experimentally and numerically in the creeping-flow limit. A series of microfluidic experiments - using Newtonian fluids - have been carried out in different cross-section aspect ratios to support our numerical simulations. The numerical simulations rely on a volume of fluid method and make use of a log-conformation formulation in conjunction with the simplified viscoelastic Phan-Thien and Tanner model. Downstream from the central cross, once the flow has become fully developed, we also estimate analytically the thickness of each fluid layer for both two- and three-dimensional cases. In addition to providing a benchmark test for our numerical solver, these analytical results also provide insight into the role of the viscosity ratio. Injecting two fluids with different elastic properties from each inlet arm is shown to be an effective approach to stabilize the purely elastic instability observed in the cross-slot geometry based on the properties of the fluid with the larger relaxation time. Our results show that interfacial tension can also play an important role in the shape of the interface of the two fluids near the free-stagnation point (i.e. in the central cross). By reducing the interfacial tension force, the interface of the two fluids becomes curved and this can consequently change the curvature of streamlines in this region which, in turn, can modify the purely elastic flow transitions. Thus, increasing interfacial tension is shown to have a stabilizing effect on the associated steady symmetry-breaking purely elastic instability. However, at high values of the viscosity ratio, a new time-dependent purely elastic instability arises most likely due to the change in streamline curvature observed under these conditions. Even when both fluids are Newtonian, outside of the two-dimensional limit, a weak instability arises such that the fluid interface in the depth (neutral) direction no longer remains flat.