Title: Coalescence of viscoelastic sessile drops: the small and large contact angle limits Show Chinese title

Title: 粘弹性液滴的聚并：小接触角和大接触角极限

Abstract: The coalescence and breakup of drops are classic examples of flows that feature singularities. The behavior of viscoelastic fluids near these singularities is particularly intriguing - not only because of their added complexity, but also due to the unexpected responses they often exhibit. In particular, experiments have shown that the coalescence of viscoelastic sessile drops can differ significantly from their Newtonian counterparts, sometimes resulting in a sharply defined interface. However, the mechanisms driving these differences in dynamics, as well as the potential influence of the contact angle, remain largely qualitative or unknown. Here, we study two different flow regimes effectively induced by varying the contact angle and demonstrate how that leads to markedly different coalescence behaviors. We show that the coalescence dynamics is effectively unaltered by viscoelasticity at small contact angles. The Deborah number, which is the ratio of the relaxation time of the polymer to the timescale of coalescence, scales as $\theta^3$ for $\theta \ll 1$, thus rationalizing the near-Newtonian response. On the other hand, it has been shown previously that viscoelasticity alters the shape of the interface during coalescence at large contact angles but does not affect the temporal evolution of the shape. We study this large contact angle limit using experiments and 2D numerical simulations of the equation of motion, using the Oldroyd-B model for the constitutive representation. We show that the departure of the coalescence dynamics from the Newtonian case is a function of the Deborah number and the elastocapillary number. Show Chinese abstract

Abstract: 液滴的聚结与破裂是流体力学中具有奇点的经典例子。 在这些奇点附近，粘弹性流体的行为尤其引人入胜——不仅因为它们增加了复杂性，还由于它们经常表现出意想不到的响应。 特别是，实验表明，粘弹性非浮凸液滴的聚结可能与其牛顿流体的对应物大不相同，有时会导致界面定义得非常清晰。 然而，导致这些动态差异的机制以及接触角的潜在影响仍然主要是定性的或者未知的。 在这里，我们研究了两种不同的流动状态，这些状态是由改变接触角有效诱导的，并展示了这如何导致显著不同的聚结行为。 我们表明，在小接触角的情况下，粘弹性对聚结动力学几乎没有影响。 Deborah数，即聚合物松弛时间与聚结时间尺度之比，在 $\theta \ll 1$时，缩放为 $\theta^3$，从而合理化了近牛顿响应。 另一方面，先前的研究已经表明，在大接触角下，粘弹性会改变聚结过程中界面的形状，但不会影响形状的时间演化。 我们使用实验和运动方程的二维数值模拟研究了这个大接触角极限，使用Oldroyd-B模型来表示本构关系。 我们证明了聚结动力学偏离牛顿情况的程度是Deborah数和弹性能数的函数。