悬浮于黏弹性流体中的牛顿液滴的缓慢热毛细运动
Creeping thermocapillary motion of a Newtonian droplet suspended in a viscoelastic fluid
AI总结：
本研究针对微重力下黏弹性流体中牛顿液滴的热毛细运动问题，采用双重摄动展开结合Oldroyd-B模型推导速度与形状表达式，揭示了Weissenberg数、黏度比等对液滴运动的影响规律，小参数下理论预测与数值模拟吻合良好。
摘要：
本工作从理论层面研究了牛顿液滴在外部施加温度梯度作用下、于静止无限黏弹性流体中的运动问题。外部流体采用Oldroyd-B方程建模，针对小Weissenberg数（韦森贝格数）和小Capillary数（毛细数）的情形，通过双重摄动展开方法求解该问题。\n 我们假设处于微重力条件，忽略能量与动量的对流输运，推导得到了液滴迁移速度及其形状关于两种流体物性的表达式。在无形状变形的情况下，对于黏度足够大的内部流体，液滴速度随Weissenberg数单调下降；而对于内外黏度比较小的流体，液滴速度随Weissenberg数先增大后减小。对于较小但有限的Capillary数，当Capillary数与Weissenberg数的比值固定时，液滴速度随施加的温度梯度呈单调变化。我们证明这一行为与聚合物应力使液滴沿迁移方向发生变形有关，而液滴速度的相关变化本质上属于牛顿流体特性，与液滴流体动力学阻力及其内部温度分布的变化相关。与数值模拟结果对比表明，我们的理论在Capillary数和Weissenberg数足够小的情况下具有良好的预测能力。
英文摘要：
In this work we consider theoretically the problem of a Newtonian droplet moving in an otherwise quiescent infinite viscoelastic fluid under the influence of an externally applied temperature gradient. The outer fluid is modelled by the Oldroyd-B equation, and the problem is solved for small Weissenberg and Capillary numbers in terms of a double perturbation expansion. We assume microgravity conditions and neglect the convective transport of energy and momentum. We derive expressions for the droplet migration speed and its shape in terms of the properties of both fluids. In the absence of shape deformation, the droplet speed decreases monotonically for sufficiently viscous inner fluids, while for fluids with a smaller inner-to-outer viscosity ratio, the droplet speed first increases and then decreases as a function of the Weissenberg number. For small but finite values of the Capillary number, the droplet speed behaves monotonically as a function of the applied temperature gradient for a fixed ratio of the Capillary and Weissenberg numbers. We demonstrate that this behaviour is related to the polymeric stresses deforming the droplet in the direction of its migration, while the associated changes in its speed are Newtonian in nature, being related to a change in the droplet's hydrodynamic resistance and its internal temperature distribution. When compared to the results of numerical simulations, our theory exhibits a good predictive power for sufficiently small values of the Capillary and Weissenberg numbers.
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