The dynamics of a neutrally buoyant, eccentric compound drop, suspended in a Poiseuille flow, in the presence of an external temperature gradient have been analyzed here. Assuming the energy and momentum transport to be diffusion-dominated, we derive approximate analytical solutions for the temperature and the velocity fields and subsequently deduce the deformation using asymptotic analysis in bispherical coordinates. We establish that depending on the direction, the presence of an imposed temperature gradient may speed up or slow down the drops. The temperature gradient has a stronger influence on the velocity of the inner drop at different eccentricities, which in turn alters the relative velocity between the drops. As a result, it is possible to achieve equilibrium configurations, where both the drops move with the same velocity. Two such equilibrium configurations exist for temperature gradients beyond a critical limit, one of which is stable. It is revealed that the imposed temperature gradient always increases the deformation as compared to an isothermal flow. Depending on the position of the inner core with respect to the outer drop center and the direction of the applied temperature gradient, the shape of the inner drop may change from prolate to oblate (or vice versa), as it travels within the outer drop. The deformation in the inner drop increases with eccentricity, while the outer drop sees very little deformation even for relatively large capillary numbers.

中文翻译：

---

热毛细管效应对泊肃叶流中偏心复合液滴的影响

这里分析了在存在外部温度梯度的情况下悬浮在泊肃叶流中的中性浮力、偏心复合液滴的动力学。假设能量和动量传输以扩散为主，我们推导出温度和速度场的近似解析解，然后在双球坐标中使用渐近分析推导出变形。我们确定，根据方向，施加的温度梯度的存在可能会加速或减缓下降。温度梯度对不同偏心率下内部液滴的速度有更大的影响，这反过来又会改变液滴之间的相对速度。因此，可以实现平衡配置，其中两个液滴以相同的速度移动。对于超过临界极限的温度梯度，存在两种这样的平衡配置，其中一种是稳定的。结果表明，与等温流动相比，施加的温度梯度总是会增加变形。根据内核相对于外滴中心的位置和施加的温度梯度的方向，内滴的形状可能从扁长变为扁圆（或反之亦然），因为它在外滴内行进。内部液滴的变形随着偏心而增加，而外部液滴即使对于相对较大的毛细管数也几乎没有变形。结果表明，与等温流相比，施加的温度梯度总是会增加变形。根据内核相对于外滴中心的位置和施加的温度梯度的方向，内滴的形状可能从扁长变为扁圆（或反之亦然），因为它在外滴内行进。内部液滴的变形随着偏心而增加，而外部液滴即使对于相对较大的毛细管数也几乎没有变形。结果表明，与等温流动相比，施加的温度梯度总是会增加变形。根据内核相对于外滴中心的位置和施加的温度梯度的方向，内滴的形状可能从扁长变为扁圆（或反之亦然），因为它在外滴内行进。内部液滴的变形随着偏心而增加，而外部液滴即使对于相对较大的毛细管数也几乎没有变形。