Physics Department, Carnegie Mellon University, Pittsburgh, PA 15213, USA; Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA.
Aix-Marseille Université, CNRS, CINaM UMR 7325, 13288 Marseille, France.
J Colloid Interface Sci. 2016 Jan 15;462:88-99. doi: 10.1016/j.jcis.2015.09.043. Epub 2015 Sep 21.
The equilibrium configuration of compound sessile drops has been calculated previously in the absence of gravity. Using the Laplace equations, we establish seven dimensionless parameters describing the axisymmetric configuration in the presence of gravity. The equilibrium axisymmetric configuration can be either stable or unstable depending on the fluid properties. A stability criterion is established by calculating forces on a perturbed Laplacian shape. In the zero Bond number limit, the stability criterion depends on the density ratio, two ratios of interfacial tensions, the volume ratio of the two drops, and the contact angle. We use Surface Evolver to examine the stability of compound sessile drops at small and large Bond numbers and compare with the zero Bond number approximation. Experimentally, we realize a stable axisymmetric compound sessile drop in air, where the buoyancy force exerted by the air is negligible. Finally, using a pair of fluids in which the density ratio can be tuned nearly independently of the interfacial tensions, the stability transition is verified for the axisymmetric configuration. Even though the perturbations are different for the theory, simulations and experiments, both simulations and experiments agree closely with the zero Bond number approximation, exhibiting a small discrepancy at large Bond number.
先前已经在无重力条件下计算了复合固着液滴的平衡构型。我们利用拉普拉斯方程，建立了七个描述存在重力时轴对称构型的无因次参数。平衡轴对称构型可能是稳定的，也可能是不稳定的，这取决于流体的性质。通过计算微扰拉普拉斯形状上的力，建立了一个稳定性判据。在零邦德数极限下，稳定性判据取决于密度比、两个界面张力比、两个液滴的体积比和接触角。我们使用表面进化器来研究小和大邦德数下复合固着液滴的稳定性，并与零邦德数近似进行比较。实验上，我们在空气中实现了稳定的轴对称复合固着液滴，其中空气产生的浮力可以忽略不计。最后，使用一对密度比可以几乎独立于界面张力进行调节的流体，验证了轴对称构型的稳定性转变。尽管理论、模拟和实验中的微扰不同，但模拟和实验都与零邦德数近似值非常吻合，在大邦德数下存在微小差异。
