Department of Mechanical and Aerospace Engineering, University of California-San Diego, La Jolla, California 92093-0411, USA.
Langmuir. 2011 Sep 6;27(17):10705-13. doi: 10.1021/la202077w. Epub 2011 Aug 15.
The extent of a droplet's spreading over a flat, smooth solid substrate and its equilibrium height in the presence of gravity are determined approximately, without a numerical solution of the governing nonlinear differential equation, by assuming that the droplet takes on the shape of an oblate spheroidal cap and by minimizing the corresponding free energy. The comparison with the full numerical evaluations confirms that the introduced approximation and the obtained results are accurate for contact angles below about 120° and for droplet sizes on the order of the capillary length of the liquid. The flattening effect of gravity is to increase the contact radius and decrease the height of the droplet, with these being more pronounced for higher values of the Bond number.
液滴在平坦、光滑的固体基底上的扩展程度及其在重力存在下的平衡高度，可以通过假设液滴呈扁球形帽的形状并最小化相应的自由能来近似确定，而无需对控制非线性微分方程进行数值求解。与完全数值评估的比较证实，对于接触角低于约 120°和液滴尺寸大约为液体的毛细长度的情况下，所引入的近似和得到的结果是准确的。重力的压扁效应会增加接触半径并降低液滴的高度，对于较大的邦数，这种效应更为明显。
