We theoretically analyzed the movement of a droplet in a narrow gap driven by a surface energy difference. Specifically, we derived the moving speed of a droplet in a narrow gap using the following two methods: (1) A method in which the moving speed is derived by substituting the pressure gradient inside the droplet caused by the Laplace pressure into the Poiseuille flow equation and (2) A method in which the moving speed is derived from the equation for the balance of the driving forces caused by the viscous friction force of the wall surfaces and the change in surface energy. The moving speed of the droplet derived using these two methods should essentially be the same, but the equations obtained were different. However, we found that the contradiction could be resolved by taking into account the moving resistance of the triple line in the latter method. We also determined the conditions under which a droplet will stop or flow back due to a pressure difference outside the droplet.
OGASAWARA et al. (Wed,) studied this question.