A force balance is presented for a particle attached to the surface of a larger bubble that oscillates such as it would immediately after a coalescence event. Similar previous analyses have neglected the Basset history force, the added mass of the particles, and the drag force imparted by the fluid upon the particles. Methods of crudely estimating the upper-bound of the Basset history force and the drag are proposed, and it is shown that these, along with the d’Alembert force due to particle acceleration, govern the value of the compensating capillary force and therefore the position of the three-phase contact line. The weight, buoyancy, and hydrostatic force due to meniscus depression are insignificant. The position of the three-phase constant line demonstrates an approximately first order lag to a stimulus. Because of this, the true position of the three-phase contact line can be estimated, and this must require that the three-phase contact angle demonstrates oscillatory behavior. It is possible that this phase-lag may underpin the process of particle detachment.
Industrial & Engineering Chemistry Research Vol. 48, Issue 17, p. 8024-8029