Attachment of a particle to a pendant drop was experimentally investigated by Feng et al. [Phys. Fluids 34, 032120 (2022)]. The attachment force on the particle, consisting of the surface tension force and the pressure force, can overcome the gravity force. The attachment in equilibrium is possibly hard to maintain in practice due to instabilities. This paper aims to discover the condition for the particle to be successfully attached under the liquid drop (bridge) through analyzing the stabilities of the capillary system. With disturbances potentially existing for both the liquid bridge and the particle, the two corresponding types of stabilities are studied. Considering the cases with liquid surfaces checked to be stable, we find four regimes for the attachment of the particle: the regimes of stable attachment, possibly stable attachment, overloaded attachment, and nonphysical attachment. Only the first two regimes mean feasible attachments in practice. Our prediction of feasible attachments agrees well with Feng et al., indicating the validity of our stability theory. Whether for fixed-density particles of different sizes or fixed-size particles of different densities, the attachment capability for the liquid bridge first decreases, then increases, and decreases again as the volume of the liquid bridge increases. This can guide practice for lifting particles of higher weight with the pendant drop.

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• Fluid-particle interactions
• Interfacial flows
• Liquid bridges
• Surface & interfacial phenomena