The process of attachment of organic droplets and cells at a liquid-liquid interface is studied in the system of a dropping mercury electrode in an aqueous cell suspension. Attachment frequency of droplets and cells is experimentally monitored, and a model for the dynamics of arrival and attachment of particles at the expanding mercury interface is proposed. The model accounts for the van der Waals and hydrophobic forces between the mercury and oil droplets and cells while the electrostatic force is negligible due to the high salt concentration. The important role of the Marangoni convection is emphasized as an active flow pushing the particles to attach on the mercury surface.