Efforts to stabilize emulsions against coalescence in flow have often focused on modifying properties of the interface between the continuous and dispersed phases, to create a repulsive barrier against coalescence. But prior to experiencing any interaction force, the liquid film between two colliding drops has to drain, and if this drainage process is arrested, coalescence will be suppressed. In this work, scaling analyses and thin-film lubrication simulations are used to study the hydrodynamic drainage properties of thin films of a Bingham fluid (a yield stress fluid, which flows only when a critical stress is exceeded) created between two drops colliding under the action of a constant force. Our study shows that the hydrodynamic drainage process can be arrested completely when the film reaches a critical thickness, before attractive forces result in the rupture of the film, provided that the film shape is in the dimpled configuration. This critical thickness is h(f) = 6 tau R-2(0)3/gamma(2), where tau(0) is the yield stress of the suspending medium, R is the drop radius and gamma is the interfacial tension between the fluids. The yield stress can thus serve as an independent tuning parameter that sets an upper bound on the drop size beyond which coalescence is turned off in sheared emulsions. (C) 2016 Elsevier Inc. All rights reserved.