  Coalescence of micrometer-scale droplets is impacted by several parameters,
including droplet size, viscosities of the two phases, droplet velocity and
angle of approach, as well as interfacial tension and surfactant coverage. The
dynamics and thinning of films between coalescing droplets can be particularly
complex in the presence of surfactants, due to the generation of Marangoni
stresses and reduced film mobility. In this work, a microfluidic hydrodynamic
Stokes trap is used to gently steer and trap surfactant-laden micrometer-sized
droplets at the center of a cross-slot. Incoming droplets are made to coalesce
with the trapped droplet, yielding measurements of the film drainage time.
Water droplets are formed upstream using a microfluidic T-junction, in heavy
and light mineral oils and stabilized using SPAN 80, an oil-soluble surfactant.
Film drainage times are measured as a function of continuous phase viscosity,
incoming droplet speed, trapped droplet size, and surfactant concentrations
above and below the critical micelle concentration (CMC). As expected, systems
with higher surfactant concentrations, higher continuous phase viscosity, and
slower droplet speed exhibit longer film drainage times. Perhaps more
surprisingly, larger droplets and high confinement also result in longer film
drainage times. The results are used here to determine critical conditions for
coalescence, including both an upper and a lower critical Capillary number.
Moreover, it is shown that induced surfactant concentration gradient effects
enable coalescence events after the droplets had originally flocculated, at
surfactant concentrations above the CMC. The microfluidic hydrodynamic trap
provides new insights into the role of surfactants in film drainage and opens
avenues for controlled coalescence studies at micrometer length scales and
millisecond time scales.
