Flow-induced coalescence of a pair of polymeric drops was studied at the level of individual drops, using a four-roll mill, to understand how the process is affected by the presence of a copolymer at the drop interface. The experimental system consisted of polybutadiene (PBd) drops suspended in polydimethylsiloxane (PDMS). Copolymers were produced at the drop interface by a reaction between functionalized homopolymers (PBd-COOH and PDMS-NH2). The experiments were carried out over wider ranges of parameters than our earlier studies of
Hu et al. [Phys. Fluids 12, 484 (2000)]
Ha et al. [Phys. Fluids 15, 849 (2003)]
, in an attempt to understand the puzzling results found in our earlier studies. The experimental results were consistent with a qualitative mechanism of immobilization of the boundaries of the thin film between drops due to a flow-induced Marangoni effect. A critical or minimum copolymer interfacial coverage (Γmin) exists, above which the copolymer effect becomes independent of the coverage or the viscosity ratio. Using self-consistent mean field theory, the Γmin was found to be approximately 0.08 chain/nm2 corresponding to Δσe ≅ 0.45 mN/m, which is around 30% of the saturation concentration, Γ∞ ≅ 0.25 chain/nm2. However, a whole new set of phenomena was discovered when the copolymer coverage is smaller (Γe<Γmin). In this case, we found that there was a strong surfactant effect at small Ca values, but that there was a transition capillary number (Cat) above which the Marangoni effect apparently becomes negligible. In this case, two critical capillary numbers for coalescence (Cac,high and Cac,low) exist, and there are two ranges of Ca and offset where coalescence is possible. The first is for Ca<Cac,low and small offsets. The second is for Cat<Ca<Cac,high, where Cac,high has almost the same values as the critical capillary number for a clean interface system. Between Cac,low and Cat, coalescence is not possible. For the copolymer systems, coalescence at Cac occurred at the angle just prior to the apparent separation of the drops in the extensional quadrant. The nonmonotonic change in Cac with copolymer concentration, found in our earlier study, is due to the fact that the separation angle increases with increased concentration, as can be seen by examination of the collision trajectory data. A copolymer with a smaller molecular weight was also used to probe the potential significance of non-hydrodynamic effects related to the molecular weight. We observed the same saturated limit for the copolymer effect (when Γe ≥ Γmin) as in the case of the higher molecular weight copolymer system. We conclude that the Marangoni effect is the main mechanism for the suppression of coalescence in the current polymer/copolymer system.