Experimental investigation of the effects of copolymer surfactants on flow-induced coalescence of drops

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)] and 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 0.08chain∕nm2 corresponding to Δσe≅0.45mN∕m, which is around 30% of the saturation concentration, Γ∞≅0.25chain∕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