Flow-induced coalescence of two deformable drops

In the present study, the flow-induced coalescence of two deformable drops was investigated experimentally and numerically. In contrast to the conventional blending studies, we experimentally studied the flow-induced coalescence process at the level of individual drops, using a four-roll mill. The goal of the experimental studies is to understand how the coalescence process is affected by the presence of a copolymer at the drop interface. The critical conditions for coalescence were examined for polybutadiene (PBd) drops suspended in polydimethysiloxane (PDMS) by systematically changing the hydrodynamic parameters and copolymer concentration. The experimental results were qualitatively consistent with the analysis based on the Marangoni effect. A small amount of copolymer (PBd-PDMS) at the interface was sufficient to greatly suppress coalescence, and a critical or minimum copolymer interfacial coverage (Gammamin) exists, above which the copolymer effect becomes independent of the coverage and the viscosity ratio. The required minimum concentration was quantified, and the mechanism by which the compatibilizer influences the coalescence was discussed. We also developed the numerical simulations for the interaction between two deformable drops with clean interfaces in an axisymmetric flow, using a boundary-integral method. An adaptive mesh refinement method was used to resolve the local small-scale dynamics in the gap and to retain a reasonable speed of computation. The thin film dynamics was successfully studied with sufficient stability and accuracy, up to a film thickness of O(10-4) times undeformed drop radius, over broad parameter ranges. The results were compared with the experimental data and provided good insight into the flow-induced coalescence process. The simulation, using a Hamaker constant with a fixed value calculated via Lifshitz theory, qualitatively predicts the experimental results for the collisions for time-independent flow (termed "head-on" collisions in the experimental studies). For the collisions in a time-dependent flow, which approximate coalescence in "glancing collisions", the simulations predicted many aspects of the experimental results. The results, however, were only quantitatively accurate, in comparison with the experimental data, for the lowest viscosity ratio of 0.19. We discussed some of the limitations of the current numerical study in interpreting the real coalescence problem.