Dry-brush entropic attraction in block-copolymer stabilized drops significantly reduces the drainage time in flow-induced coalescence

Ref [1] measured the drainage time during flow-induced head-on coalescence experiments of two polymeric drops in an immiscible polymeric matrix, stabilized by block-copolymers (BCs), acting as insoluble surfactants in the creeping flow regime. In ref [1], this value was matched by boundary integral simulations. However, at high surfactant concentration, the attractive disjoining pressure had to be increased by 50, leading to a reduction of the numerical drainage time by 70%. Ref [1] speculated that this concentration-dependent attraction was due to the entropic attraction between the drop interfaces since the BCs were in a dry-brush (DB) regime. Here, we calculate the exact interaction energy between two hard wall interfaces with grafted polymer DBs, through self-consistent mean field theory and include it in the boundary integral code. An excellent agreement with the experiments is found. However, the hard wall repulsions hinder coalescence in the final stages of drainage, the thin film forms a wimple and later becomes flat. This result shows that the entropic attraction should be considered in numerical models, and new models should be developed for the soft nature of the interface and its stability.

[1] Yoon Y., Husu A., Leal L.G. Phys. Fluids 2007

[2] Vannozzi C. Phys Fluids 2012