Copolymers and stirring are commonly used to produce fine dispersions of immiscible homopolymers. Recent experiments call into question the classical view that copolymers promote the mixing by reducing the interfacial tension, suggesting rather that copolymers induce repulsive interactions between droplets and thus inhibit collision-induced coalescence events. We present a dynamical theory of the breakup and coalescence of polymer droplets in a mixing shear flow, including hydrodynamic and repulsive interactions between droplets. We find that a low surface coverage of copolymers, of the order of one chain per square radius of gyration, is sufficient to inhibit collisions between submicron-sized droplets, while giving a negligible reduction in interfacial tension.

No abstract

We present three-dimensional numerical simulations of the classical Taylor experiment on droplet deformation within a shear flow. We have used the promising Lattice-Boltzmann method numerical scheme to simulate single droplet deformation and breakup under simple shear flow. We first compute the deformation of the droplet and find excellent agreement with the theoretical prediction. We have used the same method to simulate the shear and breakup for larger values of the shear rate. We find that the Lattice Boltzmann method used in conjunction with the interface force model of Shan and Chen results in an excellent treatment of the entire process from small deformation to breakup into multiple droplets.Our results could be extended to study the rheology of dispersed droplets and the dynamics of droplet breakup and coalescence in shear flow.

We present a finite-volume formulation for the lattice Boltzmann method (FVLBM) based on standard bilinear quadrilateral elements in two dimensions. The accuracy of this scheme is demonstrated by comparing the velocity field with the analytical solution of the Navier-Stokes equations for time dependent rotating Couette flow and Taylor vortex flow. To demonstrate the flexibility of the scheme, we have also simulated a modified rotating Couette flow, where the inner cylinder has an elliptical shape. The results agree with those obtained from the traditional marker-and-cell method. The FVLBM scheme is applicable to arbitrarily shaped two-dimensional regions, and thus the range of applicability of the lattice Boltzmann method has been significantly extended.

No abstract