Self-assembly of polymeric particles in Poiseuille flow: A hybrid Lattice Boltzmann / External Potential Dynamics simulation study

We present a hybrid simulation method which allows one to study the dynamical evolution of self-assembling (co)polymer solutions in the presence of hydrodynamic interactions. The method combines an established dynamic density functional theory for polymers that accounts for the nonlocal character of chain dynamics at the level of the Rouse model, the external potential dynamics (EPD) model, with an established Navier-Stokes solver, the Lattice Boltzmann (LB) method. We apply the method to study the self-assembly of nanoparticles and vesicles in two-dimensional copolymer solutions in a typical microchannel Poiseuille flow profile. The simulations start from fully mixed systems which are suddenly quenched below the spinodal line. In order to isolate effects caused by walls, we use a reverse Poiseuille flow geometry with periodic boundary conditions. We identify three stages of self assembly, i.e., initial spinodal decomposition, particle nucleation, and particle growth (ripening). We find that (i) In the presence of shear, the nucleation of droplets is delayed by an amount roughly proportional to the shear rate, (ii) Shear flow greatly increases the rates of particle fusions, (iii) in later stages of self-assembly, stronger shear flows may induce irreversible shape transformation {\em via} finger formation, in particular in vesicle systems. The combination of these effects lead to an accumulation of particles close to the center of the Poiseuille flow profile, and the polymeric matter has a double peak distribution centered around the flow maximum.