Phase-Field Methods for Structure Evolution in Sheared Multiphase Systems
A homogeneous disordered phase separates into ordered structures when quenched into a broken-symmetry phase. The competition of broken-symmetry phases to select an equilibrium state may be studied in terms of coarse-grained order parameters described by a suitable Landau free-energy function. A network of equilibrium-phase domains develops on quenching and coarsens with time with a topology that may be controlled by shear. We use three-dimensional simulations, in which time-dependent models for conserved-order parameters coupled to Navier-Stokes fluid models are solved, to investigate the evolution of such domains, e.g. spinodal decompositions of polymeric materials under shear. The numerical problems are formidable because of the strong nonlinearities inherent in the coupled model, and these are amongst the first 3D calculations undertaken. In linear shear fields we find stable nanostrings, also recently seen in experiments. The affinity of the ordered phases to boundaries plays a role in the form of the structures that develop, with stacked plate-like phase distributions emerging under certain conditions. Such methods appear quite promising for design and analysis of multiphase and complex fluid formulations. The behavior of foams in such conditions is of particular interest in microgravity environments. Additional information can be found in the original extended abstract.