Floating Solids: Combining Phase Field and Fluid-Structure Interactions

A mixed-stress formulation presented here combines the methodologies of phase field and fluid-structure interactions in order to simulate phase transformations involving moving and rotating solid bodies interacting with fluids. The Navier-Stokes equations are solved everywhere, with an additional strain tensor field overlaid on the solid, such that elastic stress can be incorporated into the equation of motion. An additional term in the equation for strain evolution provides rotation due to local vorticity. The results exhibit a small amount of artificial erosion of the solid due to nonzero normal velocity within the diffuse interface at separation points; this is discussed here as a phenomenon common to all diffuse interface formulations incorporating convection. Two-dimensional simulations presented here demonstrate oscillations due to feedback between surface tension and elastic stress, and rigid body motion with particle collision and agglomeration which involves a change in the topology of the fluid-solid interface. The formulation and simulations presented here use isotropic Cahn-Hilliard free energy, and extension of the formulation to three-dimensional and anisotropic systems is straightforward. Likewise, these simulations describe linear elastic solids with Poisson ratio of 1 (equivalent to ½ in three dimensions), and extension to more complex mechanical constitutive behavior is discussed. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)