Simulation of Complex Fluids and Soft Materials Using Stochastic Eulerian Lagrangian Methods with Shear Boundary Conditions

We introduce computational methods for rheological studies of soft materials and complex fluids. The approach allows for investigations of the roles played by the microstructure interactions and kinetics and by the dynamics of the fluid. The approach takes into account consistently the elastic mechanics of the microstructures, hydrodynamics, and thermal fluctuations. To study rheological responses to shear, generalized periodic boundary conditions are developed. These impose a specified rate of shear on the fluid and microstructures only at the boundaries of the unit cell. A number of challenges arise in practice. This includes discontinuities in the fluid equations at the boundary, complications in determining appropriate stochastic driving fields to account for thermal fluctuations, and the development of consistent discretizations for use in simulations. We present stochastic numerical methods which address each of these issues. To demonstrate how the methods can be used in practice, we present results for a few specific applications. This includes the study of shear thinning of a polymeric fluid, the study of complex moduli for the oscillatory responses of a polymerized lipid vesicle, and the study of aging of the shear viscosity of a gel-like material.