Incorporating Shear into Stochastic Eulerian Lagrangian Methods for Rheological Studies of Complex Fluids and Soft Materials

We introduce computational methods based on fluctuating hydrodynamics for investigations of the rheological responses of complex fluids and soft materials. Our approach allows for different types of shear to be imposed on the unit periodic cell and is shown to take into account consistently the microstructure elastic mechanics, fluid-structure hydrodynamic coupling, and thermal fluctuations. New discretizations and stochastic field generation methods are developed to handle in a computationally efficient manner the generalized periodic boundary conditions that impose the shear. To show in practice how the new methods can be used for the investigation of diverse rheological responses, we present several illustrative applications. These include 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 a gel-like material.