Generalized Rotne–Prager–Yamakawa approximation for Brownian dynamics in shear flow in bounded, unbounded, and periodic domains

Cichocki, Bogdan and Szymczak, Piotr and Zuk, Pawel (2021) Generalized Rotne–Prager–Yamakawa approximation for Brownian dynamics in shear flow in bounded, unbounded, and periodic domains. Journal of Chemical Physics, 154 (12): 124905. ISSN 0021-9606

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Abstract

Inclusion of hydrodynamic interactions is essential for a quantitatively accurate Brownian dynamics simulation of colloidal suspensions or polymer solutions. We use the generalized Rotne–Prager–Yamakawa (GRPY) approximation, which takes into account all long-ranged terms in the hydrodynamic interactions, to derive the complete set of hydrodynamic matrices in different geometries: unbounded space, periodic boundary conditions of Lees–Edwards type, and vicinity of a free surface. The construction is carried out both for non-overlapping as well as for overlapping particles. We include the dipolar degrees of freedom, which allows one to use this formalism to simulate the dynamics of suspensions in a shear flow and to study the evolution of their rheological properties. Finally, we provide an open-source numerical package, which implements the GRPY algorithm in Lees–Edwards periodic boundary conditions.