Modeling complex particle suspensions: Perspectives on the rigid multiblob method

Many suspensions contain particles with complex shapes that are affected not only by hydrodynamics but also by thermal fluctuations, internal activity, kinematic constraints, and other long-range nonhydrodynamic interactions. Modeling these systems represents a significant numerical challenge due to the interplay between different effects and the need to accurately capture multiscale phenomena. In this article we review recent developments to model large suspensions of particles of arbitrary shapes and multiple couplings with controllable accuracy within the rigid multiblob framework. We discuss the governing equations, highlight key numerical developments, and illustrate applications ranging from microswimmers to complex colloidal suspensions. This review illustrates the effectiveness and versatility of the rigid multiblob method in tackling a wide range of physical problems in fluid mechanics, soft matter physics, biophysics, materials, and colloidal science.