Direct numerical simulations of viscous suspensions with variably shaped crystals

Abstract

Our ability to numerically model and understand the complex flow behavior of solid-bearing suspensions has increased significantly over the last couple of years, partly due to direct numerical simulations that compute flow around individual immersed particles. Direct numerical simulations hence resolve suspension dynamics in unprecedented detail. While most previous studies focus on spherical particles, we develop a direct numerical approach to also capture rectangular particles. Our approach uses distributed Lagrange multipliers to enforce rigid-body motion in the solid domain in combination with an immersed boundary method to correctly enforce the no-slip constraint on the solid-fluid interfaces. An important component of our model is an efficient particle collision scheme that prevents overlap between particles of different shapes and allows for the transfer of both translational and angular momentum during particle collision. We verify and validate our numerical method through several benchmark cases. Applied to particulate suspensions, we test the hypothesize that particle rotations alter the aggregated dynamics of the suspension even if the relative rotational energy of the particles remains small as compared to the translational energy. At low solid fraction, we reproduce experimental observations of strongly nonlinear coupling between rectangular particles that is reminiscent of particle aggregation in the inertial regime but occurs at zero Reynolds number as a result of the long-range interaction between non-spherical particles. At intermediate solid fraction, we show that particle rotations can destabilize force chains. The dynamic consequences include the delayed onset of jamming and strong nonlinear coupling to the flow field in the fluid domain, which channelizes more strongly for rectangular as compared to spherical particles. Our model was motivated specifically by the need to better understand hazardous, crystal-bearing lava flows, but our insights generalize to viscous suspension flow in other scientific or engineering contexts.