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We develop efficient numerical methods for performing many-body Browniandynamics simulations of a recently-observed fingering instability in an activesuspension of colloidal rollers sedimented above a wall [M. Driscoll, B.Delmotte, M. Youssef, S. Sacanna, A. Donev and P. Chaikin, Nature Physics,2016, doi:10.1038/nphys3970]. We present a stochastic Adams-Bashforthintegrator for the equations of Brownian dynamics, which has the same cost asbut is more accurate than the widely-used Euler-Maruyama scheme, and uses arandom finite difference to capture the stochastic drift proportional to thedivergence of the configuration-dependent mobility matrix. We generate theBrownian increments using a Krylov method, and show that for particles confinedto remain in the vicinity of a no-slip wall by gravity or active flows thenumber of iterations is independent of the number of particles. Our numericalexperiments with active rollers show that the thermal fluctuations set thecharacteristic height of the colloids above the wall, both in the initialcondition and the subsequent evolution dominated by active flows. Thecharacteristic height in turn controls the timescale and wavelength for thedevelopment of the fingering instability.

Brownian Dynamics of Confined Suspensions of Active Microrollers