ABSTRACT:
Brownian motion plays a crucial role in colloidal suspension mechanics. It affects rheological properties, influences the self-assembly of aggregates, and regulates particle transport. While quantifying and predicting its effects are of modern technological importance, fast and scalable computational methods that accurately characterise Brownian motion remain outstanding. I will discuss recent work towards this goal for the force-coupling method (FCM), a regularized multipole technique for simulating suspensions at large-scale. Our approach hinges on avoiding the direct computation of random particle velocities by forcing the surrounding fluid with a white-noise stress and using the FCM framework to obtain the motion of the particle phase. We show that the resulting method yields the correct particle velocity correlations, even when higher-order terms, such as the particle stresslets, are included in the multipole expansion. I will present results from several simulations demonstrating the effectiveness of fluctuating FCM, showing also how Brownian drift can be captured by employing the appropriate time integration scheme and conjugate gradient method. I will also discuss extensions of fluctuating FCM to dense suspensions and how similar ideas might be used in conjunction with other methods.