Inline motion and hydrodynamic interaction of 2D particles in a viscoplastic fluid

In Stokes flow of a particle settling within a bath of viscoplastic fluid, a critical resistive force must be overcome in order for the particle to move. This leads to a critical ratio of the buoyancy stress to the yield stress: the critical yield number. This translates geometrically to an envelope around the particle in the limit of zero flow that contains both the particle and encapsulated unyielded fluid. Such unyielded envelopes and critical yield numbers are becoming well understood in our previous studies for single (2D) particles as well as the means of calculating. Here we address the case of having multiple particles, which introduces interesting new phenomena. First, plug regions can appear between the particles and connect them together, depending on the proximity and yield number. This can change the yielding behaviour since the combination forms a larger (and heavier) “particle.” Moreover, small particles (that cannot move alone) can be pulled/pushed by larger particles or assembly of particles. Increasing the number of particles leads to interesting chain dynamics, including breaking and reforming.