The onset of heterogeneity in the pinch-off of suspension drops

At large scales, particulate suspensions flow like homogeneous viscous liquids, but at the particle scale, the role of the local heterogeneity brought by the particles cannot be neglected. The volume fraction also matters; in dense suspensions, particulate effects can be felt across distances much larger than the particle diameter. Therefore, whether a suspension should behave as a homogeneous or heterogeneous fluid is a matter of scale. Here, we consider the canonical situation of the pinch-off of suspension drops to study the behavior of suspensions at different scales. Initially, the filament of suspension thins down like a homogeneous liquid until reaching a critical thickness at which the thinning accelerates. Eventually, a region devoid of particles appears, and the breakup occurs similarly to a homogeneous viscous liquid. Although this problem have been studied for almost 20 y, the role of heterogeneity in the acceleration of the pinch-off is still not understood. We show that the onset of heterogeneity corresponds to the dislocation of the suspensions where local fluctuations in particle concentration increase. We derive scaling laws for the dynamics in the heterogeneous regime and develop a model to predict the coherence length at which the discrete nature of the particles appears, and we demonstrate that this length depends both on the particle size and on the volume fraction of the suspension. We extend this approach to polydisperse suspensions. Our work sheds light on the mesoscopic scale below which starts the heterogeneous regime and a continuum approach is not valid anymore.