Dislocation of suspensions: a model for the accelerated pinch-off of suspension drops*

Controlling the detachment of a drop from a nozzle is crucial for many printing and additive manufacturing applications. The dynamics of non-Brownian suspensions can often be modeled as a homogeneous Newtonian liquid, whose macroscopic viscosity is increased by the particles. However, this continuous behavior only holds as long as the liquid neck, which binds the drop to the nozzle, is much wider than the particle size. Close to the pinch-off, the discrete nature of the particles comes into play.. Previous studies have shown that the pinch-off is thus accelerated, and is actually faster than that of a homogeneous liquid of equivalent viscosity. However, the mechanism behind this accelerated pinch-off remains unclear. We propose to describe it as the dislocation of the suspension, during which minimizing viscous dissipation causes particles to spread rather than to slide or to spin. Therefore, we consider an extensional flow of the particles rather than a shear flow. This approach leads to scaling laws describing the onset and the end of the dislocation, as well as the thinning dynamics, all of which match our experimental results. Our model also holds when considering polydisperse suspensions, provided that the viscosity and the average particle size of the suspension are known.