Modelling capillary break-up of particulate suspensions

We have constructed a simple one-dimensional model of capillary break-up to demonstrate the thinning behaviour of particulate suspensions previously observed in experiments. The presence of particles increases the bulk viscosity of a fluid and so is expected to retard thinning and consequently delay the time to break-up. However, experimental measurements suggest that once the filament thins to approximately five particle diameters, the thinning no longer follows the behaviour predicted by the bulk viscosity; instead thinning is “accelerated” due to the effects of finite particle size. Our model shows that accelerated thinning arises from variations in local particle density. As the filament thins, fluctuations in the local volume fraction are amplified, leading ultimately to particle-free sections in the filament. The local viscosity of the fluid is determined from the local particle density, which is found by tracking individual particles within the suspension. In regions of low particle density, the fluid is less viscous and can therefore thin more easily. Thus, we are able to model the accelerated thinning regime found in experiments. Furthermore, we observe a final thinning regime in which the thinning is no longer affected by particle dynamics but follows the behaviour of the solvent.