Clogging of particle suspensions in networks

In many biological, biomedical and industrial systems, particles are transported via fluids through confined networks, in which clogging can disrupt function. However, we lack a predictive theoretical framework that couples particle transport, suspension rheology and network flow resistance. Here, we develop a model and solution algorithm for particle suspension flow in networks based on vessel-level continuum modelling and particle distribution at nodes connecting vessels. We apply the model to study transport of dense particle suspensions in minimal and physiological biological networks. A key feature of our model is the coupling between particle volume fraction and particle flux: in line with the physics of dense suspensions, each network branch, or vessel, possesses a local carrying capacity for particle transport at an intermediate particle fraction between zero and the maximum packing fraction. If this flux capacity is reached, the vessel becomes flux-limited and particles can accumulate in upstream branches, causing them to enter a high-particle-fraction, high-resistance state that we refer to as 'clogged'. We show that these vessel flux limitations lead to network-level redistribution of particles, which can cause widespread clogging and emergent network-scale heterogeneity. By varying network topology, we find that in some regimes increasing network connectivity does not improve transport: paradoxically, additional pathways can promote clogging and reduce network-level particle flux, analogous to classic results in traffic flow networks. Our results provide a minimal mechanistic framework that links suspension physics, network topology, and transport failure in complex flow networks.