(380b) Modeling a Hydrodynamic Instability in Freely Settling Colloidal Gels

Attractive colloidal dispersions, suspensions of fine particles which aggregate and frequently form a space spanning elastic gel are ubiquitous materials used as thermal insulators, catalytic electrodes in fuel cells, and in many consumer care products and food stuffs. The colloidal networks in these materials can exist in a mode of free settling when the network weight exceeds its compressive yield stress. An equivalent state occurs when the network is held fixed in place and used as a filter through which the suspending fluid is pumped. In either scenario, hydrodynamic instabilities leading to loss of network integrity occur. Recent observations using ghost particle velocimetry [Secchi et al., Soft Matter, 2014] have shown that the loss of integrity is associated with the formation of eroded channels (so-called streamers) through which the fluid flows rapidly. In this talk, we use Brownian dynamics simulations of sedimenting and hydrodynamically interacting colloids in dilute colloidal gels to examine the initiation and propagation of this instability. In simulations, we measure the evolution of the network settling rate and identify a critical point in time beyond which the velocity grows rapidly. The rapid increase of the streamer volume in the network is shown to coincide with increasing settling rate. A simple phenomenological model is developed that describes dynamically the radial growth of a streamer due to erosion of the network by rapid fluid back flow. The model exhibits a finite-time blow-up - the onset of catastrophic failure in the gel - due to activated breaking of the inter-colloid bonds. The model relates blow-up time to the relevant dimensionless groups describing the network including: the ratio of buoyant forces to network strength, the particle volume fraction, and the strength of inter-particle bonds relative to the thermal forces acting on the particles. Simulations are used to test the model and show good agreement with the predicted dependence of the blow-up time on the physical properties of the network. The model dynamics are also shown to accurately replicate ghost particle velocimetry measurements of streamer growth. Finally, we summarize our findings in a stability-state diagram that provides insight into engineering strategies for avoiding settling instabilities in networks meant to have long shelf-lives.