Micro-hydrodynamics of non-spherical colloids: a Brownian dynamics study

The topic of my PhD project, under the supervision of Dr. Wouter den Otter and Prof. Stefan Luding, is the simulation of sticky spherical colloidal particles under shear. To simulate the dynamics of an individual aggregate of these particles, in Stokesian flow and subject to Brownian motion, we treat the cluster as a rigid collection of spheres. The hydrodynamic interactions between all particles are then combined into a single (11x11) constant body-based mobility matrix, allowing for a very efficient simulation of the cluster's dynamics including coupling between translation and orientation [this work was published in J. Chem. Phys. 148, 194112 (2018); the code for computing the mobility matrix is available at https://www2.msm.ctw.utwente.nl/Oseen11/]. The method also works for clusters in a shear flow. With the thermal noise turned off, we recover Jeffery orbits for clusters shaped as ellipsoids or hemi-spherical caps, allowing verification of the code against analytical solutions. With the thermal noise tuned on, we can calculate the viscosity of a dilute solution. Our simulations of ellipsoidal particles, over a wide range of aspect ratios and Peclet numbers (relative strength of shear versus rotation diffusion), largely confirm the theoretical predictions of Leal and Hinch (J. Fluid. Mech. 52, 683 (1972)] for the limits of high and low Peclet numbers.

Having established the dynamics of an individual aggregate, we use this to simulate the diffusion-limited aggregation of sticky clusters. This allows us the study the aggregation rate and the fractal dimensions of the aggregates for clustering in quiescent fluids, and to compare them with aggregation in sheared suspensions. The experimental system we are aiming for in the long run is the aggregation of carbon black particles in semi-solid flow batteries, a promising new type of battery to stabilize the electricity grid which increasingly depends on renewable energy sources, like wind and solar, that produce intermittently. The PhD project is sponsored by the “Computational Sciences for Energy Research” program of the Netherlands Organisation for Scientific Research (NWO), and co-financed by Shell Global Solutions International B.V.