# Mechanistic modeling of restructuring behavior of colloidal aggregates in shear flows

Colloidal aggregates appear after destabilizing a suspension. Due to the cohesive contact between particles, the characteristic open structure can be maintained. Stirring processes change the structure and the size of aggregates. The modeling and the quantitative estimation of this phenomena are important for the control of many industrial processes. The hydrodynamic stress acting on colloidal aggregates in a shear flow is relatively small. This is why the range of the investigation is limited to very large aggregates in experiments. However, for weakly bonded aggregates, the hydrodynamic stress may cause smaller aggregates due to breakage or restructuring. We aim to provide some quantitative evaluation for the restructuring behavior of small aggregates under shear flow.

The first task in this project concerns the hydrodynamic interaction. For a colloidal-particle system, the Reynolds number is remarkably small so that the relaxation or response time of the fluid is considered very short. In this regime, called Stokes regime, the effect of viscosity is more dominant than the inertia of fluid. If a spherical particle is isolated, the drag force is well known as Stokes' law. However, this formula cannot be applied to a many-particle system due to the disturbance of the fluid by particles. This is one of the long-term topics for scientists in fluid dynamics since the beginning of 20th century. Our project will handle this part with the finite element method (FEM, in collaboration with a research group at RWTH Aachen) and Stokesian dynamics, or some other approximation that is more realistic than the free-draining approximation. The drag forces for each particle in an aggregate is visualized in Figure 1 (left: Finite element method, Right: Stokesian dynamics).

Further, the modeling of the cohesive contact between colloidal particles needs to be considered. The interaction between colloidal particles provide a huge literature database, yet in most studies, only interaction between separating particles were investigated, as the stabilisation of colloidal suspensions is crucial to understand in this regard. The concept of double layer potential was remarkable progress to estimate the stability behavior of a suspension. On the other hand, there is not much theoretical and experimental work in the estimation of the cohesive contact, which causes the open structure of colloidal aggregates under thermal agitation or hydrodynamic stresses. Some estimation of particle pull off force comes from the JKR and DMT model, assuming elastic deformation at the contact point. However, the resistance forces for tangential and rolling displacement are required to explain the stability of the observed aggregate structure. Some direct observations of bending resistance have recently been reported by several experimentalist. We have investigated the modeling for the contact bonding between colloidal particles.

### Publications

[1] V. Becker and H. Briesen. Tangential-force model for interactions between bonded colloidal particles. Phys. Rev. E, 78:061404, 2008.

[2] V. Becker and H. Briesen. A master curve for the onset of shear induced restructuring of fractal colloidal aggregates. J. Colloid Interface Sci., 346:32–36, 2010.

[3] V. Becker, E. Schlauch, M. Behr, and H. Briesen. Restructuring of colloidal aggregates in shear flows and limitations of the free-draining approximation. J. Colloid Interface Sci., 339:362, 2009.

For more information please contact: | Research funded by: |

M Sc. Vincent Bürger | SPP 1273 Kolloidverfahrenstechnik |