On the Computer Simulation of the Deformation and Breakup of Colloidal Aggregates in Shear Flow

Abstract

Computer simulations are used to investigate the deformation and breakup of colloidal aggregates in shear flow. It is argued that the aggregate radius depends on the shear rate via a power law S-m. The behavior of the aggregates strongly depends on the parameters of the particle interactions. In general the interaction potential of spherical particles is a superposition of central and noncentral components. The former depends only upon the distance between the centers of neighboring particles, while the latter can be described as a function of the angles between adjacent bonds. If the noncentral component is present, the aggregate is rigid (m = mrigid); i.e., its internal structure responds elastically to small deformations and can be characterized by the elastic moduli (e.g., Young modulus E) and yield strength, σa, depending upon the radius of gyration, R, and the internal volume fraction of particles, φint, via power laws, E ∼ σa ∝ R-γ ∝ φγ1int. The exponent m in this case can be identified with mrigid ≡ 1/γ. The exponent γ1 is identical to the exponent characterizing the power-law dependence of the moduli of a colloid gel network consisting of interconnected fractal clusters upon volume fraction. The exponents mrigid, γ and γ1 can be related to the exponents characterizing geometrical properties of the internal structure of the aggregate and its skeleton (such as fractal dimension df , chemical dimension d1, etc.). For one special type of aggregate (fractal trees without loops with df = 1.85-2.5, d1 = 1.1-1.8) we found mrigid = 0.23-0.29, γ1 = 3.4-7.0 in 3D. The values of γ1 are in good agreement with the experimental data recently obtained for colloid gels. If the forces of the particles' interactions are purely central, the aggregate is soft (m = msoft); i.e., its internal structure does not respond elastically to small deformations. In this case the simulations of the disaggregation process in shear flow were carried out in the free draining approximation. The initial aggregate is broken into two or more secondary aggregates. It is established that the mean radius of these aggregates also depends on S via a power law with msoft = 0.4-0.5. Comparing the results of our analyses with the experimental data we found that in general mrigid and msoft can be considered the lower and upper bounds of m.