Hydrodynamic simulations of colloidal gels: Microstructure, dynamics, and rheology

The microstructure, dynamics, and rheology of colloidal suspensions with short-range depletion attraction and long-range electrostatic repulsion are studied using equilibrium predictions and a new algorithm for dynamic simulations. A focus is made on those combinations of attraction and repulsion that lead to the formation of gels. The effects of varying the strength of attraction epsilon A (0-50kT), range of attraction deltaA (0.05-0.18a), strength of repulsion epsilon R (0-54kT), and volume fraction &phis; (0.1-0.4) are investigated, where k is Boltzmann's constant, T is temperature, and a is the colloid radius. Hard-sphere thermodynamic perturbation theory is employed to predict equilibrium behavior. For &phis; ≤ 0.4, fluid phases are predicted at low epsilonA, while fluid-crystal coexistence is predicted above a certain value of epsilon A which decreases with increasing deltaA or &phis;, but increases with increasing epsilonR. A new algorithm called Fast Lubrication Dynamics (FLD) is developed as part of this work. This algorithm enables simulations including the effects of many-body hydrodynamic interactions, Brownian motion, and interparticle interactions at a speed more than 100 times faster than Stokesian Dynamics (SD) while retaining much of the relevant physics of SD. In addition, FLD is found to be nearly as fast as Brownian Dynamics (BD) due to the larger time steps allowed by FLD.;FLD simulations are performed to study the microstructural evolution of suspensions from a dispersed phase to other phases including fluids and gels. With increasing epsilonA, suspensions with short-range attraction undergo a transition from highly diffusive fluid phases to dynamically arrested gels in which particles are localized on length scales comparable to delta A. This transition first occurs by homogeneous nucleation and growth of crystalline structures which merge to form a space-spanning polycrystalline structure that coexists with a dilute fluid phase. With increasing epsilon A, the rate of nucleation increases, resulting in increasing polycrystallinity and smaller crystalline regions. For high epsilonA, a dilute fluid phase does not coexist and no crystalline structures are formed. The introduction of long-range repulsion inhibits crystallization and promotes one-dimensional cluster growth resulting in thinner structures which display greater positional fluctuations such that particles in gels are localized on length scales up to 7 times deltaA. In the presence of repulsion, for low epsilon A, small transient clusters are formed, while for high epsilon A, gels are formed by space-spanning clusters, but the time scale for gelation to occur increases exponentially with epsilonR. Comparisons with results of confocal microscopy experiments show significant differences which may be attributed to differences in initial conditions, inaccurately represented electrostatic interactions, and limitations of the simulated system size. Few changes are observed with different values of deltaA. With increasing &phis;, the average local structure around each particle in the gel changes very little while the gels becomes more dense, hindering collective motion and decreasing the length scales on which particles are localized.;BD simulations are also performed, and the results are compared with those of the FLD simulations. Remarkable agreement is observed for both the microstructure and dynamics, suggesting that the structural evolution and dynamics of colloidal suspensions with short-range attraction and long-range repulsion under quiescent conditions may not be very sensitive to the effects of hydrodynamic interactions.;FLD simulations are performed to study the rheological response of colloidal gels with a focus on the linear viscoelastic response. In addition to using ensemble averaging, we develop a new technique to improve the signal-to-noise ratio inherent in the stress of Brownian systems. By careful application of this technique, the average of two simulations sheared in opposite directions can yield a greater reduction in noise than does averaging over 10 times as many individual realizations. Steady shear and relaxation tests are performed, and the relaxation modulus G(t) is obtained from the stress response. The elastic modulus G'( w) and the viscous modulus G"(o)) are then obtained by Fourier transform of G(t). During steady shear, the stress increases with time and reaches a maximum as the gel strain softens and yields, after which the stress decreases and tends toward a steady-state value. (Abstract shortened by UMI.)...