57th Annual Report on Research 2012 Under Sponsorship of the ACS Petroleum Research Fund

Soft materials, such as gels and colloidal glasses, often exhibit different rheological properties at bulk and microscopic scales as a result of their complex microstructure. In this study, we have used multiple particle tracking microrheologies to explore how rheological properties vary with probe size in an aqueous dispersion of Laponite, a “model drilling fluid” and discotic colloidal clay that forms an aging colloidal gel under appropriate conditions. We have shown that the microrheological properties are dependent on the probe particle size, implying that the dispersion is heterogeneous across different length scales. Probing at smaller length scales results in the observation of lower viscoelastic moduli and a delay in gelation time. We have also proposed a microstructural explanation for these phenom- ena: as the material ages, a porous network structure develops that traps larger probe particles, while smaller probes generally have more time to diffuse relatively unhindered through pores and more weakly gelled regions. In support of this hypothesis, we observed that the probe dynamics develop significant spatial heterogeneity as the system ages. Analysis of these heterogeneities for different probe sizes indicates a microstructural length scale in the system that is similar to the length scales measured previously by light scattering . In light of these results, it would be interesting to further investigate the microstructural heterogeneities and their associated length scales with two-point microrheology. With this method, the viscoelastic moduli could be explored as a function of probe separation, although we reserve this study for future work. In addition to heterogeneities, we find that as the system ages the probe particles exhibit correlations between successive displacements, which has been reported to be evidence of microstructural confinement. However, by analyzing trajectories of a Brownian particle in a continuum Kelvin–Voigt material, we find that correlations between successive probe displacements are more directly related to the apparent local elasticity. We propose that a better measure of the microstruc- tual confinement is the length scale at which deviations from a simple linear scaling are observed in these successive correlations. An interesting problem for future work would be to determine the corresponding correlations for probes diffusing in a Newtonian fluid confined by solid walls, which provides a simple model of a porous microstructure. Finally, motivated by the observed probe-size dependence of rheological properties and the proposed microstructural description, we identify a concentration–probe-size super- position, obtaining approximate scalings for the observed gelation time as a function of probe size and Laponite® concentration.

The results form this part of the study will aid in the understanding of the structure and rheology of aqueous Laponite dispersions which are model systems to understand drilling fluids. Furthermore, the methods used here may also find broader general application to other structured complex fluids and gels. The methods are particularly suitable for analyzing materials that serve different functions at different length scales, and that as a result must have different rheological properties across length scales. Possible examples include the cell cytoskeleton, which provides structural stability on the length scale of the entire cell, but must also allow macromolecules and vesicles to diffuse within the pores. Finally, the results of this study show that multiple particle tracking can provide insight into the structure of evolving materials, even when the system is inhomogeneous at the probe length scale.

Next we studied the field-induced static and dynamic yield stresses for magnetorheological (MR) suspensions in an aging, yield stress matrix fluid composed of an aqueous dispersion of Laponite clay. Using a custom-built magnetorheometry fixture, the MR response is studied for magnetic field strengths up to 1 T and magnetic particle concentrations up to 30 v%. The yield stress of the matrix fluid, which serves to inhibit sedimentation of dispersed carbonyl iron magnetic microparticles, is found to have a negligible effect on the field-induced static yield stress for sufficient applied fields, and good agreement is observed between field-induced static and dynamic yield stresses for all but the lowest field strengths and particle concentrations. These results, which generally imply a dominance of inter- particle dipolar interactions over the matrix fluid yield stress, are analyzed by considering a dimensionless magnetic yield parameter that quantifies the balance of stresses on particles. By characterizing the applied magnetic field in terms of the average particle magnetization, a rheological master curve is generated for the field-induced static yield stress that indicates a concentration–magnetization superposition. The results provide guidance to formulators of MR fluids and designers of MR devices who require a field-induced static yield stress and a dispersion that is essentially indefinitely stable to sedimentation.