Visualization and quantification of shear-induced aggregation:

At low concentrations and at high shear rates, high-aspect ratio particles in suspension are mostly aligned with the flow, while at higher concentrations and lower shear rates suspensions commonly clump (flocculate) due to the combination of flow-induced interactions and attractive or frictional inter-fiber forces. Shear thinning behavior is commonly observed in steady shear viscosity measurements and can be attributed to the breakup of aggregates (flocs) by shear forces, a process which depends on fiber rigidity, the rheology of the suspending fluid, and other factors.

We developed a well-controlled model rod suspension consisting of SU-8 microrods in a density matched glycerol/glycol solution.  Our rheology measurements showed that semidilute suspensions of the microrods exhibit a dramatic reversible increase in measured steady-state viscosity with decreasing shear rate. Using a custom microscope-rheometer combination. we were able clearly identify the density variations associated with the viscosity enhancement at low shear rate. The figure below shows a series of images taken at a modest shear rate, starting from an initially homogeneous suspension (produced by subjecting the sample to high shear rates).  The intensity in the image provides an approximate measure of the density of fluorescent rods integrated across the gap of the rheometer.  The initially homogeneous image breaks up into regions of high and low intensity, with the heterogeneity forming first at the outer radius, where the shear rate is highest, and then moving inward.

Using a simple aggregation model, developed in collaboration with Prof. Aparana Baskaran at Brandeis University, we were able to describe the early-stage behavior and show that aggregate density decreased dramatically with decreasing shear rate, with a volume fraction of less that 0.15 at low shear rate [1]. We recently confirmed this result with direct quantification of the aggregate images (data not shown). In addition, a Krieger-Dougherty-type consitutive relation (commonly used to describe the impact of suspended particles on the viscosity of a suspension) was combined with this equation to yield a shear rate dependent viscosity enhancement that closely matched the measured flow curves. This result suggests that the shear thinning flow curve can be quantitatively described by the decrease in the total aggregate volume fraction with increasing shear rate arising from the increasing particle density in the individual aggregates.

Computational studies showing the importance of torsional stiffness:

Motivated by the experimental results described above, we performed a series of simulations of sheared rigid rods in the presence of strong attractive interparticle interactions [55]. We employed Dissipative Particle Dynamics (DPD), an efficient coarse-grained fluid representation that can model the complex hydrodynamic interactions between aggregating rods and the surrounding fluid and is relatively simple to implement (although computationally very expensive). The computational domain is sketched below:

We found that we could reproduce the random aggregates observed in the initial microrod experiments only if we introduced fiber-fiber bonds that display a strong resistance to rotation that enables them to resist the torques arising from the shear flow. The figure below shows a snapshot of a simulated shear flow of a suspension of rods with high resistance to rotation, of torsional stiffness. The formation of the aggregates is associated with a significant increase in computed system viscosity. More modest torsional resistance produces some aligned bundles which may then form a larger, somewhat disordered aggregate (middle panel) with a smaller increase in system viscosity. Finally, a freely rotating bond produces mostly aligned bundles of fibers that combine to form cables spanning the periodic shear direction (left panel).

At the same time, the total aggregate volume varied from a substantial fraction of the suspension volume for high torsional stiffness to a negligible fraction in the absence of resistance to rotation. The transition between aligned and disordered aggregates occurred when the torsional stiffness was comparable to the shear-induced torque on individual rods. In addition, we found that the stability of disordered aggregates and their impact on system viscosity was dependent on the competition between the attractive interaction and the shear stresses, and in particular found a simple relationship between the viscosity increase and the attractive interaction scaled by the fluid shear force on individual rods [2].

The resistance to relative rotation of the rod-rod interactions in our experimental model system likely arises from frictional interactions (static or kinetic) in the extended contacts that are created by the combination of an attractive force and the slight deformability of the rods.  Based on simple physical considerations, some level of torsional stiffness should arise in nearly any rod-rod or fiber-fiber interactions except for those due to true point-contacts, such as those found in  nearly one-dimensional rigid molecules.

[1]  Shear-Driven Aggregation of SU-8 Microrods in Suspension, Kumar, P., Gold D., Blair D. L., Baskaran A., and Urbach J. S., Soft Matter, Volume 10, p.6514–6519, (2014)

[2] Torsional stiffness determines aggregate structure in sheared colloidal rod suspensions, J. T. Stimatze, D. A. Egolf and J. S. Urbach, Soft Matter 12:7764 (2016).