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# Microscale dynamics in suspensions of non-spherical particles

#### Kumar, Amit

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https://hdl.handle.net/2142/16032

## Description

- Title
- Microscale dynamics in suspensions of non-spherical particles
- Author(s)
- Kumar, Amit
- Issue Date
- 2010-05-19T18:32:50Z
- Director of Research (if dissertation) or Advisor (if thesis)
- Higdon, Jonathan J.L.
- Doctoral Committee Chair(s)
- Higdon, Jonathan J.L.
- Committee Member(s)
- Schweizer, Kenneth S.
- Schroeder, Charles M.
- Harley, Brendan A.

- Department of Study
- Chemical & Biomolecular Engr
- Discipline
- Chemical Engineering
- Degree Granting Institution
- University of Illinois at Urbana-Champaign
- Degree Name
- Ph.D.
- Degree Level
- Dissertation
- Keyword(s)
- stokesian dynamics
- non-spherical particles
- anisotropic particles
- colloid
- rheology
- microstrucuture

- Abstract
- Numerical simulations were performed to investigate the microscale dynamics in suspensions of spherical and non-spherical particles. Two new algorithms were developed to enable studies with accurate hydrodynamics. The first algorithm was a high accuracy Stokesian Dynamics technique (SD) extended to a generic non-spherical particle shape. The many body interactions were computed using a novel scheme employing one body singularity solutions. Near field lubrication interactions employed standard asymptotic solutions for nearly touching convex particles. The second algorithm was a reduced precision near-field lubrication based method called Fast Lubrication Dynamics (FLD). In addition to the near field interactions, we introduced a novel isotropic resistance in FLD to match the mean particle mobility from the more detailed SD. The resulting FLD algorithm was shown to give results comparable to that from the detailed SD, while requiring only a fraction of the latter's computational expense. In a first series of studies using the SD technique, we computed the transport properties in equilibrium suspensions of spheres and dicolloids. The latter particle shape was modeled as two intersecting spheres of varying radii and center to center separations. It was found that the infinite frequency viscosity as well as the short-time translational self-diffusivity are non-monotonic function of aspect ratio at any given non-dilute volume fraction with the minima in viscosity and the maxima in self-diffusivity around an aspect of 1.5. In contrast, the short-time rotational self-diffusivity was found to be a monotonically decreasing function of the aspect ratio at any given volume fraction. In a second series of studies using the SD technique we investigated the microstructure, orientation, and rheology in suspensions of spheres and dicolloids over a wide range of volume fractions $0 \leq \phi \leq 0.55$. The particles had a very short range repulsive interparticle interaction. The microstructure in suspensions of all particle shapes was found to be disordered for volume fractions $\phi \leq 0.5$, while a string like ordering was observed in suspensions of spheres and other particles with small degree of anisotropy at $\phi=0.55$. Both the first and the second normal stress differences were negative for volume fractions up to $\phi=0.5$, but some were positive at the highest volume fraction studied here ($\phi=0.55$). The orientation behavior was found to be a function of both the fore-aft symmetry and the degree of anisotropy. For particles with fore-aft symmetry, in comparison to infinite dilution, a shift to higher orbit constants (increased alignment in the flow-gradient plane) was observed at low volume fractions. On the other hand, the particle lacking fore-aft symmetry showed virtually no change in its orientation distribution at low volume fractions. At higher volume fractions ($\phi \geq 0.2$), in comparison to the dilute suspensions, a shift towards lower orbit constants (increased alignment with the vorticity axis) was observed for all particle shapes. The degree of this alignment was found to increase with volume fraction for particles with small degree of anisotropy, while it was found to plateau at relatively low volume fractions in suspensions of particles with the largest degree of anisotropy. The observed orientation behavior was explained using a novel analysis technique based on the coupling of particle's angular velocity and hydrodynamic stresslet through the mobility tensor. Next, we investigated microstructure and orientation in Brownian suspensions of spheres and dicolloids using the FLD algorithm. Results are reported for two different volume fractions, $\phi=42\%$ and $\phi=55\%$. The 42\% sample had a long range repulsive electrostatic interaction, while the 55\% sample had hard-sphere type interaction. Particles with small degree of anisotropy showed microstructural transitions similar to that of spheres. In contrast, particles with relatively larger degree of anisotropy showed a significantly different microstructural behavior. At low shear rates, irrespective of the degree of anisotropy, an orientationally disordered state was observed. Upon further increase in the rate of shear, an increase in flow alignment is obtained, with the maximum flow alignment typically observed between $Pe=1$ and $Pe=20$ depending on the particle shape. With a further increase in the rate of shear, an increase in vorticity alignment is seen for all particle shapes. The degree of anisotropy and volume fraction was found to have a significant impact on the extent of increase in the flow or the vorticity alignment. Using FLD simulations we next investigated the phase behavior and rheology in charged colloidal suspensions at a volume fraction of $\phi=0.33$. It was shown that for a given screening length of the repulsive interaction, there existed a range of surface potentials for which both the ordered and disordered metastable states exist. This range was found to have a strong dependence on shear rate and was found to have a maximum width around $Pe = 0.5$, where $Pe = \dot{\gamma}a^2/D_0$. The presence of both the ordered and disordered metastable states allowed us to simultaneously characterize both the branches of viscosity as a function of shear rate. It was observed that the disordered branch can have a lower viscosity than the ordered branch at low shear rates ($Pe < 0.05$ in this study). This was attributed to the much smaller long-time self-diffusivity in the ordered state, which leads to a greater distortion of the microstructure and hence stress at the same shear rate. At higher shear rates, on the other hand, ordered states with close packed planes aligned in the flow-vorticity direction were able to minimize the distortive effects of shear, and hence have lower viscosities than the corresponding disordered states. The microstructural dynamics revealed in these studies explains the anomalous behavior and hysteresis loops in stress data reported in the literature. In a last series of studies using the FLD algorithm, we investigated the shear thickening phenomena in suspensions of spheres. Using a short range repulsive force to control the gap-size in a shearing suspension, it was shown that the suspension viscosity has a much weaker logarithmic dependence on the minimum gap size present in the suspension. This dependence of the viscosity on the minimum gap size was shown to persist even at volume fractions as high as $\phi=0.62$. This study poses intriguing questions about the origins of discontinuous shear thickening in these systems which is commonly observed in experiments.
- Graduation Semester
- 2010-5
- Permalink
- http://hdl.handle.net/2142/16032
- Copyright and License Information
- Copyright 2010 Amit Kumar

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