# Part I: Micromechanics of dense suspensions: microscopic interactions to macroscopic rheology & Part II: Motion in a stratified fluid: swimmers and anisotropic particles

**Part I: Micromechanics of dense suspensions**

Particulate suspensions are ubiquitous in the industry & nature. Fresh concrete, uncured solid rocket fuel, & biomass slurries are typical industrial applications, while milk & blood are examples of naturally occurring suspensions. These suspensions exhibit many non-Newtonian properties like rate-dependent rheology & normal stresses. Other than volume fraction, particle material, inter-particle interactions determine the rheological behavior of suspension. The average inter-particle gaps between the neighboring particles decrease significantly as the suspension volume fraction approaches the maximum packing fraction in dense suspensions. So, in this regime, the short-ranged non-contact interactions are important. In addition, the particles come into contact due to asperities on their surfaces. The surface asperities are present even in the case of so-called smooth particles, as particles in real suspensions are not perfectly smooth. Hence, contact forces become one of the essential factors to determine the rheology of suspensions.

Part I of this thesis investigates the effects of microscopic inter-particle interactions on the rheological properties of dense suspensions of non-Brownian particles by employing discrete particle simulations. We show that increasing the roughness size results in a rise in the viscosity & normal stress difference in the suspensions. Furthermore, we observe that the jamming volume fraction decreases with the particle roughness. Consequently, for suspensions close to jamming, increasing the asperity size reduces the critical shear rate for shear thickening (ST) transition, resulting in an early onset of discontinuous ST (DST, a sudden jump in the suspension viscosity) in terms of volume fraction, & enhances the strength of the ST effect. These findings are in excellent agreement with the recent experimental measurements & provide a deeper understanding of the experimental findings. Finally, we propose a constitutive model to quantify the effect of the roughness size on the rheology of dense ST suspensions to span the entire phase-plane. Thus, the constitutive model and the experimentally validated numerical framework proposed can guide experiments, where the particle surface roughness is tuned for manipulating the dense suspension rheology according to different applications.

A typical dense non-Brownian particulate suspension exhibits shear thinning (decreasing viscosity) at a low shear rate followed by a Newtonian plateau (constant viscosity) at an intermediate shear rate values which transition to ST (increasing viscosity) beyond a critical shear rate value and finally, undergoes a second shear-thinning transition at an extremely high shear rate values. This part unifies & quantitatively reproduces all the disparate rate-dependent regimes & the corresponding transitions for a dense non-Brownian suspension with increasing shear rate. The inclusion of traditional hydrodynamic interactions, attractive/repulsive DLVO (Derjaguin and Landau, Verwey and Overbeek), contact interactions, & constant friction reproduce the initial thinning as well as the ST transition. However, to quantitatively capture the intermediate Newtonian plateau and the second thinning, an additional interaction of non-DLVO origin & a decreasing coefficient of friction, respectively, are essential; thus, providing the first explanation for the presence these regimes. Expressions utilized for various interactions and friction are determined from experimental measurements, resulting in an excellent quantitative agreement with previous experiments.

**Part II: Motion in a stratified fluid**

Density variations due to temperature or salinity greatly influence the dynamics of objects like particles, drops, and microorganisms in oceans. Density stratification hampers the vertical flow & substantially affects the sedimentation of an isolated object, the hydrodynamic interactions between a pair, and the collective behavior of suspensions in various ways depending on the relative magnitude of stratification inertia (advection), and viscous (diffusion) effects. This part investigates these effects and elicits the hydrodynamic mechanisms behind some commonly observed fluid-particle transport phenomena in oceans, like aggregation in horizontal layers. The physical understanding can help us better model these phenomena and, hence, predict their geophysical, engineering, ecological, and environmental implications.

We investigate the self-propulsion of an inertial swimmer in a linear density stratified fluid using the archetypal squirmer model, which self-propels by generating tangential surface waves. We quantify swimming speeds for pushers (propelled from the rear) and pullers (propelled from the front) by direct numerical solution. We find that increasing stratification reduces the swimming speeds of swimmers relative to their speeds in a homogeneous fluid while reducing their swimming efficiency. The increase in the buoyancy force experienced by these squirmers due to the trapping of lighter fluid in their respective recirculatory regions as they move in the heavier fluid is one of the reasons for this reduction. Stratification also stabilizes the flow around a puller, keeping it axisymmetric even at high inertia, thus leading to otherwise absent stability in a homogeneous fluid. On the contrary, a strong stratification leads to instability in the motion of pushers by making the flow around them unsteady 3D, which is otherwise steady axisymmetric in a homogeneous fluid. Data for the mixing efficiency generated by individual squirmers explain the trends observed in the mixing produced by a swarm of squirmers.

In addition, the ubiquitous vertical density stratification in aquatic environments significantly alters the swimmer interactions affecting their collective motion &consequently ecological and environmental impact. To this end, we numerically investigate the interactions between a pair of model swimming organisms with finite inertia in a linear density stratified fluid. Depending on the squirmer inertia and stratification, we observe that the squirmer interactions can be categorized as i) pullers getting trapped in circular loops, ii) pullers escaping each other with separating angle decreasing with increasing stratification, iii) pushers sticking to each other after the collision and deflecting away from the collision plane, iv) pushers escaping with an angle of separation increasing with stratification. Stratification also increases the contact time for squirmer pairs. The results presented can help understand the mechanisms behind the accumulation of planktonic organisms in horizontal layers in a stratified environment like oceans and lakes.

Much work has been done to understand the settling dynamics of spherical particles in a homogeneous and stratified fluid. However, the effects of shape anisotropy on the settling dynamics in a stratified fluid are not entirely understood. To this end, we perform numerical simulations for settling oblate and prolate spheroids in a stratified fluid. We find that both the oblate and prolate spheroids reorient to the edge-wise and partially edge-wise orientations, respectively, as they settle in a stratified fluid completely different from the steady-state broad-side on orientation observed in a homogeneous fluid. We observe that reorientation instabilities emerge when the velocity magnitude of the spheroids falls below a particular threshold. We also report the enhancement of the drag on the particle from stratification. The torque due to buoyancy effects tries to orient the spheroid in an edge-wise orientation, while the hydrodynamic torque tries to orient it to a broad-side orientation. The buoyancy torque dominates below the velocity threshold, resulting in reorientation instability.

## Funding

### NSF grants: CBET-1604423, CBET-1705371, and CBET-1700961

## History

## Degree Type

- Doctor of Philosophy

## Department

- Mechanical Engineering

## Campus location

- West Lafayette