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In this dissertation I set out to determine how shape and size influence the kinematics and mass flux of Taylor-lengthscale-sized particles in homogeneous isotropic turbulence. Through laboratory experiments, I investigated different sized and shaped flat particles to determine what happens with the spinning and tumbling of those particles in turbulent environments. The results of this first set of experiments showed dependence on size, but not shape. The size-dependent results from the flat particles agreed with the findings for fibers (Oehmke et al., 2021) and cuboids (Pujara et al., 2018). To determine the mass flux of Taylor-lengthscale-sized particles, I developed a new particle to study dissolution in turbulence. This particle was made from a sugar-glass recipe and had the characteristics of being neutrally buoyant and shape-similar while it dissolved (Oehmke and Variano, 2021). Based on results from previous work that characterized motion (Pujara et al., 2018, Bordoloi and Variano 2017, Byron et al., 2015), I created rod- and disc-like particles and compared their surface area, volume, and surface-area-to-volume ratios. In all cases, the disc-shaped particles dissolved faster than the rod-shaped particles signifying that shape plays an important role in dissolution dynamics.

This dissertation develops a modeling framework to address the problem of particle manipulation in low Reynolds number fluid flows. This framework combines singularity methods in low Reynolds number fluid dynamics with the theory of transport in phase space of dynamical systems. While dynamical systems theory offers tools to study the properties of geometric features in systems such as fluid flows, singularity methods enable the construction of models for low Reynolds number flows that are simple to work with and yet, preserve the essential geometric features of the flow. Hence, the combination of these techniques offers a natural framework for the study of particle transport in varied problems of the viscous/low Reynolds number flow regime. The first problem studied is that of inertial particle manipulation in microfluidic channels integrated with acoustically excited micro-bubbles. The Lagrangian Coherent Structures(LCS) of micro-bubble streaming flows serve as a guideline for placement of micro-bubbles within the channel in a manner that enhances focusing and size based separation of inertial particles. Second, the dynamics of viscous micro-rotors within a bounded domain is modeled. The influence of viscous boundary effects on the dynamics is assessed. The application of micro-rotors for the purpose of chaotic micro-mixing is explored using numerical simulations.

Particle-laden turbulent shear flows are ubiquitous in environmental and industrial flow-systems, and their analysis is thus of prime importance. In this work, we study the motion of a dilute suspension of particles in a non-stationary homogeneous turbulent shear flow (HTSF), subject to varying levels of imposed mean-shear, gravity, and inertia. We use direct numerical simulations (DNS) of the fluid velocity field (coupled with Lagrangian particle tracking), to assess the influence of flow-anisotropy and gravity on the motion of the particles. We first discuss numerical challenges encountered while performing DNS of HTSF at higher Reynolds numbers. The presence of sharp velocity gradients in the HTSF flow field is found to cause premature loss of resolution at the small scales, leading to shortened simulation-times. To counter this, the existing pseudo-spectral DNS setup is augmented with a Weighted Essentially Non-Oscillatory (WENO) scheme, enabling numerically-stable HTSF simulations at higher Reynolds numbers. We then consider the motion of individual particles as they interact with the anisotropic topology of the turbulence. In contrast to isotropic turbulence, particles are found to collect within vortex layers, regions where strong vorticity and strain are coupled with low streamline curvature. Shear-induced anisotropy in the turbulence also leads to reduced gravitational settling speeds for intermediate-inertia particles, though stronger gravity overcomes this effect. Particle velocity variances are found to be highly anisotropic at stronger shear, while gravity now tends to diminish this effect by limiting the interaction-time between particles and turbulence. Shear and gravity acting together cause particle acceleration variances to exceed those of the underlying fluid, corroborating findings from past turbulent boundary layer experiments. Analytical expressions are derived for the mean velocities and accelerations of the particles, and are in agreement with the DNS results. Finally, we analyze the relative velocities and clustering characteristics of particle pairs, and find that stronger shear and gravity suppress path-history effects for particles with stronger inertia. Shear-induced anisotropy in pair-statistics is affected by both inertia and gravity, with stronger gravity seen to oppose the action of shear. Changes in the relative-velocity anisotropy are correlated to the trends shown by single-particle velocity variances. Particle collision rates increase with stronger shear, and are found to scale in proportion to the underlying turbulence timescales.

This work consists of three independent experimental studies. The first studies inhomogeneous turbulence with (even symmetric) non-Gaussian velocity probability density functions, created by partitioning an active grid in a wind tunnel. The turbulence is like that encountered in the environment (e.g., by wind turbines) or produced by fractal grids. The statistics of the turbulence are shown in particular to depend simply upon the spatial derivatives of the velocity r.m.s. field. The second study characterizes the intermittent nature of an inertial particle mixing layer, where a particle-laden flow entrains a particle-free flow. This is the case at the boundary of a cloud and affects its growth and hence climate modelling. The flow is accomplished with water droplets in a wind tunnel downstream of a splitter plate; the experiments are done for both homogeneous turbulence and where the active grid is partitioned to create an inhomogeneous interface like in the first study. We show the droplets to be entrained in intermittent, large-scale bursts, preserving the properties of the air and turbulence ambient to them, which in a cloud are critical to droplet growth. Gravitational settling effects are isolated by rotation of the apparatus. The third and final study takes a more fundamental look at inertial particles in isotropic conditions using both numerical simulations and water droplets in air turbulence from 32 loudspeaker jets aimed at a central point. Turbulent settling speeds, velocity variance and variance anisotropy are measured over an unprecedented parameter range, identifying all relevant parameterizations of particle inertia and buoyancy affecting their response to turbulence, with applications to all particle-carrying flows. The three mechanisms by which turbulence modifies settling speeds (as compared to in quiescent flow) are isolated for the first time, with vertical turbulent motions shown to be responsible for settling reductions and horizontal ones to be for enhancements. The three experiments rely on hot-wire anemometry, phase Doppler particle analysis (PDPA) and high-speed camera Lagrangian particle tracking techniques. The body of the text consists of three stand-alone papers. The dissertation work provides fundamental understanding for wide-ranging environmental and industrial engineering problems.

An initially uniform distribution of inertial particles will spontaneously organize themselves into clusters in a turbulent flow, driven primarily by the small-scale turbulent fluctuations. Accurate prediction of such clustering of inertial particles, along with their relative velocity statistics, is essential for computing their binary collision rates, an important quantity that determines the evolution of the size distribution of these particles, under conditions when collisions lead to agglomeration or coalescence. In large-eddy simulations (LES) of turbulent flows, only the largescale turbulent fluctuations are represented on the grid whereas the small-scales (or subgrid scales) need to be modeled. None of the existing LES subgrid models are able to accurately predict the particle collision rates across the entire range of particle inertia, where inertia is parameterized by the Stokes number (St) defined as the ratio of the particle response time to the Kolmogorov time-scale ([tau][eta] ). In this work, we present new subgrid models designed to recover the clustering and relative velocity statistics of inertial particles. We begin by considering the effect of the subgrid scales on our statistics of interest. We do this by analyzing the exact distribution of particles obtained from direct numerical simulations (DNS) and comparing them with the ones obtained from a filtered DNS (FDNS). FDNS is obtained by filtering out the 'subgrid' scales and represents a 'perfect' LES with an exact representation of the large-scales (free of any subgrid modeling error). This provides a benchmark study and points to the need of incorporating the mech- anism by which the small-scales affect particle statistics, into the LES subgrid models designed to recover clustering and relative velocities of inertial particles. We then consider a subgrid model based on kinematic simulations of turbulence (so-called KSSGM), and show that it can accurately predict the relative velocity statistics for all St, but can capture clustering only for St [GREATER-THAN OR EQUAL TO] 2.0. We investigate the reasons for its failure to predict clustering at St < 2.0, and identify the important small-scale statistics that a subgrid model needs to predict in order to capture clustering correctly. We conclude that none of the existing subgrid models are capable of recovering the necessary small-scale statistics, and recognize the difficulty in doing so in a single-particle framework. We therefore shift our attention to a two-particle framework, based on the understanding that clustering is driven by two-point dynamics, and the recognition that all of the existing theories of particle clustering and collisions are formulated in this framework. We then develop a novel satellite particle simulation (SPS) methodology that allows us to efficiently simulate pair-wise interactions of particles in turbulence, thereby providing an ideal test-bed for the development and testing of two-particle models. We derive models from existing theories of inertial particle clustering primarily focussing on low St, and test them using the SPS. We analyze a class of models, that are referred to as Drift-Diffusion Models (DDMs), and show how they can be derived from statistical mechanical theories of clustering. We consider the theories by Chun et al. (2005) (CT) and Zaichik and Alipchenkov (2009) (ZT). We show that the DDM-CT gives good results for St [LESS-THAN OR EQUAL TO] 0.05, whereas the DDM-ZT works well for St [LESS-THAN OR EQUAL TO] 0.2. Such models represent an entirely new framework for subgrid modeling of inertial particle motion in a LES, and the initial results provide strong evidence regarding the viability of such an approach. Finally, we discuss some issues related to implementing these two-particle models in a single-particle tracking framework.