Shape and chemically anisotropic colloidal particles: A theoretical study of their structure, phase behavior, and slow dynamics

A detailed non-equilibrium state diagram of shape-anisotropic particle fluids is constructed. The effects of particle shape are explored using Naive Mode Coupling Theory (NMCT), and a single particle Non-linear Langevin Equation (NLE) theory. The dynamical behavior of non-ergodic fluids are discussed. We employ a rotationally frozen approach to NMCT in order to determine a transition to center of mass (translational) localization. Both ideal and kinetic glass transitions are found to be highly shape dependent, and uniformly increase with particle dimensionality. The glass transition volume fraction of quasi 1- and 2- dimensional particles fall monotonically with the number of sites (aspect ratio), while 3-dimensional particles display a non-monotonic dependence of glassy vitrification on the number of sites. Introducing interparticle attractions results in a far more complex state diagram. The ideal non-ergodic boundary shows a glass-fluid-gel re-entrance previously predicted for spherical particle fluids. The non-ergodic region of the state diagram presents qualitatively different dynamics in different regimes. They are qualified by the different behaviors of the NLE dynamic free energy. The caging dominated, repulsive glass regime is characterized by long localization lengths and barrier locations, dictated by repulsive hard core interactions, while the bonding dominated gel region has short localization lengths (commensurate with the attraction range), and barrier locations. There exists a small region of the state diagram which is qualified by both glassy and gel localization lengths in the dynamic free energy. A much larger (high volume fraction, and high attraction strength) region of phase space is characterized by short gel-like localization lengths, and long barrier locations. The region is called the attractive glass and represents a 2-step relaxation process whereby a particle first breaks attractive physical bonds, and then escapes its topological cage. The dynamic fragility of fluids are highly particle shape dependent. It increases with particle dimensionality and falls with aspect ratio for quasi 1- and 2- dimentional particles. An ultralocal limit analysis of the NLE theory predicts universalities in the behavior of relaxation times, and elastic moduli. The equlibrium phase diagram of chemically anisotropic Janus spheres and Janus rods are calculated employing a mean field Random Phase Approximation. The calculations for Janus rods are corroborated by the full liquid state Reference Interaction Site Model theory. The Janus particles consist of attractive and repulsive regions. Both rods and spheres display rich phase behavior. The phase diagrams of these systems display fluid, macrophase separated, attraction driven microphase separated, repulsion driven microphase separated and crystalline regimes. Macrophase separation is predicted in highly attractive low volume fraction systems. Attraction driven microphase separation is charaterized by long length scale divergences, where the ordering length scale determines the microphase ordered structures. The ordering length scale of repulsion driven microphase separation is determined by the repulsive range. At the high volume fractions, particles forgo the enthalpic considerations of attractions and repulsions to satisfy hard core constraints and maximize vibrational entropy. This results in site length scale ordering in rods, and the sphere length scale ordering in Janus spheres, i.e., crystallization. A change in the Janus balance of both rods and spheres results in quantitative changes in spinodal temperatures and the position of phase boundaries. However, a change in the block sequence of Janus rods causes qualitative changes in the type of microphase ordered state, and induces prominent features (such as the Lifshitz point) in the phase diagrams of these systems. A detailed study of the number of nearest neighbors in Janus rod systems reflect a deep connection between this local measure of structure, and the structure factor which represents the most global measure of order.

Studies of turbulent flows in continuous casting of steel with and without magnetic field

This thesis develops and tests various transient and steady-state computational models such as direct numerical simulation (DNS), large eddy simulation (LES), filtered unsteady Reynolds-averaged Navier-Stokes (URANS) and steady Reynolds-averaged Navier-Stokes (RANS) with and without magnetic field to investigate turbulent flows in canonical as well as in the nozzle and mold geometries of the continuous casting process. The direct numerical simulations are first performed in channel, square and 2:1 aspect rectangular ducts to investigate the effect of magnetic field on turbulent flows. The rectangular duct is a more practical geometry for continuous casting nozzle and mold and has the option of applying magnetic field either perpendicular to broader side or shorter side. This work forms the part of a graphic processing unit (GPU) based CFD code (CU-FLOW) development for magnetohydrodynamic (MHD) turbulent flows. The DNS results revealed interesting effects of the magnetic field and its orientation on primary, secondary flows (instantaneous and mean), Reynolds stresses, turbulent kinetic energy (TKE) budgets, momentum budgets and frictional losses, besides providing DNS database for two-wall bounded square and rectangular duct MHD turbulent flows. Further, the low- and high-Reynolds number RANS models (k-ε and Reynolds stress models) are developed and tested with DNS databases for channel and square duct flows with and without magnetic field. The MHD sink terms in k- and ε-equations are implemented as proposed by Kenjereš and Hanjalić using a user defined function (UDF) in FLUENT. This work revealed varying accuracies of different RANS models at different levels. This work is useful for industry to understand the accuracies of these models, including continuous casting. After realizing the accuracy and computational cost of RANS models, the steady-state k-ε model is then combined with the particle image velocimetry (PIV) and impeller probe velocity measurements in a 1/3rd scale water model to study the flow quality coming out of the well- and mountain-bottom nozzles and the effect of stopper-rod misalignment on fluid flow. The mountain-bottom nozzle was found more prone to the longtime asymmetries and higher surface velocities. The left misalignment of stopper gave higher surface velocity on the right leading to significantly large number of vortices forming behind the nozzle on the left. Later, the transient and steady-state models such as LES, filtered URANS and steady RANS models are combined with ultrasonic Doppler velocimetry (UDV) measurements in a GaInSn model of typical continuous casting process. LES-CU-LOW is the fastest and the most accurate model owing to much finer mesh and a smaller timestep. This work provided a good understanding on the performance of these models. The behavior of instantaneous flows, Reynolds stresses and proper orthogonal decomposition (POD) analysis quantified the nozzle bottom swirl and its importance on the turbulent flow in the mold. Afterwards, the aforementioned work in GaInSn model is extended with electromagnetic braking (EMBr) to help optimize a ruler-type brake and its location for the continuous casting process. The magnetic field suppressed turbulence and promoted vortical structures with their axis aligned with the magnetic field suggesting tendency towards 2-d turbulence. The stronger magnetic field at the nozzle well and around the jet region created large scale and lower frequency flow behavior by suppressing nozzle bottom swirl and its front-back alternation. Based on this work, it is advised to avoid stronger magnetic field around jet and nozzle bottom to get more stable and less defect prone flow.