Effects of particle size ratio on single particle motion in colloidal dispersions

The motion of a single Brownian particle of arbitrary size through a dilute colloidal dispersion of neutrally buoyant bath spheres of another characteristic size in a Newtonian solvent is examined in two contexts. First, the particle in question, the probe particle, is subject to a constant applied external force drawing it through the suspension as a simple model for active and nonlinear microrheology. The strength of the applied external force, normalized by the restoring forces of Brownian motion, is the Péclet number, Pe. This dimensionless quantity describes how strongly the probe is upsetting the equilibrium distribution of the bath particles. The mean motion and fluctuations in the probe position are related to interpreted quantities of an effective viscosity of the suspension. These interpreted quantities are calculated to first order in the volume fraction of bath particles and are intimately tied to the spatial distribution, or microstructure, of bath particles relative to the probe. For weak Pe, the disturbance to the equilibrium microstructure is dipolar in nature, with accumulation and depletion regions on the front and rear faces of the probe, respectively. With increasing applied force, the accumulation region compresses to form a thin boundary layer whose thickness scales with the inverse of Pe. The depletion region lengthens to form a trailing wake. The magnitude of the microstructural disturbance is found to grow with increasing bath particle size -- small bath particles in the solvent resemble a continuum with effective microviscosity given by Einstein's viscosity correction for a dilute dispersion of spheres. Large bath particles readily advect toward the minimum approach distance possible between the probe and bath particle, and the probe and bath particle pair rotating as a doublet is the primary mechanism by which the probe particle is able to move past; this is a process that slows the motion of the probe by a factor of the size ratio. The intrinsic microviscosity is found to force thin at low Péclet number due to decreasing contributions from Brownian motion, and force thicken at high Péclet number due to the increasing influence of the configuration-averaged reduction in the probe's hydrodynamic self mobility. Nonmonotonicity at finite sizes is evident in the limiting high-Pe intrinsic microviscosity plateau as a function of bath-to-probe particle size ratio. The intrinsic microviscosity is found to grow with the size ratio for very small probes even at large-but-finite Péclet numbers. However, even a small repulsive interparticle potential, that excludes lubrication interactions, can reduce this intrinsic microviscosity back to an order one quantity. The results of this active microrheology study are compared to previous theoretical studies of falling-ball and towed-ball rheometry and sedimentation and diffusion in polydisperse suspensions, and the singular limit of full hydrodynamic interactions is noted.

Second, the probe particle in question is no longer subject to a constant applied external force. Rather, the particle is considered to be a catalytically-active motor, consuming the bath reactant particles on its reactive face while passively colliding with reactant particles on its inert face. By creating an asymmetric distribution of reactant about its surface, the motor is able to diffusiophoretically propel itself with some mean velocity. The effects of finite size of the solute are examined on the leading order diffusive microstructure of reactant about the motor. Brownian and interparticle contributions to the motor velocity are computed for several interparticle interaction potential lengths and finite reactant-to-motor particle size ratios, with the dimensionless motor velocity increasing with decreasing motor size. A discussion on Brownian rotation frames the context in which these results could be applicable, and future directions are proposed which properly incorporate reactant advection at high motor velocities.

Movement of a Spherical Brownian Particle Between Infinite Parallel Plates: Hindered Dispersion and Sedimentation

The dispersion of an isolated, spherical, Brownian particle immersed in a Newtonian fluid between infinite parallel plates is investigated. Expressions are developed for both a 'molecular' contribution to dispersion, which arises from random thermal fluctuations, and a 'convective' contribution, arising when a shear flow is applied between the plates. These expressions are evaluated numerically for all sizes of the particle relative to the bounding plates, and the method of matched asymptotic expansions is used to develop analytical expressions for the dispersion coefficients as a function of particle size to plate spacing ratio for small values of this parameter.

It is shown that both the molecular and convective dispersion coefficients decrease as the size of the particle relative to the bounding plates increase. When the particle is small compared to the plate spacing, the coefficients decrease roughly proportional to the particle size to plate spacing ratio. When the particle closely fills the space between the plates, the molecular dispersion coefficient approaches zero slowly as an inverse logarithmic function of the particle size to plate spacing ratio, and the convective dispersion coefficent approaches zero approximately proportional to the width of the gap between the edges of the sphere and the bounding plates.

Analysis and optimization of stress wave propagation in two-dimensional granular crystals with defects

Granular crystals are compact periodic assemblies of elastic particles in Hertzian contact whose dynamic response can be tuned from strongly nonlinear to linear by the addition of a static precompression force. This unique feature allows for a wide range of studies that include the investigation of new fundamental nonlinear phenomena in discrete systems such as solitary waves, shock waves, discrete breathers and other defect modes. In the absence of precompression, a particularly interesting property of these systems is their ability to support the formation and propagation of spatially localized soliton-like waves with highly tunable properties. The wealth of parameters one can modify (particle size, geometry and material properties, periodicity of the crystal, presence of a static force, type of excitation, etc.) makes them ideal candidates for the design of new materials for practical applications. This thesis describes several ways to optimally control and tailor the propagation of stress waves in granular crystals through the use of heterogeneities (interstitial defect particles and material heterogeneities) in otherwise perfectly ordered systems. We focus on uncompressed two-dimensional granular crystals with interstitial spherical intruders and composite hexagonal packings and study their dynamic response using a combination of experimental, numerical and analytical techniques. We first investigate the interaction of defect particles with a solitary wave and utilize this fundamental knowledge in the optimal design of novel composite wave guides, shock or vibration absorbers obtained using gradient-based optimization methods.

Grain growth in protoplanetary disks

The majority of young, low-mass stars are surrounded by optically thick accretion disks. These circumstellar disks provide large reservoirs of gas and dust that will eventually be transformed into planetary systems. Theory and observations suggest that the earliest stage toward planet formation in a protoplanetary disk is the growth of particles, from sub-micron-sized grains to centimeter- sized pebbles. Theory indicates that small interstellar grains are well coupled into the gas and are incorporated to the disk during the proto-stellar collapse. These dust particles settle toward the disk mid-plane and simultaneously grow through collisional coagulation in a very short timescale. Observationally, grain growth can be inferred by measuring the spectral energy distribution at long wavelengths, which traces the continuum dust emission spectrum and hence the dust opacity. Several observational studies have indicated that the dust component in protoplanetary disks has evolved as compared to interstellar medium dust particles, suggesting at least 4 orders of magnitude in particle- size growth. However, the limited angular resolution and poor sensitivity of previous observations has not allowed for further exploration of this astrophysical process.

As part of my thesis, I embarked in an observational program to search for evidence of radial variations in the dust properties across a protoplanetary disk, which may be indicative of grain growth. By making use of high angular resolution observations obtained with CARMA, VLA, and SMA, I searched for radial variations in the dust opacity inside protoplanetary disks. These observations span more than an order of magnitude in wavelength (from sub-millimeter to centimeter wavelengths) and attain spatial resolutions down to 20 AU. I characterized the radial distribution of the circumstellar material and constrained radial variations of the dust opacity spectral index, which may originate from particle growth in these circumstellar disks. Furthermore, I compared these observational constraints with simple physical models of grain evolution that include collisional coagulation, fragmentation, and the interaction of these grains with the gaseous disk (the radial drift problem). For the parameters explored, these observational constraints are in agreement with a population of grains limited in size by radial drift. Finally, I also discuss future endeavors with forthcoming ALMA observations.

The Flocculation of E. coli with Polyethyleneimine

A comprehensive study was made of the flocculation of dispersed E. coli bacterial cells by the cationic polymer polyethyleneimine (PEI). The three objectives of this study were to determine the primary mechanism involved in the flocculation of a colloid with an oppositely charged polymer, to determine quantitative correlations between four commonly-used measurements of the extent of flocculation, and to record the effect of varying selected system parameters on the degree of flocculation. The quantitative relationships derived for the four measurements of the extent of flocculation should be of direct assistance to the sanitary engineer in evaluating the effectiveness of specific coagulation processes.

A review of prior statistical mechanical treatments of absorbed polymer configuration revealed that at low degrees of surface site coverage, an oppositely- charged polymer molecule is strongly adsorbed to the colloidal surface, with only short loops or end sequences extending into the solution phase. Even for high molecular weight PEI species, these extensions from the surface are theorized to be less than 50 Å in length. Although the radii of gyration of the five PEI species investigated were found to be large enough to form interparticle bridges, the low surface site coverage at optimum flocculation doses indicates that the predominant mechanism of flocculation is adsorption coagulation.

The effectiveness of the high-molecular weight PEI species 1n producing rapid flocculation at small doses is attributed to the formation of a charge mosaic on the oppositely-charged E. coli surfaces. The large adsorbed PEI molecules not only neutralize the surface charge at the adsorption sites, but also cause charge reversal with excess cationic segments. The alignment of these positive surface patches with negative patches on approaching cells results in strong electrostatic attraction in addition to a reduction of the double-layer interaction energies. The comparative ineffectiveness of low-molecular weight PEI species in producing E. coli flocculation is caused by the size of the individual molecules, which is insufficient to both neutralize and reverse the negative E.coli surface charge. Consequently, coagulation produced by low molecular weight species is attributed solely to the reduction of double-layer interaction energies via adsorption.

Electrophoretic mobility experiments supported the above conclusions, since only the high-molecular weight species were able to reverse the mobility of the E. coli cells. In addition, electron microscope examination of the seam of agglutination between E. coli cells flocculation by PEI revealed tightly- bound cells, with intercellular separation distances of less than 100-200 Å in most instances. This intercellular separation is partially due to cell shrinkage in preparation of the electron micrographs.

The extent of flocculation was measured as a function of PEl molecular weight, PEl dose, and the intensity of reactor chamber mixing. Neither the intensity of mixing, within the common treatment practice limits, nor the time of mixing for up to four hours appeared to play any significant role in either the size or number of E.coli aggregates formed. The extent of flocculation was highly molecular weight dependent: the high-molecular-weight PEl species produce the larger aggregates, the greater turbidity reductions, and the higher filtration flow rates. The PEl dose required for optimum flocculation decreased as the species molecular weight increased. At large doses of high-molecular-weight species, redispersion of the macroflocs occurred, caused by excess adsorption of cationic molecules. The excess adsorption reversed the surface charge on the E.coli cells, as recorded by electrophoretic mobility measurements.

Successful quantitative comparisons were made between changes in suspension turbidity with flocculation and corresponding changes in aggregate size distribution. E. coli aggregates were treated as coalesced spheres, with Mie scattering coefficients determined for spheres in the anomalous diffraction regime. Good quantitative comparisons were also found to exist between the reduction in refiltration time and the reduction of the total colloid surface area caused by flocculation. As with turbidity measurements, a coalesced sphere model was used since the equivalent spherical volume is the only information available from the Coulter particle counter. However, the coalesced sphere model was not applicable to electrophoretic mobility measurements. The aggregates produced at each PEl dose moved at approximately the same vlocity, almost independently of particle size.

PEl was found to be an effective flocculant of E. coli cells at weight ratios of 1 mg PEl: 100 mg E. coli. While PEl itself is toxic to E.coli at these levels, similar cationic polymers could be effectively applied to water and wastewater treatment facilities to enhance sedimentation and filtration characteristics.

Digested sludge: delineation and modeling for ocean disposal

Experimental work was performed to delineate the system of digested sludge particles and associated trace metals and also to measure the interactions of sludge with seawater. Particle-size and particle number distributions were measured with a Coulter Counter. Number counts in excess of 10¹² particles per liter were found in both the City of Los Angeles Hyperion mesophilic digested sludge and the Los Angeles County Sanitation Districts (LACSD) digested primary sludge. More than 90 percent of the particles had diameters less than 10 microns.

Total and dissolved trace metals (Ag, Cd, Cr, Cu, Fe, Mn, Ni, Pb, and Zn) were measured in LACSD sludge. Manganese was the only metal whose dissolved fraction exceeded one percent of the total metal. Sedimentation experiments for several dilutions of LACSD sludge in seawater showed that the sedimentation velocities of the sludge particles decreased as the dilution factor increased. A tenfold increase in dilution shifted the sedimentation velocity distribution by an order of magnitude. Chromium, Cu, Fe, Ni, Pb, and Zn were also followed during sedimentation. To a first approximation these metals behaved like the particles.

Solids and selected trace metals (Cr, Cu, Fe, Ni, Pb, and Zn) were monitored in oxic mixtures of both Hyperion and LACSD sludges for periods of 10 to 28 days. Less than 10 percent of the filterable solids dissolved or were oxidized. Only Ni was mobilized away from the particles. The majority of the mobilization was complete in less than one day.

The experimental data of this work were combined with oceanographic, biological, and geochemical information to propose and model the discharge of digested sludge to the San Pedro and Santa Monica Basins. A hydraulic computer simulation for a round buoyant jet in a density stratified medium showed that discharges of sludge effluent mixture at depths of 730 m would rise no more than 120 m. Initial jet mixing provided dilution estimates of 450 to 2600. Sedimentation analyses indicated that the solids would reach the sediments within 10 km of the point discharge.

Mass balances on the oxidizable chemical constituents in sludge indicated that the nearly anoxic waters of the basins would become wholly anoxic as a result of proposed discharges. From chemical-equilibrium computer modeling of the sludge digester and dilutions of sludge in anoxic seawater, it was predicted that the chemistry of all trace metals except Cr and Mn will be controlled by the precipitation of metal sulfide solids. This metal speciation held for dilutions up to 3000.

The net environmental impacts of this scheme should be salutary. The trace metals in the sludge should be immobilized in the anaerobic bottom sediments of the basins. Apparently no lifeforms higher than bacteria are there to be disrupted. The proposed deep-water discharges would remove the need for potentially expensive and energy-intensive land disposal alternatives and would end the discharge to the highly productive water near the ocean surface.

Part I. Kinetics of coarsening of the gamma-prime precipitate in nickel-silicon alloys. Part II. Rate of crystallization of an amorphous Fe-P-C alloy

The coarsening kinetics of Ni₃ Si(γ') precipitate in a binary Ni-Si alloy containing 6.5 wt. % silicon was studied by magnetic techniques and transmission electronmicroscopy. A calibration curve was established to determine the concentration of silicon in the matrix. The variation of the Si content of the Ni-rich matrix as a function of time follows Lifshitz and Wagner theory for diffusion controlled coarsening phenomena. The estimated values of equilibrium solubility of silicon in the matrix represent the true coherent equilibrium solubilities.

The experimental particle-size distributions and average particle size were determined from dark field electron micrographs. The average particle size varies linearly with t^-1/3 as suggested by Lifshitz and Wagner. The experimental distributions of particle sizes differ slightly from the theoretical curve at the early stages of aging, but the agreement is satisfactory at the later stages. The values of diffusion coefficient of silicon, interfacial free energy and activation energy were calculated from the results of coarsening kinetics. The experimental value of effective diffusion coefficient is in satisfactory agreement with the value predicted by the application of irreversible the rmodynamics to the process of volume constrained growth of coherent precipitate during coarsening. The coherent γ' particles in Ni-Sialloy unlike those in Ni-Al and Ni-Ti seem to lose coherency at high temperature. A mechanism for the formation of semi-coherent precipitate is suggested.