This dissertation describes two experimental studies of a vibrofluidized granular medium and a preliminary study of two-phase fluid flow in a porous medium using Nuclear Magnetic Resonance (NMR). The first study of granular medium is to test a scaling law of the rise in center of mass in a three-dimensional vibrofluidized granular system. Our granular system consisted of mustard seeds vibrated vertically at 40 Hz from 0g to 14g. We used Magnetic Resonance Imaging (MRI) to measure density profile in vibrated direction. We observed that the rise in center of mass scaled as ν 0α/Nlβ with α = 1.0 ± 0.2 and β = 0.5 ± 0.1, where ν 0 is the vibration velocity and Nl is the number of layers of grains in the container. A simple theory was proposed to explain the scaling exponents. In the second study we measured both density and velocity information in the same setup of the first study. Pulsed Field Gradient (PFG)-NMR combined with MRI was used to do this measurement. The granular system was fully fluidized at 14.85g 50 Hz with Nl ≤ 4. The velocity distributions at horizontal and vertical direction at different height were measured. The distributions were nearly-Gaussian far from sample bottom and non-Gaussian near sample bottom. Granular temperature profiles were calculated from the velocity distributions. The density and temperature profile were fit to a hydrodynamic theory. The theory agreed with experiments very well. A temperature inversion near top was also observed and explained by additional transport coefficient from granular hydrodynamics. The third study was the preliminary density measurement of invading phase profile in a two-phase flow in porous media. The purpose of this study was to test an invasion percolation with gradient (IPG) theory in two-phase flow of porous media. Two phases are dodecane and water doped with CuSO4. The porous medium was packed glass beads. The front tail width σ and front width of invading phase were extracted from fitting of the invading front profile. The front tail scaled as σ∞Ca −α, where Ca is capillary number and α is 0.4 ± 0.08. The result is very close to IPG predication 0.25.

We report capacitive measurements of the hysteresis and avalanche properties of $\sp4$He in Nuclepore. Hysteresis was measured on global loops and subloops for Nuclepore with 30 nm and 200 nm diameter pores. Subloops exhibit the property of return point memory, but subloops between the same chemical potential end points were not congruent. The failure of congruence showed that the Preisach model, in which the pores do not interact, does not describe this system. Modification of the Preisach model to allow for pore intersection within the membrane resulted in qualitative agreement with the data. Using a model for hystersis by Mason which included pore-pore interactions, we calculated the pore size distribution for Nuclepore. Close examination of the primary desorption curve resulted in the observation of large groups of pores draining together. This was the first observation of avalanches in the draining of fluid from a porous material. The properties of the avalanches were documented for 200 nm and 30 nm pore diameter Nuclepore. Using two capacitors on the same Nuclepore substrate, we found that avalanche events were spatially extended involving a low density of pores. With a composite porous/nonporous sample we showed that pore coupling occurred via the superfluid $\sp4$He film.

Abstract not available

We have measured the viscosity of a dilute mixture of 3He in 4He at temperatures from 5 to 100 mK and in magnetic fields of 0.35, 2.01 and 8.76 T using a vibrating wire viscometer. Subject to our choice of calibration function, the data at 0.35 T is in good agreement with theory. Due to an interaction of our viscometer with the magnetic field the motion of the wire at 2.01 and 8.76 T is not understood; however, the 2.01 T data can be brought into agreement with the 0.35 T data by adjusting a geometrical constant. An increase in the low temperature viscosity between 2.01 and 8.76 T is in qualitative agreement with theory (using an alternate choice of calibration function a decrease in viscosity between 2.01 and 8.76 T is observed).

A statistical equilibrium theory in two-dimensional turbulence is used to study the emergence of coherent structures. Macroscopic states are described by a local probability measure on the fluctuating vorticity field. The most probable macroscopic state is characterized by maximizing entropy subject to a family of constraints derived from the conserved quantities of the incompressible Euler equations. Coherent structures are identified with such macrostates. Attention is focused on the special case of enstrophy-moments and a doubly periodic domain. The algorithm of Turkington and Whitaker is applied to this special case. The convergence properties of the algorithm are derived from the optimization structure of the constraint maximization problem. The algorithm produces an entropy increasing sequence. The trivial case of conserving energy and enstrophy serves as the starting equilibrium state when implementing the algorithm. The probability density of the energy-enstrophy model is Gaussian and we perturb away from the trivial case by imposing higher enstrophy moments. Perturbing away from the trivial case forces the model to become nonlinear. It is found that the preferred statistical equilibrium state of the maximum entropy problem is determined by kurtosis. For high kurtosis a dipole is preferred and for low kurtosis a shear-layer is preferred. Several local solutions are found which converge to the maximum entropy state for high energy.

This dissertation presents a theoretical study of a variety of charged polymer systems: Critical conditions are determined for adsorption of a charged polymer chain in an electrolyte solution by a curved, charged surface; the scaling behavior and density profiles of a polyelectrolyte brush is examined; the stretch-colapse transition of a charged, grafted polymer layers in a poor solvent is analyzed; and, the sequence dependence of heteropolymer configurations is calculated. These problems are studied theoretically using standard techniques of statistical mechanics.

We have investigated $\sp3$He spin diffusion in two dilute solutions of $\sp3$He in $\sp4$He, with atomic fraction $x\sp3=1.82\times 10\sp{-3}$ and 6.26 $\times$ 10$\sp{-4}$, spin-polarized by an 8 T field. We do not find evidence that the diffusion coefficient for spins transverse to the average magnetization ($D\sb\perp$) declines or saturates at temperatures down to 0.20$T\sb{\rm F}$, contrary to previous experiment (Gully and Mullin 1984) but in accord with current theory. We have compared our measurements with the latest theory of Jeon and Mullin (1991); our data is mostly in good agreement with their theory if a slightly modified version of a $\sp3$He-$\sp3$He interaction due to Ebner (1967) is used. The congruence between data and theory supports the conclusion that the s-wave approximation to the interaction is not useful for transport calculations even for these rather dilute solutions. There may be an one unresolved discrepancy: our diffusion constant for the lowest concentration at the lowest temperatures is 25% higher than theory predicts. This could be due to a polarization dependance for $D\sb\perp$ or to a modification of the boundary condition by a bound $\sp3$He state, or possibly due to errors in the theoretical calculation.

In this dissertation we report new theoretical results—both analytical and numerical—concerning a variety of polymeric systems. Applying path-integral and differentiable manifolds techniques, we have obtained original results concerning the statistics of a Gaussian polymer embedded on a sphere, a cylinder, a cone and a torus. Generally, we found that the curvature of the surfaces induces a geometrical localization area. Next we employ field theoretical (instanton calculus) and differential equations techniques (Darboux method) to obtain approximate and exact new results regarding the average size and the Green function of a Gaussian, one-dimensional polymer chain subjected to a multi-stable potential (the tunnel effect in polymer physics). Extending the multiple scattering formalism, we have investigated the steady-state dynamics of suspensions of spheres and Gaussian polymer chains without excluded volume interactions. We have calculated the self-diffusion and friction coefficients for probe objects (sphere and polymer chain) and the shear viscosity of the suspensions. At certain values of the concentration of the ambient medium, motion of probe objects freezes. Deviation from the Stokes-Einstein behavior is observed and interpreted. Next, we have calculated the diffusion coefficient and the change in the viscosity of a dilute solution of freely translating and rotating diblock, Gaussian copolymers. Regimes that lead to increasing the efficiency of separation processes have been identified. The parallel between Navier-Stokes and Lamé equations was exploited to extend the effective medium formalism to the computation of the effective shear and Young moduli and the Poisson ratio of a composite material containing rigid, monodispersed, penetrable spheres. Our approach deals efficiently with the high concentration regime of inclusions.

Herein are described some model problems, means of solution, and some properties of solutions for the equilibrium of self-gravitating isothermal gases in interstellar configurations, with magnetic field. The approach is from the viewpoint of the calculus of variations, with flux-freezing being modelled as well as flux loss through partial ionization. In this work such a treatment is presented for the first time, incorporating aspects of the physical problem as previously studied by authors Woltjer, Mouschovias, and others, and presenting a new application of recently developed variational methods, extending their previous applications from fluid dynamics and terrestrial plasma problems to the present situation. In this approach the problem is formulated and solved as a non-linear, free-boundary problem in variational form with linear and non-linear constraints. The full extent of the matter is considered, from model construction, through construction of solutions to dimensionless PDE, to interpretation of results and their physical and mathematical meaning. Computational methods for calculating the physical and mathematical meaning. Computational methods for calculating the solutions are applied. The construction and justification of this solution method forms the basis for a constructive proof of the existence of solutions. A foundation is prepared for complete analytical investigations of the model or prototype problem, as well as for computational investigation of important realistic physical situations.

1a. Two model porous media and a precise drying protocol are employed in numerical simulation of fluid configurations in partially saturated porous media. Over a substantial range of partial saturation $N\sb{L},$ the liquid-vapor configurations are inhomogeneous on a length scale that is a sensitive function of $N\sb{L}.$ Several measures of the characteristics of fluid configurations are developed. Details of the fluid configurations are found in the study of $p(x;\ell,N\sb{L}),$ the probability density for a porous medium of partial saturation $N\sb{L}$ to contain a piece of material of size $\ell\sp{d}$ having partial saturation x. This probability density is a gauge of inhomogeneity and appears importantly in NMR studies of porous media. 1b. The equations governing magnetization evolution in fluid filled pore systems are developed. In pore systems with a range of pore sizes (and/or decay rates) the magnetization evolution is described exactly by a spectrum of decay rates, leading to multiple exponential decay. We study this spectrum of decay rates as a function of coupling strength between pores using perturbation theory, effective medium theory, and matrix diagonalization. The spectrum of decay rates evolves from the individual pore decay rate distribution, at zero coupling, to a delta function distribution, at infinite coupling. The effect of coupling between pores is important in NMR studies of temperature dependence of characteristic decay rates in porous media. 2. The equation of motion describing a borehole elastic system (BES) is studied in the form of a perturbation problem, i.e. as the sum of terms describing a model elastic system (MES) and terms describing the departure of the BES being studied from the MES. The MES is chosen such that the departure terms in the BES equation of motion are small. The Green tensor for an infinite, azimuthally symmetric borehole is developed. As an illustration of the perturbation technique, the consequences of a mudcake layer on the borehole wall are explored. Comparison of first order perturbation calculations confirms the perturbation method is a valid technique for probing small changes to a model elastic system.