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.

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.

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.