Ensemble phase averaged equations for bubbly flows

A system of averaged equations describing the motion of a mixture of spherical compressible bubbles in an inviscid liquid is derived by the ensemble?averaging method introduced in an earlier paper [Zhang and Prosperetti, J. Fluid Mech. 267, 185 (1994)]. The averaging procedure introduces new terms in the equations, among which a contribution to the liquid stress tensor is of special interest. An extension of the well?known Rayleigh–Plesset equation to the case of bubbles interacting with the flow is also found. The general system of equations is closed in a rigorous manner in the dilute limit generalizing and correcting earlier averaged equations models. The results are illustrated by considering the problem of linear pressure wave propagation in a nonuniform bubbly liquid. Gradients of the bubble concentration are shown to dampen or amplify the wave strength

The Added Mass, Basset, and Viscous Drag Coefficients in Nondilute Bubbly Liquids Undergoing Small-Amplitude Oscillatory Motion

The motion of bubbles dispersed in a liquid when a small?amplitude oscillatory motion is imposed on the mixture is examined in the limit of small frequency and viscosity. Under these conditions, for bubbles with a stress?free surface, the motion can be described in terms of added mass and viscous force coefficients. For bubbles contaminated with surface?active impurities, the introduction of a further coefficient to parametrize the Basset force is necessary. These coefficients are calculated numerically for random configurations of bubbles by solving the appropriate multibubble interaction problem exactly using a method of multipole expansion. Results obtained by averaging over several configurations are presented. Comparison of the results with those for periodic arrays of bubbles shows that these coefficients are, in general, relatively insensitive to the detailed spatial arrangement of the bubbles. On the basis of this observation, it is possible to estimate them via simple formulas derived analytically for dilute periodic arrays. The effect of surface tension and density of bubbles (or rigid particles in the case where the no?slip boundary condition is applicable) is also examined and found to be rather small

The effect of inter-particle contact time in granular flows -- A network theory

In a kinetic theory, it is usually assumed that the time duration of particle collision is vanishingly small and only binary collisions are considered. The validity of these assumptions depends on the ratio of collision time to mean free flight time. If this ratio is small, the kinetic theory description is appropriate. In a dense system, however, this ratio is usually large, and the dynamics of the multi-particle interactions have to be considered. For instance, during a collision, the contacting pair usually has a relative tangential velocity that causes a change in the direction of rebound. This implies a dependence of the granular stress on the vorticity of the mean flows field. Due to the inherent energy dissipation in a particle collision, and the consistent rearrangement of particles, there are relaxation times associated with them. In a binary collision, this energy dissipation is represented by coefficient of restitution. In a dense granular system, multi-particle interactions occur frequently. The energy dissipation and system relaxation have to be studied by the consideration of the dynamics in the duration of particle interaction and cannot be represented by a single coefficient of restitution. In this case, the relaxation times must be introduced explicitly. By modification of the network theory for rubber material, a constitutive model for dense granular material is developed based on the dynamics of multi-particle interaction. The finite particle interaction time and system relaxation times are considered

Period multiplication and chaotic phenomena in atmospheric dielectric-barrier glow discharges

In this letter, evidence of temporal plasma nonlinearity in which atmospheric dielectric-barrier discharges undergo period multiplication and chaos using a one-dimensional fluid model is reported. Under the conditions conducive for chaotic states, several frequency windows are identified in which period multiplication and secondary bifurcations are observed. Such time-domain nonlinearity is important for controlling instabilities in atmospheric glow discharges

Rigidity percolation by next-nearest-neighbor bonds on generic and regular isostatic lattices.

Theoretical Physic

First normal stress difference and crystallization in a dense sheared granular fluid

The first normal stress difference (${\mathcal N}_1$) and the microstructure in a dense sheared granular fluid of smooth inelastic hard-disks are probed using event-driven simulations. While the anisotropy in the second moment of fluctuation velocity, which is a Burnett-order effect, is known to be the progenitor of normal stress differences in {\it dilute} granular fluids, we show here that the collisional anisotropies are responsible for the normal stress behaviour in the {\it dense} limit. As in the elastic hard-sphere fluids, ${\mathcal N}_1$ remains {\it positive} (if the stress is defined in the {\it compressive} sense) for dilute and moderately dense flows, but becomes {\it negative} above a critical density, depending on the restitution coefficient. This sign-reversal of ${\mathcal N}_1$ occurs due to the {\it microstructural} reorganization of the particles, which can be correlated with a preferred value of the {\it average} collision angle $\theta_{av}=\pi/4 \pm \pi/2$ in the direction opposing the shear. We also report on the shear-induced {\it crystal}-formation, signalling the onset of fluid-solid coexistence in dense granular fluids. Different approaches to take into account the normal stress differences are discussed in the framework of the relaxation-type rheological models.Comment: 21 pages, 13 figure

Electron Localization in a 2D System with Random Magnetic Flux

Using a finite-size scaling method, we calculate the localization properties of a disordered two-dimensional electron system in the presence of a random magnetic field. Below a critical energy $E_c$ all states are localized and the localization length $\xi$ diverges when the Fermi energy approaches the critical energy, {\it i.e.} $\xi(E)\propto |E-E_c|^{-\nu}$. We find that $E_c$ shifts with the strength of the disorder and the amplitude of the random magnetic field while the critical exponent ($\nu\approx 4.8$) remains unchanged indicating universality in this system. Implications on the experiment in half-filling fractional quantum Hall system are also discussed.Comment: 4 pages, RevTex 3.0, 5 figures(PS files available upon request), #phd1

Off-Diagonal Long Range Order and Scaling in a Disordered Quantum Hall System

We have numerically studied the bosonic off-diagonal long range order, introduced by Read to describe the ordering in ideal quantum Hall states, for noninteracting electrons in random potentials confined to the lowest Landau level. We find that it also describes the ordering in disordered quantum Hall states: the proposed order parameter vanishes in the disordered ($\sigma_{xy}=0$) phase and increases continuously from zero in the ordered ($\sigma_{xy}=e^2/h$) phase. We study the scaling of the order parameter and find that it is consistent with that of the one-electron Green's function.Comment: 10 pages and 4 figures, Revtex v3.0, UIUC preprint P-94-03-02

Very long optical path-length from a compact multi-pass cell

The multiple-pass optical cell is an important tool for laser absorption spectroscopy and its many applications. For most practical applications, such as trace-gas detection, a compact and robust design is essential. Here we report an investigation into a multi-pass cell design based on a pair of cylindrical mirrors, with a particular focus on achieving very long optical paths. We demonstrate a path-length of 50.31 m in a cell with 40 mm diameter mirrors spaced 88.9 mm apart - a 3-fold increase over the previously reported longest path-length obtained with this type of cell configuration. We characterize the mechanical stability of the cell and describe the practical conditions necessary to achieve very long path-lengths

Effects of Spartina alterniflora invasion on distribution of Moerella iridescens in a tidal flat of western Pacific Ocean

The invasion of Spartina alterniflora significantly affected the local ecosystem of Western Pacific Ocean where Moerella iridescens lives. Five patches with different invasion stages of S. alterniflora were selected and the influence on distribution of M. iridescens was studied on the coast of Wenzhou Bay, China in 2007. The aggregated distribution pattern was proved by using Taylor's power regression and Iwao's plot regression methods (p<0.001). The densities were significantly affected by the factors of S. alterniflora invasion stage and season (p<0.001), but no significant effect of interaction (p=0.805) occurred. M. iridescens mainly clumped in the habitats of no invasion and initial invasion of S. alterniflora was in the high tidal zone, and the lowest density was recorded where complete invasion occurred. The densities were larger in warmer than in cooler seasons. There were significant positive correlations among the average densities in seasons. Density variation must be the response of M. iridescens to the environment, including S. alterniflora invasion stage, temperate stress and interspecific associations