Numerical simulation of small bubble-big bubble-liquid three-phase flows

Numerical simulations of the small bubble-big bubble-liquid three phase heterogeneous flow\ud in a square cross-sectioned bubble column were carried out with the commercial CFD\ud package CFX-4.4 to explore the effect of superficial velocity and inlet dispersed phase\ud fractions on the flow patterns. The approach of Krishna et al. (2000) was adopted in the\ud Euler-Euler framework to numerically simulate the gas-liquid heterogeneous flow in bubble\ud columns. On basis of an earlier study (Zhang et al. 2005), the extended multiphase k - ε\ud turbulence model (Pfleger and Becker, 2001) was chosen to model the turbulent viscosity in\ud the liquid phase and implicitly account for the bubble-induced turbulence. The obtained\ud results suggest that, first of all, the extended multiphase k - ε turbulence model of Pfleger and\ud Becker (2001) is capable of capturing the dynamics of the heterogeneous flow. With\ud increasing superficial velocity, the dynamics of the flow, as well as the total gas hold-up\ud increases. It is observed that with increasing inlet phase fraction of the big bubbles, the total\ud gas holdup decreases while the dynamic nature of the flow increases, which indicates that the\ud small bubble phase mainly determines the total gas holdup while the big bubble phase\ud predominantly agitates the liquid

Detailed modeling of hydrodynamics mass transfer and chemical reactions in a bubble column using a discrete bubble model

A 3D discrete bubble model is adopted to investigate complex behavior involving hydrodynamics, mass transfer and chemical reactions in a gas¿liquid bubble column reactor. In this model a continuum description is adopted for the liquid phase and additionally each individual bubble is tracked in a Lagrangian framework, while accounting for bubble¿bubble and bubble¿wall interactions via an encounter model. The mass transfer rate is calculated for each individual bubble using a surface renewal model accounting for the instantaneous and local properties of the liquid phase in its vicinity. The distributions in space of chemical species residing in the liquid phase are computed from the coupled species balances considering the mass transfer from bubbles and reactions between the species. The model has been applied to simulate chemisorption of CO2 bubbles in NaOH solutions. Our results show that apart from hydrodynamics behavior, the model is able to predict the bubble size distribution as well as temporal and spatial variations of each chemical species involved

Detailed 3D modelling of mass transfer processes in two phase flows with dynamic interfaces

We developed a method that will enable us to determine mass transfer coefficients for a\ud large number of two phase flow conditions based on numerical simulation. A three-dimensional\ud direct numerical simulation based on the Front Tracking technique taking into account the mass\ud transfer process was chosen for this purpose. The dissolved species concentration in the liquid\ud phase is tracked using a scalar mass balance while the value of the concentration at the interface\ud is determined via an immersed boundary technique. In the present study, simulations are carried\ud out to investigate the effect of the bubble shape on the dissolved species concentration fiel

Optical control of solar sails using distributed reflectivity

The dynamics of solar sails with a variable surface reflectivity distribution are investigated. When changing the reflectivity across the sail film, which can be achieved using electro-chromic coatings, the solar radiation pressure forces and torques across the sail film can be controlled without changing the attitude of the spacecraft relative to the Sun and without using mechanical systems. The paper presents two approaches. First, a continuous reflectivity distribution is presented to control the sail attitude under the influence of, for example, gravity gradient torques in Earth orbit. The second approach assumes discrete on/o reflectivity regions across the surface. Both concepts of `optical reconfiguration' of solar sails enable a more flexible steering of the spacecraft and minimize actuation effort

Natural boundary for the susceptibility function of generic piecewise expanding unimodal maps

We consider the susceptibility function Psi(z) of a piecewise expanding unimodal interval map f with unique acim mu, a perturbation X, and an observable phi. Combining previous results (deduced from spectral properties of Ruelle transfer operators) with recent work of Breuer-Simon (based on techniques from the spectral theory of Jacobi matrices and a classical paper of Agmon), we show that density of the postcritical orbit (a generic condition) implies that Psi(z) has a strong natural boundary on the unit circle. The Breuer-Simon method provides uncountably many candidates for the outer functions of Psi(z), associated to precritical orbits. If the perturbation X is horizontal, a generic condition (Birkhoff typicality of the postcritical orbit) implies that the nontangential limit of the Psi(z) as z tends to 1 exists and coincides with the derivative of the acim with respect to the map (linear response formula). Applying the Wiener-Wintner theorem, we study the singularity type of nontangential limits as z tends to e^{i\omega}. An additional LIL typicality assumption on the postcritical orbit gives stronger results.Comment: LaTex, 23 pages, to appear ETD

Emotional dysfunction in schizophrenia spectrum psychosis: the role of illness perceptions

Background. Assessing illness perceptions has been useful in a range of medical disorders. This study of people with a recent relapse of their psychosis examines the relationship between illness perception, their emotional responses and their attitudes to medication.Method. One hundred patients diagnosed with a non-affective psychotic disorder were assessed within 3 months of relapse. Measures included insight, self-reported. illness perceptions, medication adherence, depression, self-esteem and anxiety.Results. Illness perceptions about psychosis explained 46, 36 and 34% of the variance in depression, anxiety and self-esteem respectively. However, self-reported medication adherence was more strongly associated with a measure of insight.Conclusions. Negative illness perceptions in psychosis are clearly related to depression, anxiety and self-esteem. These in turn have been linked to symptom maintenance and recurrence. Clinical interventions that foster appraisals of recovery rather than of chronicity and severity may therefore improve emotional well-being in people with psychosis. It might be better to address adherence to medication through direct attempts at helping them understand their need for treatment

Discrete bubble modeling of a wire-mesh bubble column reactor

Abstract only

Quantum Corrections to Fidelity Decay in Chaotic Systems

By considering correlations between classical orbits we derive semiclassical expressions for the decay of the quantum fidelity amplitude for classically chaotic quantum systems, as well as for its squared modulus, the fidelity or Loschmidt echo. Our semiclassical results for the fidelity amplitude agree with random matrix theory (RMT) and supersymmetry predictions in the universal Fermi golden rule regime. The calculated quantum corrections can be viewed as arising from a static random perturbation acting on nearly self-retracing interfering paths, and hence will be suppressed for time-varying perturbations. Moreover, using trajectory-based methods we show a relation, recently obtained in RMT, between the fidelity amplitude and the cross-form factor for parametric level correlations. Beyond RMT, we compute Ehrenfest-time effects on the fidelity amplitude. Furthermore our semiclassical approach allows for a unified treatment of the fidelity, both in the Fermi golden rule and Lyapunov regimes, demonstrating that quantum corrections are suppressed in the latter.Comment: 14 pages, 4 figure

Distinguishing step relaxation mechanisms via pair correlation functions

Theoretical predictions of coupled step motion are tested by direct STM measurement of the fluctuations of near-neighbor pairs of steps on Si(111)-root3 x root3 R30 - Al at 970K. The average magnitude of the pair-correlation function is within one standard deviation of zero, consistent with uncorrelated near-neighbor step fluctuations. The time dependence of the pair-correlation function shows no statistically significant agreement with the predicted t^1/2 growth of pair correlations via rate-limiting atomic diffusion between adjacent steps. The physical considerations governing uncorrelated step fluctuations occurring via random attachment/detachment events at the step edge are discussed.Comment: 17 pages, 4 figure

The gradient of potential vorticity, quaternions and an orthonormal frame for fluid particles

The gradient of potential vorticity (PV) is an important quantity because of the way PV (denoted as $q$) tends to accumulate locally in the oceans and atmospheres. Recent analysis by the authors has shown that the vector quantity \bdB = \bnabla q\times \bnabla\theta for the three-dimensional incompressible rotating Euler equations evolves according to the same stretching equation as for \bom the vorticity and \bB, the magnetic field in magnetohydrodynamics (MHD). The \bdB-vector therefore acts like the vorticity \bom in Euler's equations and the \bB-field in MHD. For example, it allows various analogies, such as stretching dynamics, helicity, superhelicity and cross helicity. In addition, using quaternionic analysis, the dynamics of the \bdB-vector naturally allow the construction of an orthonormal frame attached to fluid particles\,; this is designated as a quaternion frame. The alignment dynamics of this frame are particularly relevant to the three-axis rotations that particles undergo as they traverse regions of a flow when the PV gradient \bnabla q is large.Comment: Dedicated to Raymond Hide on the occasion of his 80th birthda