On the role of the chaotic velocity in relativistic kinetic theory

In this paper we revisit the concept of chaotic velocity within the context of relativistic kinetic theory. Its importance as the key ingredient which allows to clearly distinguish convective and dissipative effects is discussed to some detail. Also, by addressing the case of the two component mixture, the relevance of the barycentric comoving frame is established and thus the convenience for the introduction of peculiar velocities for each species. The fact that the decomposition of molecular velocity in systematic and peculiar components does not alter the covariance of the theory is emphasized. Moreover, we show that within an equivalent decomposition into space-like and time-like tensors, based on a generalization of the relative velocity concept, the Lorentz factor for the chaotic velocity can be expressed explicitly as an invariant quantity. This idea, based on Ellis' theorem, allows to foresee a natural generalization to the general relativistic case.Comment: 12 pages, 2 figure

Relaxation time for the temperature in a dilute binary mixture from classical kinetic theory

The system of our interest is a dilute binary mixture, in which we consider that the species have different temperatures as an initial condition. To study their time evolution, we use the full version of the Boltzmann equation, under the hypothesis of partial local equilibrium for both species. Neither a diffusion force nor mass diffusion appears in the system. We also estimate the time in which the temperatures of the components reach the full local equilibrium. In solving the Boltzmann equation, we imposed no assumptions on the collision term. We work out its solution by using the well known Chapman-Enskog method to first order in the gradients. The time in which the temperatures relax is obtained following Landau's original idea. The result is that the relaxation time for the temperatures is much smaller than the characteristic hydrodynamical times but greater than a collisional time. The main conclusion is that there is no need to study binary mixtures with different temperatures when hydrodynamical properties are sought

Entropy Production in Relativistic Binary Mixtures

In this paper we calculate the entropy production of a relativistic binary mixture of inert dilute gases using kinetic theory. For this purpose we use the covariant form of Boltzmann's equation which, when suitably transformed, yields a formal expression for such quantity. Its physical meaning is extracted when the distribution function is expanded in the gradients using the well-known Chapman-Enskog method. Retaining the terms to first order, consistently with Linear Irreversible Thermodynamics we show that indeed, the entropy production can be expressed as a bilinear form of products between the fluxes and their corresponding forces. The implications of this result are thoroughly discussed

Oxigenação de águas em colunas de borbulhamento inclinadas com um sistema de anteparos perfurados

Apresenta-se um estudo teórico e experimental sobre transferência de oxigénio para água em colunas de borbulhamento inclinadas. Para permitir a absorção, instalou-se ao longo da coluna um sistema de anteparos perfurados igualmente espaçados. A inclinação variou entre 0º (vertical) e 60º. Desenvolve-se um modelo simples de transferência de massa considerando a coluna como uma série de “tanques” perfeitamente agitados e uma metodologia de análise que permite prever o perfil de concentrações numa coluna com qualquer número de anteparos, a partir dos valores de KLA (coeficiente de transferência de massa vezes a área interfacial) obtidos numa coluna idêntica com reduzido número de anteparos

Gas-liquid flow dispersion in a vertical pipe

The main purpose of this work was to analyse the transport f a solute dissolved in a flowing liquid in upward direction at low velocity along a vertical column, in the bottom of which slugs are injected. These experiments were carried out in a column with an internal diameter of 19 mm and height of 344.2 cm. Liquid flowrates of 1.0, 2.5 and 5.5 cm3/s were utilized, and an enlarged variety of gas flowrates were injected; in these conditions the slugs were normally formed at a frequency between 0.78 and 88.1 s-1. The scientific techniques used in this study based on the measurement, at the top of the column, of a tracer solution injected in its bottom. A simplified physical model was developed to explain the results obtained, which was based on two hypotheses: (i) the flow of the liquid between two slugs is laminar, being the respective profile of velocity approximate to the Poiseuille law; (ii) the stirring action provoked by each slug in the liquid is limited to a small region, the wake of slug, which can be taken as a “perfectly mixed tank”. One of the most relevant conclusions derived from this work and which at first analysis would appear paradoxical, is that, it is possible to proceed in such a way that the bubbling of gas through a liquid will provoke less dispersion in the residence time of liquid than which would be obtained in the absence of the introduction of gas

Mass transfer models for oxygen-water co-current flow in vertical bubble columns

The present work reports a theoretical and experimental study of mass transfer for oxygen-water co-current flow in vertical bubble columns. The axial dispersion of liquid phase was also studied. Experiments were carried out in a 32 mm internal diameter and 5.35 and 5.37 m height columns. The superficial liquid velocity ranged from 0.3 to 0.8 m/s and volumetric flow rate ratio of gas to liquid ranged from 0.015 to 0.25. Mathematical models were developed to predict concentration of gas dissolved in the liquid as function of different physical and dynamic variables for two-phase cocurrent downflow and upflow. We obtained for the ratio of the liquid side mass transfer coefficient to initial bubbles radius, kL/r0=0.12 s-1

In Vitro Blood Flow Behaviour in Microchannels with Simple and Complex Geometries

Over the years, various experimental methods have been applied in an effort to understand the blood flow behaviour in microcirculation. The development of optical experimental techniques has contributed to obtain possible explanations on the way the blood flows through microvessels. In recent years, due to advances in computers, optics, and digital image processing techniques, it has become possible to combine a conventional particle image velocimetry (PIV) system with an inverted microscope and consequently improve both spatial and temporal resolution. The present review outlines our most relevant studies on the flow properties of blood at a microscale level by using current micro-PIV and confocal micro-PIV techniques. In this chapter, our recent studies about in vitro blood flow behaviour in microchannels both in straight and with complex geometries are presented. In straight microchannels we present some phenomena such as Fahraeus effect and Fahraeus-Lindqvist effect, the flow of particles and red blood cells (RBCs) in diluted suspensions, the flow of RBCs in concentrated suspensions, the cell-free layer and sedimentations effects. The most recent studies in blood flow through complex geometries such as bifurcations, confluences and stenosis are also reviewed. By using a chromatographic method, the flow of RBC s through a network of microcapillaries is presented.The authors acknowledge the financial support provided by: PTDC/SAUBEB/ 108728/2008, PTDC/SAU-BEB/105650/2008 and PTDC/EME-MFE/099109/2008 from the FCT (Science and Technology Foundation) and COMPETE, Portugal