Single and Two-Phase Flows on Chemical and Biomedical Engineering

3D structured materials, especially monoliths have been used for decades in the removal of pollutants in automotive and stationary stations, bulk chemical production and so on. Their applications are expected to rise due to the ever growing concern of global warming. Despite the clear advantages of using materials with a well defined 3D structure, their implementation is often hindered by the absence of detailed information of what happens inside the channels. SpaciMS is a minimum invasive spatially resolved capillary-inlet mass spectroscopy system, often combined with other analytical probes such as thin thermocouples. The probes can be positioned at multiple axial and/or radial locations within the working monolith, enabling for the generation of detailed spatio-temporal maps of the reactions and breakthrough fronts. This antagonist approach from the conventional ‘end-pipe’ analysis which can be often misleading to describe the internal behaviour of structured materials, offers the possibility to test the validity of a pre-conceived kinetic and/or hydrodynamic model instead of the common occurrence of fitting a model from ‘end-pipe’ measurements.

One of de most important environmental problems nowadays is the abatement of NOx emissions. NOx are involved in photochemical reactions that produce smog and acid rain, and (together with CO2, CH4 and H2O), take part in the greenhouse effect. One of the most efficient ways to reduce NOx emissions is Selective Catalytic Reduction (SCR). In SCR NOx are reduced to N2 and H2O by reaction with ammonia or urea. Ammonia is most commonly used and is the reactant considered in this study. Conventionally, this reaction is performed in steady fixed bed reactors, but there are other reactor types that can be used, including those operating in dynamic conditions, such as Reverse Flow Reactors (RFR). RFR consist of a fixed bed catalytic reactor in which the direction of the inlet flow is reversed periodically. Among other advantages, the periodic change in the inlet flow allows autothermal operation even for weakly exothermal reactions. This study is devoted to the modeling a monolithic RFR used for NH3-SCR. An unsteady one-dimensional heterogeneous model has been developed for simulating the reactor behaviour. The model is formed by differential equations corresponding to conservation equations, applied separately to the gas and solid phases, and algebraic equations used for estimating the physical and transport properties. The model considers internal and external mass and heat transfer resistances, and axial dispersion. Experimental validation of the model allows its use for the optimization of the most important variables that affect the process.

The accurate description of flow in nano-scale pores or channels is very important for the reliable design of materials and processes in the areas of MEMS, mesoporous media, and vacuum technologies. Use of classical flow equations fails in this regime since the continuum assumption is not valid. This is due to the fact that the mean free path is comparable to the characteristic dimensions of the system, and rarefaction effects dominate the process. Such a difficulty arises notably in the intermediate Knudsen number regime (Kn=0.1 to 10), commonly referred to as the “transition” flow regime. To remedy this, slip flow conditions have been adopted in the literature, following the simple first-order approach of the velocity near the walls given by Maxwell, and extended to higher-order treatments. Alternatively, direct deterministic or stochastic atomistic and mesoscopic techniques have been employed for the flow description, which solve the Boltzmann or the Burnett equations and use kinetic theory approaches pertinent to this flow regime. A description of recent advances in simulation techniques, namely, the “continuum” slip approaches, and some direct mesoscopic techniques are presented in this chapter. Illustrative simulation results of permeability and viscosity coefficients in mesoporous media using the DSMC and LB methods are also given, followed by comparisons with classical continuum formulations.

The first mixing studies on chemical reactor engineering date from approximately fifty years ago. There are several reviews on mixing that are generally focused on a specific topic, such as chaotic mixing. This chapter presents an overall picture of the evolution on mixing science and its impact on chemical reactor engineering. The works reviewed in this chapter are single-phase flows although some of the concepts presented in this chapter are also applied to multiphase reactors.

In studies of a turbulent flow with mixing-sensitive chemical reactions, the equations for the PDF of scalars (temperature and mixture component concentrations) are applied in combination with the conventional turbulence models that contain the equations for statistical moments. The PDF method advantage is an accurate representation of the chemistry influence in model equations. However, to calculate correlations responsible for an averaged chemical reaction rate, one needs a more thorough description of micromixing. As micromixing is governed by the small-scale flow structure, the latter can be considered statistically homogeneous. So, the well-developed homogeneous turbulence theory is used for closing the micromixing models. Just the adequate description of micromixing connected not only with the successful modeling of the chemistry influence, but first with a reasonable analysis of the entire mixing process, remains a stumbling block for the PDF method. This problem has received particular attention in the present work where the problem on mixing with chemical reacting in the homogeneous turbulent flow is stated by means of both the method of statistical moments for turbulence parameters and the mixture fraction PDF method for closing unknown correlations responsible for chemical reacting. Several known micromixing models (LSME/IEM, Langevin, multi-zone PDF) applicable in the PDF transfer equation are compared to explain their influence on an averaged reaction rate to be calculated.

Wastewater treatment modelling combining hydrodynamics, mass transfer and kinetic issues remains one of the major goals of chemical engineering. The reactor design is frequently based on Activated Sludge Models (ASM) that describe the biological processes in an Activated Sludge (AS) process. The ASM are generally implemented on ideal models of chemical reactors that do not account for the actual hydrodynamics of the reactor. Nowadays, it is possible to obtain hydrodynamic information of an AS tank from computational fluid dynamic (CFD) simulations that provide information about the mass transfer in the flow field of the AS tank and enable determining the residence time distribution (RTD). This chapter focuses on the use of CFD data coupled to the state-of-the-art ASM1, and resumes the work developed by many researchers on this issue. The influence of the RTD on the results of the simulations using ASM1, is analyzed from the simulations of the ASM1 using various reactor models. A procedure is proposed for the coupling of the CFD simulations information with the ASM1 biological model.

Hydrogenation of vegetable oils is an important process in the food industry because of its widespread application to produce margarines, shortenings, and other food components. Supercritical technology has proven to be a reliable alternative to conventional hydrogenation process because not only the trans isomer levels can be reduced, but also offers a clean, economic and environmental friendly process. Computational Fluid Dynamics (CFD) modeling applied to the supercritical hydrogenation reaction can be useful in visualizing and understanding the mass transfer phenomena involved. CFD is applied to the study of the catalytic hydrogenation of sunflower oil in the presence of a supercritical solvent. A mix of sunflower oil, hydrogen and supercritical propane (used as a solvent) is the flowing fluid. Their transport properties at high pressure are incorporated within a CFD commercial code in order to estimate them online within the simulation process. A 2D CFD model of a single Pd-based catalyst pellet is presented. Intra-particle and surface concentration profiles and surface mass fluxes for all species present in the mixture (oil triglycerides and hydrogen) are obtained and compared against experimental results. Different temperatures, flow velocities and particle sizes are studied and external and internal mass transfer phenomena are analyzed. External mass transfer coefficients for hydrogen and oil triglycerides are obtained and a correlation for estimating them is presented.

The present work describes the mass transfer process between a moving fluid and a soluble solid mass (a sphere, a cylinder or a plane surface aligned with the flow, a cylinder in cross-flow, a prolate spheroid and a oblate spheroid) buried in a packed bed of small inert particles with uniform voidage. Numerical solutions of the partial differential equations describing solute mass conservation were undertaken (for solute transport by both advection and diffusion) to obtain the concentration field in the vicinity of the soluble surface and the mass transfer flux was integrated to give the Sherwood number as a function of the relevant parameters (e.g., Peclet number, Schmidt number, aspect ratio of the soluble mass). Mathematical expressions are proposed that describe accurately the dependencies found. The solutions of these problems are useful in the analysis of a variety of physical situations, as in the analytical models of continuous injection of solute at a point source, in a uniform stream, to estimate the distance from the “contaminant source” beyond which the levels of contaminant are expected to fall below some safe limit.

The increasing necessity for use of synthetic polymer products, such as for production of packaging, parts of appliances, electronics, cars, biomaterials for medical applications, etc., has led to the polymer industry to seek reduction of waste and increase product quality and productivity. Consequently, a better understanding of how the rheological properties of polymers affect their processing and final product quality is of great importance. In order to obtain faster results with less cost, the studies of modeling and simulation of polymer processing are increasing every day. This chapter aims to describe new tools for CFD simulations of viscoelastic fluids, implemented in the OpenFOAM CFD package due to advantages offered by this software, such as the possibility to use multigrid techniques and data processing parallelization, besides being a free software and open source. The constitutive models of Maxwell, UCM, Oldroyd-B, White-Metzner, Giesekus, Leonov, FENE-P, FENE-CR, linear and exponential PTT, Pom-Pom, XPP and DCPP were included in the general multimode form. In order to validate the developed solver, comparisons with numerical and experimental results from literature were carried out. The results were satisfactory giving credibility to the implemented solver and ensure the availability of a powerful tool for the study of viscoelastic fluids to be used both in academia and in industry. An extension of this tool, used for analysis of free-surface viscoelastic fluid flows using the VOF methodology, is also presented. The die swell experiment, a classical flow phenomenon used in the rheology literature to present the concept of viscoelastic effects, was also simulated. The results obtained using Giesekus model showed the great potential of the developed formulation, once all phenomena observed experimentally were reproduced in the simulations.

The generation of flow configuration (design, shape, structure, patterns, rhythms) is a phenomenon that occurs across the board, in animate and inanimate flow systems. Scientists have struggled to understand the origins of this phenomenon. Among the configurations, tree-shaped structures dominate the design of natural and man-made flow systems. Why are they so important? Is there a physics principle from which their configuration can be deduced?

Constructal theory, conceived by Adrian Bejan, is the view that the generation of configuration in nature is a universal phenomenon, which is covered by a law of physics-the constructal law. This chapter addresses the generation of tree-shaped design in the light of constructal theory. First, we briefly review the constructal theory that is applicable to animate and inanimate flow systems. Next, we review the studies that are focused on the constructal view of tree-shaped flow structures. The constructal theory presented in this chapter introduces a new paradigm that is universally applicable in nature, engineering and social sciences.

This paper presents a combined approach to study the impact of the structure of cellular materials on their transport properties. This work is based on the use of the morphological 3D analysis software (iMorph), to precisely characterize the geometry of cellular solids, extensive experimental characterization at sample scale and numerical simulation of heat and mass transfer at pore scale. With these approaches, and the study on a wide range of metallic foams, we identify the geometrical relevant criteria for the single and two-phase flow properties understanding.

Conventional ‘single point’ spectroscopic techniques have been very convenient in helping to understand underlying phenomena in gas-solid processes, leading to concepts that rely on pseudo-homogeneous descriptions. These concepts, however, are either not sufficiently valid at different spatial scales, or mature enough to be able to describe local events since they use averaged profiles of concentration, temperature and packing structure. Nevertheless, spatially-resolved optical techniques are increasingly cited due to developments in tunable lasers, 2D array detectors and communication technology. Optical techniques allow experiments to be performed nonintrusively at high spatiotemporal resolution. The present review presents two experimental procedures based on spatially-resolved near-infrared (NIR) imaging, in order to observe temperature and concentration maps in gas-solid packed beds subjected to effects of the entrance aspect ratio and non isothermal conditions. The first technique was applied to a gas-solid fluidized bed reactor with a low aspect ratio of tube to particle diameters (Dt/dp). The technique used NIR broadband light, interference optical filters centred on absorbing and non-absorbing wavelengths of water vapour, a Vidicon NIR camera and simple back-projection of collected images. The second technique was applied to water vapour flow in a packed bed filled with a hydrophobic resin, using a tunable diode laser, focal planar array detector and tomographic reconstruction procedure. By “looking into” a thin fluidized bed, the proposed technique allowed existing models of fixed bed reactors to be extended to pseudo-static bed operations. The technique was applied to ceria-silica reduction in a fluidized bed reactor, where radial profiles of water concentration allowed the distinction between surface and bulk reduction regimes of ceria-silica packing. The tomography technique however, which observes 3D spatially resolved imaging of temperature and water vapour concentration in packed beds, revealed cold and hot spots, concentration maps and flow dynamics in the core packed bed and in the vicinity of the wall. In addition, heat uptake from the wall and mass transfer between and inside resin particles were found to be strongly affected by local concentration, temperature and packing structure profiles.

This chapter summarizes various theoretical approaches for interfacial area modelling in two-phase flow studies. The interfacial area concentration is defined as the contact area between the two phases per unit volume of the two-phase mixture. As the surface available for mass, momentum and energy exchanges between the two phases, this quantity is of the utmost importance. Various approaches were developed for its modelling in the few last decades and we can classify these approaches mainly in two groups. The first group is based on the restrictive assumption of spherical particles (bubbles or droplets) and the interfacial area modelling is often based on an evolution equation for this quantity. This evolution equation can be derived from a Liouville- Boltzmann equation written for the distribution function of a quantity characterizing the size of the particle (currently its diameter or its volume). The second group is completely different and is based on local instantaneous evolution equations for pieces of interfaces and their orientation in the flow, defined by the unit normal vector. Here, the major assumption is the one of closed interfaces but the fluid particle shapes can be arbitrary. The two kinds of approaches involve an interfacial area balance equation, but they are different in their theoretical basis. The link between these two approaches is given in the context of spherical particles. In the more general context of anisotropic interfaces (i.e., arbitrary shapes), the interfacial area evolution equation is supplemented by additional evolution equations characterizing the interface anisotropy. Two possible mathematical formalisms are presented here: the first one is based on the concept of the interface anisotropy tensor introduced a long time ago in the study of liquid-liquid dispersions (e.g., polymer blends) and the second one is based on two equations for the averaged mean and Gaussian curvatures.

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, k_L/r₀=0.12 s^-1.

The hydrodynamics of gas-liquid bubble columns operated in the churnturbulent regime are studied by examining the liquid turbulence along the height of the bubble bed (based on chaotic and statistical methods). In the case of air-water and nitrogen-PSS8 systems based on comparison of the KE values along the height of the bubble bed it is shown that the degree of liquid turbulence (chaos) is stronger in the vicinity of the gas distributor and it increases again in the upper part of the reactor. These results help to understand better the occurrence of the circulation zones in the bubble bed. The work includes results from five different bubble columns (0.1, 0.16, 0.19, 0.38 and 0.8 m in inner diameter) equipped with porous or perforated plate distributor or cross sparger. The boundaries of the various flow regimes in different gasliquid systems are also identified. Five different liquids (tap water, Therminol LT, polyalphaolefin liquid (PSS8), 1-butanol and gasoline) and two different gases (nitrogen and air) are used. Different measurement techniques (Computer-Automated Radioactive Particle Tracking, Computed Tomography, Nuclear Gauge Densitometry, differential pressure and absolute pressure transducers) are employed. It is found that by means of the Kolmogorov entropy (KE) algorithm, average cycle time and the average absolute deviation can be identified the boundaries of chain-bubbling regime, bubbly flow regime, first and second transition regimes and coalesced bubble regimes (consisting of 4, 3, 2 and 1 regions). The results can be used for the preparation of flow regime maps.

Flotation is successfully applied in various processes, such as galvanic tailings purification, washing and lubricating liquids treatment, oil/water emulsions separation, etc. An interesting implementation appears to be using flotation as pretreatment in membrane separations. The prospective engineering approach for contaminated wastewaters treatment is combined membrane-electroflotation process.Membrane-electroflotation is a complex physico-chemical process taking place in “liquid-gas-solid” system, based on the hydrodynamic phenomena of gas-liquid streams. In case of membrane flotation the dependence of gas content on bubbling rate has been determined. There are two areas of dependence—at low gas content (5-17%), area I and at higher gas content (17-29%), area II. Based on the value of single bubble emersion rate calculated for every measured bubble diameter, an average volumetric single and group bubble emersion rate in membrane flotation was determined. In electroflotation the average radius of hydrogen bubbles increases from 20 microns to 90 microns depending on module’ height; and stationary distribution of bubbles is achieved upon 1-4 min. Hydrogen bubbles content versus the process time is characterized by the time of retard. At the same time the oxygen appears in electroflotation unit at the very beginning of the process without any retard time. Increase of hydrogen bubbles residence time in the upper sections of electroflotation module leads to rise of average radius and decrease of bubbles containing from 0.00525 to 0.00109.

Pulse Wave Velocity (PWV) is recognized by clinicians as an index of mechanical properties of human blood vessels. This concept is based on the Moens- Korteweg equation, which describes the PWV in ideal elastic tubes. However, measured PWV of real human blood vessels cannot be always interpreted by the Moens-Korteweg equation because this formula is not precisely applicable to living blood vessels. It is important to understand the wave propagation in blood vessels for a more reliable diagnosis of vascular disease. In this study, we modeled uniform arteries in a threedimensional coupled fluid-solid interaction computational scheme, and analyzed the pulse wave propagation. A commercial code (Radioss, Altair Engineering) was used to solve the fluid-solid interactions. We compared the regional PWV values obtained from various computational models with those from the Moens-Korteweg equation, and discuss the accuracy of our computation. The PWV values from the thick-walled artery model are lower than those from the Moens-Korteweg equation. Nevertheless, the differences are less than 7% up to 12 m/s of the PWV, indicating these computational methods for the PWV analysis are accurate enough to evaluate its value quantitatively.

As blood circulates through the arterial tree, the flow and pressure pulse distort. Principal factors to this distortion are reflections from arterial bifurcations and the viscous character of the blood flow. Both of them are listed and expounded in the literature. Nevertheless, apart from direct numerical simulations, based on Navier-Stokes like equations, where the nonlinearities of inertial effects are taken into account, there isn’t any qualitative, as well as quantitative, analytical formula that explains their role in the distortion of the pulse. We derive an analytical quasi-linear formula, which emanates from a generalized Bernoulli’s equation for a linear viscoelastic flow in a quasi-elastic cylindrical vessel. We report that close to the heart (e.g., aortic arc), convection effects related to the change in the magnitude of the velocity of blood dominate the alteration of the shape of the pressure pulse, while at remote sites of the vascular tree, convection of vorticity, related to the change in the direction of the velocity of blood with respect to a mean axial flow, prevails. Comparison between the an-harmonic theory and related pressure measurements is also performed.

Wall shear rates and pressure developed in blood vessels play an important role on the development of some clinical problems such as atherosclerosis and thrombosis. In the present work, blood flow behaviour was numerically studied in simplified domains and several relevant local properties were determined. We believe that the obtained results will be useful in the interpretation of some phenomena associated to some clinical problems. To describe the rheological behaviour of blood, three constitutive equations were usedconstant viscosity, power-law and Carreau model. Numerical predictions for the blood flow in stenosed channels were in good agreement with analytical results, indicating that the computational model used to describe the studied problem is reliable. Pressure attains maximum values close to the top of the atheroma and shear rates achieved maximum values at the walls located in the nearby of the atheroma. It was also observed that, with the studied flows, the impact of the non-Newtonian behaviour of the blood on the velocity profiles was not significant. This observation can be explained by the magnitude of the obtained shear rates.

Over the years, various experimental methods have been applied in an effort to understand the blood flow behavior in microcirculation. Most of our current knowledge in microcirculation is based on macroscopic flow phenomena such as Fahraeus effect and Fahraeus-Linqvist effect. The development of optical experimental techniques has contributed to obtain possible explanations on the way the blood flows through microvessels. Although the past results have been encouraging, detailed studies on blood flow behavior at a microscopic level have been limited by several factors such as poor spatial resolution, difficulty to obtain accurate measurements at such small scales, optical errors arisen from walls of the microvessels, high concentration of blood cells, and difficulty in visualization of results due to insufficient computing power and absence of reliable image analysis techniques. However, 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 the most relevant studies on the flow properties of blood at a microscale level by using past video-based methods and current micro-PIV and confocal micro-PIV techniques. Additionally the most recent computational fluid dynamics studies on microscale hemodynamics are also reviewed.

Microfluidics is changing the way modern biology is performed and is becoming a key technology in the field of micro arrays, DNA sequencing, and Lab on a Chip applications. Microsystems, being compact in size, disposable, and ensuring high speed of analysis using decreased sample volumes, allow to replace large-scale conventional laboratory instrumentation with miniaturized devices, reducing hardware costs, and assuring low reagent consumption and faster analysis. At the microscale mixing of species becomes crucial to i) improve the effectiveness of and ii) speed up chemical reactions, but it is often critical to be achieved, since microfluidics is characterized mainly by very low Reynolds flows, and cannot take advantage of turbulence in order to enhance mixing. Hence, given that diffusion-driven mixing in very low Reynolds number flow regimes is characterized by long time scales, methods for enhancing the rate of the mixing process are essential in microfluidics. In order to enhance mixing, several techniques have been developed. In general, mixing strategies can be classified as either active or passive, according to the operational mechanism. Active mixers employ external forces in order to perform mixing, so that actuation system must be embedded into the microchips. On the contrary, passive mixers avoid resorting to external electrical or mechanical sources by exploiting characteristics of specific flow fields in microchannel geometries to mix species, offering the advantage to be easy to be produced and integrated. In this work, a survey of the passive micromixing solutions currently adopted is presented. In detail, the most widely used microchannel geometries and the metrics used to quantify mixing effectiveness in microfluidic applications are discussed.

Vascular endothelial cells are constantly stimulated by blood flow-induced shear stress throughout the vasculature and respond by changing morphology and cytoskeletal structures as well as by modulating cell physiological functions. In particular, since endothelial cell responses to fluid shear stress have been implicated in the localization of atherosclerosis, the effects of fluid shear stress on endothelial cell morphology and functions have been exclusively studied. In fact, previous observations have given preferential localization of lipid accumulation in atherosclerosis in the arterial tree, such as branching and curved regions where blood flow is unsteady and spatially and temporally altered. So far, a lot of efforts have been made to study endothelial mechanotransduction to flow, indicating the fact that after applying fluid shear stress to endothelial cell monolayer, cells exhibit marked elongation and orientation in the direction of flow. It is now accepted that morphological changes of endothelial cells are closely associated with modulation of cell physiology and pathology. The need for experimental techniques for studying endothelial responses to flow has lead to development of different types of flow chambers. Conventional flow chambers include a cone-and-plate flow chamber and a parallel-plate flow chamber, both of which provide steady, fully-developed laminar flow. Furthermore, in order to provide non-steady flow and disturbed flow, novel flow chambers have been developed, such as a tapered channel and an obstacle-included channel. More recently, microfluidic flow chambers have emerged with a great potential for a high throughput analysis. The purpose of this review is to first summarize many types of flow chambers that apply fluid shear stress onto a monolayer of endothelial cells. Next, experimental studies on endothelial cell responses to fluid shear stress are highlighted, focusing on changes in cell morphology associated with cytoskeletal remodeling.

An investigation to measure the flow behavior of magnetic nanoparticles through a 100μm microchannel is conducted. The magnetic field is applied externally by a permanent magnet and by using a micro-PTV system it was possible to measure the flow behavior of magnetic nanoparticles at different flow rates and magnetic fields through a 100μm glass capillary. A strong dependence on both magnetic and hydrodynamic force is observed on the nanoparticles fluidic paths. Based on these in vitro studies, important parameters and issues that require further understanding and investigation are point out.

Intracranial aneurysms are local dilations of the arterial wall which have a very high morbidity rate if they rupture. Although the mechanism initiation, growth, and rupture of intracranial aneurysms are still unknown yet, it is believed to be closely related to both biosolid and biofluid mechanics. Therefore, a multi-physical model is needed to study the pathophysiology of intracranial aneurysms. In this study, we introduce a numerical model on the development of intracranial aneurysms considering the interaction between fluid and structure interaction. The blood flow is considered to be incompressible, Newtonian, and laminar. The vessel wall is considered to be elastic and isotropic. The coupling between the structural and fluid domain is performed using a two-way weak coupling method. Three general shapes are adopted in this study, namely a straight vessel, a curved vessel, and a vessel with bifurcations. They represent vessel geometries that are most typical to the cerebral vasculature. The numerical model is a "rule-base" one in a sense that different kinds of rules can be tested. In our study, we adopt the high wall shear stress hypothesis as a cause for aneurysm initiation and development. A threshold value is used for the wall shear stress. It is shown that aneurysm initiation and development can be realized using our numerical model. And the influence of WSS threshold, the Reynolds number and some other parameters are also discussed.