Hairpin vortex solution in planar Couette flow: a tapestry of knotted vortices

A numerical continuation method has been carried out seeking solutions for two distinct flow configurations, planar Couette flow (PCF) and laterally heated flow in a vertical slot (LHF). We found that the spanwise vortex solution in LHF identifies a new solution in PCF. The vortical structure of our new solution has the shape of a hairpin observed ubiquitously in high-Reynolds-number turbulent flow, and we believe this discovery may provide the paradigm for a hierarchical organization of coherent structures in turbulent shear layers.

Use of computational fluid dynamics in the design of bubble column reactors

Investigations into the modelling techniques that depict the transport of discrete phases (gas bubbles or solid particles) and model biochemical reactions in a bubble column reactor are discussed here. The mixture model was used to calculate gas-liquid, solid-liquid and gasliquid-solid interactions. Multiphase flow is a difficult phenomenon to capture, particularly in bubble columns where the major driving force is caused by the injection of gas bubbles. The gas bubbles cause a large density difference to occur that results in transient multi-dimensional fluid motion. Standard design procedures do not account for the transient motion, due to the simplifying assumptions of steady plug flow. Computational fluid dynamics (CFD) can assist in expanding the understanding of complex flows in bubble columns by characterising the flow phenomena for many geometrical configurations. Therefore, CFD has a role in the education of chemical and biochemical engineers, providing the examples of flow phenomena that many engineers may not experience, even through experimentation. The performance of the mixture model was investigated for three domains (plane, rectangular and cylindrical) and three flow models (laminar, k-e turbulence and the Reynolds stresses). mThis investigation raised many questions about how gas-liquid interactions are captured numerically. To answer some of these questions the analogy between thermal convection in a cavity and gas-liquid flow in bubble columns was invoked. This involved modelling the buoyant motion of air in a narrow cavity for a number of turbulence schemes. The difference in density was caused by a temperature gradient that acted across the width of the cavity. Multiple vortices were obtained when the Reynolds stresses were utilised with the addition of a basic flow profile after each time step. To implement the three-phase models an alternative mixture model was developed and compared against a commercially available mixture model for three turbulence schemes. The scheme where just the Reynolds stresses model was employed, predicted the transient motion of the fluids quite well for both mixture models. Solid-liquid and then alternative formulations of gas-liquid-solid model were compared against one another. The alternative form of the mixture model was found to perform particularly well for both gas and solid phase transport when calculating two and three-phase flow. The improvement in the solutions obtained was a result of the inclusion of the Reynolds stresses model and differences in the mixture models employed. The differences between the alternative mixture models were found in the volume fraction equation (flux and deviatoric stress tensor terms) and the viscosity formulation for the mixture phase.

Coalescence of secondary dispersions in packed beds

A study has been made of the coalescence of secondary dispersions in beds of monosized glass ballotini. The variables investigated were superficial velocity, bed depth, ballotini size and dispersed phase concentration. Equipment was designed to generate a toluene ln water dispersion with phase ratios from 0.1 - 1.0 v/v % and whose mean drop size was determined using a Coulter Counter. The coalesced drops were sized by photography and the mean diameter of the effluent drops was determined using a Malvern Particle Size Analyser. Previous models describing single phase flow in porous media are reviewed and it was found that the experimental data obtained in this study is best represented by the Carman-Kozeny equations. Relative permeability correlations were used to predict the saturation profiles across the bed from measured two phase pressure drop data. Theoretical comparison of drop capture mechanisms indicated that direct and indirect interception are predominant. The total capture efficiency for the bed can also be evaluated using Spielman and Fitzpatrick's correlation.The resulting equation is used to predict the initial, local drop capture rate in a coalescer. A mathematical description of the saturation profiles is formulated and verified by the saturation profiles obtained by relative permeability. Based on the Carman-Kozeny equation, an expression is derived analytically to .predict the two phase pressure drop using the parameters which characterise the saturation profiles. By specifying the local saturation at the inlet face for a given velocity and phase ratio, good agreement between experimental pressure drop data and the model predictions was obtained. An attempt to predict the exit drop size has been made using an analogy for flow through non cylindrical channels.

The separation of secondary oil-water dispersions in particulate beds

The literature relating to haze formation, methods of separation, coalescence mechanisms, and models by which droplets <100 μm are collected, coalesced and transferred, have been reviewed with particular reference to particulate bed coalescers. The separation of secondary oil-water dispersions was studied experimentally using packed beds of monosized glass ballotini particles. The variables investigated were superficial velocity, bed depth, particle size, and the phase ratio and drop size distribution of inlet secondary dispersion. A modified pump loop was used to generate secondary dispersions of toluene or Clairsol 350 in water with phase ratios between 0.5-6.0 v/v%.Inlet drop size distributions were determined using a Malvern Particle Size Analyser;effluent, coalesced droplets were sized by photography. Single phase flow pressure drop data were correlated by means of a Carman-Kozeny type equation. Correlations were obtained relating single and two phase pressure drops, as (ΔP2/μc)/ΔP1/μd) = kp Ua Lb dcc dpd Cine A flow equation was derived to correlate the two phase pressure drop data as, ΔP2/(ρcU2) = 8.64*107 [dc/D]-0.27 [L/D]0.71 [dp/D]-0.17 [NRe]1.5 [e1]-0.14 [Cin]0.26  In a comparison between functions to characterise the inlet drop size distributions a modification of the Weibull function provided the best fit of experimental data. The general mean drop diameter was correlated by: q_p q_p p_q /β      Γ ((q-3/β) +1) d qp = d fr  .α        Γ ((P-3/β +1 The measured and predicted mean inlet drop diameters agreed within ±15%. Secondary dispersion separation depends largely upon drop capture within a bed. A theoretical analysis of drop capture mechanisms in this work indicated that indirect interception and London-van der Waal's mechanisms predominate. Mathematical models of dispersed phase concentration m the bed were developed by considering drop motion to be analogous to molecular diffusion.The number of possible channels in a bed was predicted from a model in which the pores comprised randomly-interconnected passage-ways between adjacent packing elements and axial flow occured in cylinders on an equilateral triangular pitch. An expression was derived for length of service channels in a queuing system leading to the prediction of filter coefficients. The insight provided into the mechanisms of drop collection and travel, and the correlations of operating parameters, should assist design of industrial particulate bed coalescers.

Formation of droplets from the liquid wall film passing through the inlet port of a spark ignition engine

The available literature has been surveyed to determine the parameters affecting fuelling requirements of spark ignition engines and their relation to engine performance and emissions. Theories and experiment relating to two phase and multi-component flows have also been examined and the techniques employed in the measurement of droplet sizes and liquid wall films have been reviewed. Following preliminary steady flow visualisation experiments to examine the trajectories of droplets discharging from the valve port an extensive practical investigation of the spectrum of droplet sizes formed by the break up of the wall film has produced results which have been correlated in terms of the important fuel and airflow parameters. It is concluded that the Sauter mean diameter of droplets formed by the break up of the wall film will vary between 70 and 150 m, depending on the operating conditions of the engine. The spectra of droplet sizes measured show that a significant proportion of the total mass of the wall film breaks into drops which will be too large to burn completely and, by comparison with measurements of unburned hydrocarbon emissions from engines supplied with a homogeneous mixture of air and gaseous hydrocarbons, it is concluded that the droplets from the wall film are likely to increase emissions by 50%.

Formulation of immunomodulatory agents

Reversed-phase high-performance liquid chromatography procedures were developed for the analysis of pyrimidine-based drugs bropirimine and its derivatives (2-N-acetyl- and 2-N-propanoyl-) and for pyrimethamine and its 2/4- substituted derivatives (2, N-propanoyl and 2,4-N, N-dipropanoyl-) and its 6- substituted (methyl-, ethyl-, propyl- and isopropyl- carboxylates) analogues. Stability studies indicated that these derivatives were not sufficiently labile to act as potential prodrugs. Solubility-pH profiles were constructed from which the dissociation constants were calculated. The physicochemical properties of these compounds were studied and attempts were made to increase the poor aqueous solubility of bropirimine (35μg/mL) by prodrug synthesis, solvate formation (acetic acid, N, N-dimethylformamide and N-methylformamide) and the use of co-solvents and additives. The first two methods proved to be fruitless whereas the latter method resulted in an intravenous formulation incorporating 32mg/mL of bropirimine. An in-vitro method for the detection of precipitation was developed and the results suggested that by using low injection rates (< 0.24mL/min) and high mobile phase flow rates (> 500mL/hr) precipitation could be minimised. Differential scanning calorimetry showed that bropirimine debrominates in the presence of a number of additives commonly used in formulation work but the temperature at which this occurred were usually > 200oC. In-vitro work gave encouraging results for the possibility of rectal delivery of bropirimine but in-vivo work on rabbits showed considerable variations in the resulting plasma levels and pharmacokinetic parameters.

Gas-liquid-solid flow modelling in a bubble column

An alternative approach to the modelling of solid-liquid and gas-liquid-solid flows for a 5:1 height to width aspect ratio bubble column is presented here. A modified transport equation for the volume fraction of a dispersed phase has been developed for the investigation of turbulent buoyancy driven flows (Chem. Eng. Proc., in press). In this study, a modified transport equation has been employed for discrete phase motion considering both solid-liquid and gas-liquid-solid flows. The modelling of the three-phase flow in a bubble column was achieved in the following case: injecting a slug of solid particles into the column for 10 s at a velocity of 0.1 m s-1 and then the gas phase flow was initiated with a superficial gas velocity of 0.02 cm s-1. © 2003 Elsevier B.V. All rights reserved.

Shapes and Dynamics of Blood Cells in Poiseuille and Shear Flows

The dynamics, shape, deformation, and orientation of red blood cells in microcirculation affect the rheology, flow resistance and transport properties of whole blood. This leads to important correlations of cellular and continuum scales. Furthermore, the dynamics of RBCs subject to different flow conditions and vessel geometries is relevant for both fundamental research and biomedical applications (e.g drug delivery). In this thesis, the behaviour of RBCs is investigated for different flow conditions via computer simulations. We use a combination of two mesoscopic particle-based simulation techniques, dissipative particle dynamics and smoothed dissipative particle dynamics. We focus on the microcapillary scale of several μm. At this scale, blood cannot be considered at the continuum but has to be studied at the cellular level. The connection between cellular motion and overall blood rheology will be investigated. Red blood cells are modelled as viscoelastic objects interacting hydrodynamically with a viscous fluid environment. The properties of the membrane, such as resistance against bending or shearing, are set to correspond to experimental values. Furthermore, thermal fluctuations are considered via random forces. Analyses corresponding to light scattering measurements are performed in order to compare to experiments and suggest for which situations this method is suitable. Static light scattering by red blood cells characterises their shape and allows comparison to objects such as spheres or cylinders, whose scattering signals have analytical solutions, in contrast to those of red blood cells. Dynamic light scattering by red blood cells is studied concerning its suitability to detect and analyse motion, deformation and membrane fluctuations. Dynamic light scattering analysis is performed for both diffusing and flowing cells. We find that scattering signals depend on various cell properties, thus allowing to distinguish different cells. The scattering of diffusing cells allows to draw conclusions on their bending rigidity via the effective diffusion coefficient. The scattering of flowing cells allows to draw conclusions on the shear rate via the scattering amplitude correlation. In flow, a RBC shows different shapes and dynamic states, depending on conditions such as confinement, physiological/pathological state and cell age. Here, two essential flow conditions are studied: simple shear flow and tube flow. Simple shear flow as a basic flow condition is part of any more complex flow. The velocity profile is linear and shear stress is homogeneous. In simple shear flow, we find a sequence of different cell shapes by increasing the shear rate. With increasing shear rate, we find rolling cells with cup shapes, trilobe shapes and quadrulobe shapes. This agrees with recent experiments. Furthermore, the impact of the initial orientation on the dynamics is studied. To study crowding and collective effects, systems with higher haematocrit are set up. Tube flow is an idealised model for the flow through cylindric microvessels. Without cell, a parabolic flow profile prevails. A single red blood cell is placed into the tube and subject to a Poiseuille profile. In tube flow, we find different cell shapes and dynamics depending on confinement, shear rate and cell properties. For strong confinements and high shear rates, we find parachute-like shapes. Although not perfectly symmetric, they are adjusted to the flow profile and maintain a stationary shape and orientation. For weak confinements and low shear rates, we find tumbling slippers that rotate and moderately change their shape. For weak confinements and high shear rates, we find tank-treading slippers that oscillate in a limited range of inclination angles and strongly change their shape. For the lowest shear rates, we find cells performing a snaking motion. Due to cell properties and resultant deformations, all shapes differ from hitherto descriptions, such as steady tank-treading or symmetric parachutes. We introduce phase diagrams to identify flow regimes for the different shapes and dynamics. Changing cell properties, the regime borders in the phase diagrams change. In both flow types, both the viscosity contrast and the choice of stress-free shape are important. For in vitro experiments, the solvent viscosity has often been higher than the cytosol viscosity, leading to a different pattern of dynamics, such as steady tank-treading. The stress-free state of a RBC, which is the state at zero shear stress, is still controversial, and computer simulations enable direct comparisons of possible candidates in equivalent flow conditions.

Multi-physics modeling of aluminium reduction cells

Aluminium cells involve a range of complex physical processes which act simultaneously to provide a narrow satisfactory operating range. These processes involve electromagnetic fields, coupled with heat transfer and phase change, two phase fluid flow with a range of complexities plus the development of stress in the cell structure. All of these phenomena are coupled in some significant sense and so to provide a comprehensive model of these processes involves their representation simultaneously. Conventionally, aspects of the process have been modeled separately using uncoupled estimates of the effects of the other phenomena; this has enabled the use of standard commercial CFD and FEA tools. In this paper we will describe an approach to the modeling of aluminium cells which describes all the physics simultaneously. This approach uses a finite volume approximation for each of the phenomena and facilitates their interactions directly in the modeling-the complex geometries involved are addressed by using unstructured meshes. The very challenging issues to be overcome in this venture will be outlined and some preliminary results will be shown.

Hierarchical Forest Management Planning: A Bilevel Wood Supply Modelling Approach

Le processus de planification forestière hiérarchique présentement en place sur les terres publiques risque d’échouer à deux niveaux. Au niveau supérieur, le processus en place ne fournit pas une preuve suffisante de la durabilité du niveau de récolte actuel. À un niveau inférieur, le processus en place n’appuie pas la réalisation du plein potentiel de création de valeur de la ressource forestière, contraignant parfois inutilement la planification à court terme de la récolte. Ces échecs sont attribuables à certaines hypothèses implicites au modèle d’optimisation de la possibilité forestière, ce qui pourrait expliquer pourquoi ce problème n’est pas bien documenté dans la littérature. Nous utilisons la théorie de l’agence pour modéliser le processus de planification forestière hiérarchique sur les terres publiques. Nous développons un cadre de simulation itératif en deux étapes pour estimer l’effet à long terme de l’interaction entre l’État et le consommateur de fibre, nous permettant ainsi d’établir certaines conditions pouvant mener à des ruptures de stock. Nous proposons ensuite une formulation améliorée du modèle d’optimisation de la possibilité forestière. La formulation classique du modèle d’optimisation de la possibilité forestière (c.-à-d., maximisation du rendement soutenu en fibre) ne considère pas que le consommateur de fibre industriel souhaite maximiser son profit, mais suppose plutôt la consommation totale de l’offre de fibre à chaque période, peu importe le potentiel de création de valeur de celle-ci. Nous étendons la formulation classique du modèle d’optimisation de la possibilité forestière afin de permettre l’anticipation du comportement du consommateur de fibre, augmentant ainsi la probabilité que l’offre de fibre soit entièrement consommée, rétablissant ainsi la validité de l’hypothèse de consommation totale de l’offre de fibre implicite au modèle d’optimisation. Nous modélisons la relation principal-agent entre le gouvernement et l’industrie à l’aide d’une formulation biniveau du modèle optimisation, où le niveau supérieur représente le processus de détermination de la possibilité forestière (responsabilité du gouvernement), et le niveau inférieur représente le processus de consommation de la fibre (responsabilité de l’industrie). Nous montrons que la formulation biniveau peux atténuer le risque de ruptures de stock, améliorant ainsi la crédibilité du processus de planification forestière hiérarchique. Ensemble, le modèle biniveau d’optimisation de la possibilité forestière et la méthodologie que nous avons développée pour résoudre celui-ci à l’optimalité, représentent une alternative aux méthodes actuellement utilisées. Notre modèle biniveau et le cadre de simulation itérative représentent un pas vers l’avant en matière de technologie de planification forestière axée sur la création de valeur. L’intégration explicite d’objectifs et de contraintes industrielles au processus de planification forestière, dès la détermination de la possibilité forestière, devrait favoriser une collaboration accrue entre les instances gouvernementales et industrielles, permettant ainsi d’exploiter le plein potentiel de création de valeur de la ressource forestière.

Simulations of droplet dispersion in the wakes of cylinders and icing tunnel spray bars

Simulations of droplet dispersion behind cylinder wakes and downstream of icing tunnel spray bars were conducted. In both cases, a range of droplet sizes were investigated numerically with a Lagrangian particle trajectory approach while the turbulent air flow was investigated with a hybrid Reynolds-Averaged Navier-Stokes/Large-Eddy Simulations approach scheme. In the first study, droplets were injected downstream of a cylinder at sub-critical conditions (i.e. with laminar boundary layer separation). A stochastic continuous random walk (CRW) turbulence model was used to capture the effects of sub-grid turbulence. Small inertia droplets (characterized by small Stokes numbers) were affected by both the large-scale and small-scale vortex structures and closely followed the air flow, while exhibiting a dispersion consistent with that of a scalar flow field. Droplets with intermediate Stokes numbers were centrifuged by the vortices to the outer edges of the wake, yielding an increased dispersion. Large Stokes number droplets were found to be less responsive to the vortex structures and exhibited the least dispersion. Particle concentration was also correlated with vorticity distribution which yielded preferential bias effects as a function of different particle sizes. This trend was qualitatively similar to results seen in homogenous isotropic turbulence, though the influence of particle inertia was less pronounced for the cylinder wake case. A similar study was completed for droplet dispersion within the Icing Research Tunnel (IRT) at the NASA Glenn Research Center, where it is important to obtain a nearly uniform liquid water content (LWC) distribution in the test section (to recreate atmospheric icing conditions).. For this goal, droplets are diffused by the mean and turbulent flow generated from the nozzle air jets, from the upstream spray bars, and from the vertical strut wakes. To understand the influence of these three components, a set of simulations was conducted with a sequential inclusion of these components. Firstly, a jet in an otherwise quiescent airflow was simulated to capture the impact of the air jet on flow turbulence and droplet distribution, and the predictions compared well with experimental results. The effects of the spray bar wake and vertical strut wake were then included with two more simulation conditions, for which it was found that the air jets were the primary driving force for droplet dispersion, i.e. that the spray bar and vertical strut wake effects were secondary.

Scaling laws and thermodynamic analysis for vascular branching of microvessels

When blood flows through small vessels, the two-phase nature of blood as a suspension of red cells (erythrocytes) in plasma cannot be neglected, and with decreasing vessel size, a homogeneous continuum model become less adequate in describing blood flow. Following the Haynes’ marginal zone theory, and viewing the flow as the result of concentric laminae of fluid moving axially, the present work provides models for fluid flow in dichotomous branching composed by larger and smaller vessels, respectively. Expressions for the branching sizes of parent and daughter vessels, that provides easier flow access, are obtained by means of a constrained optimization approach using the Lagrange multipliers. This study shows that when blood behaves as a Newtonian fluid, Hess – Murray law that states that the daughters-to-parent diameter ratio must equal to 2^(-1/3) is valid. However, when the nature of blood as a suspension becomes important, the expression for optimum branching diameters of vessels is dependent on the separation phase lengths. It is also shown that the same effect occurs for the relative lengths of daughters and parent vessels. For smaller vessels (e. g., arterioles and capillaries), it is found that the daughters-to-parent diameter ratio may varies from 0,741 to 0,849, and the daughters-to-parent length ratio varies from 0,260 to 2,42. For larger vessels (e. g., arteries), the daughters-to-parent diameter ratio and the daughters-to-parent length ratio range from 0,458 to 0,819, and from 0,100 to 6,27, respectively. In this paper, it is also demonstrated that the entropy generated when blood behaves as a single phase fluid (i. e., continuum viscous fluid) is greater than the entropy generated when the nature of blood as a suspension becomes important. Another important finding is that the manifestation of the particulate nature of blood in small vessels reduces entropy generation due to fluid friction, thereby maintaining the flow through dichotomous branching vessels at a relatively lower cost.

Sistemas aquosos bifásicos: fundamentos e aplicações para partição/purificação de proteínas

By the year 2005 the world biochemical market will reach an estimated $ 100 billion and separation processes are a vital link between lab discoveries and the fulfillment of this commercialization potential. The practical application of aqueous two-phase systems (ATPS) to extraction processes has been exploited for several years for the recovery of biological products. Unfortunately, this has not resulted in an extensive presence of the technique in commercial processes. In this paper a critical overview of the fundamental thermodynamic properties related to formation of aqueous two-phase systems and their application to extraction and purification of bioparticules is presented.

Changes in temporomandibular joint disc position and form following Herbst and fixed orthodontic treatment

Objective: To determine the changes in the position and form of the temporomandibular joint articular disc in adolescents with Class II division 1 malocclusion and mandibular retrognathism treated with the Herbst appliance (phase I) and fixed orthodontic appliance (phase II). Materials and Methods: Thirty-two consecutive adolescents went through phase I of treatment and 23 completed phase II. The temporomandibular joints were evaluated qualitatively by means of magnetic resonance images at the beginning of treatment (T1), during phase I (T2), at the end of phase I (T3), and at the end of phase II (T4). Results: Significant changes in disc position were not observed with the mouth closed between T1 X T3 (P = .317), T3 X T4 (P = .287), or T1 X T4 (P = .261). At T2, on average, the disc was positioned regressively. With the mouth open, no difference was observed between T1 X T3 (P = .223) or T1 X T4 (P = .082). We did observe a significant difference between T3 X T4 (P < .05). Significant changes in the disc form were found with the mouth closed between T1 X T2 (P < .001) and T2 X T3 (P < .001). Conclusions: At the end of the two-phase treatment, in general terms, the position and form of the initial articular discs were maintained; however, in some temporomandibular joints some seemingly adverse effects were observed at T4. (Angle Orthod. 2010;80:843-852.)

Microstructural characterization of rapidly solidified and heat-treated Ti(92)B(8) eutectic alloy

In this work, Ti(92)B(8) alloy was processed via rapid solidification (splat-cooling) and then heat-treated at 700 degrees C and 1000 degrees C. A careful microstructural characterization indicated that, after rapid solidification, a very fine two-phase microstructure was produced with no significant saturation of B in alpha/beta Ti. There was no indication of amorphous formation in the rapidly solidified splats. Both alpha Ti and TiB were observed in the microstructures of the splats after heat-treatment at 700 degrees C and 1000 degrees C, confirming the stability of the alpha Ti+TiB two-phase region in this temperature range. (C) 2008 Elsevier Inc. All rights reserved.