Inertial migration based concentration factors for suspensions of Chlorella micro-algae in branched tubes

When a dilute suspension flows in the laminar regime through a tube, under certain conditions the suspended particles migrate radially to an equilibrium radial position. Branched tubes can use this radial concentration distribution to concentrate dilute suspensions. Suspensions of microalgae, Chlorella vulgaris, were pumped through tubes of various diameters for tube Reynolds number ranging from 47–1839 and photographed. Upstream particle concentration profdes were obtained by image analysis of the photographs. The dividing stream surfaces in branched tubes were obtained from the three-dimensional numerical solutions of the Navier-Stokes equations for steady, laminar, and homogeneous flow through tubes having one and two orthogonal branches. Concentration factors for Chlorella suspensions in branched tubes, predicted by a general method, fall in the range of 1.0–1.3     

Flow in a mechanical bileaflet heart valve at laminar and near-peak systole flow rates: CFD simulations and experiments

Time-accurate, fully 3D numerical simulations and particle image velocity laboratory experiments are carried out for flow through a fully open bileaflet mechanical heart valve under steady (nonpulsatile) inflow conditions. Flows at two different Reynolds numbers, one in the laminar regime and the other turbulent (near-peak systole flow rate), are investigated. A direct numerical simulation is carried out for the laminar flow case while the turbulent flow is investigated with two different unsteady statistical turbulence modeling approaches, unsteady Reynolds-averaged Navier-Stokes (URANS) and detached-eddy simulation (DES) approach. For both the laminar and turbulent cases the computed mean velocity profiles are in good overall agreement with the measurements. For the turbulent simulations, however, the comparisons with the measurements demonstrate clearly the superiority of the DES approach and underscore its potential as a powerful modeling tool of cardiovascular flows at physiological conditions. The study reveals numerous previously unknown features of the flow.     

Experimental analysis of the influence of stenotic geometry on steady flow.

We studied the flow behavior under steady flow conditions in four models of cylindrical stenoses at Reynolds numbers from 150 to 920. The flow upstream of the constrictions was always fully developed. The constriction ratios of the rigid tubes (D) to the stenoses (d) were d/D = 0.273; 0.505; 0.548; 0.786. The pressure drop at various locations in the stenotic models was measured with water manometers. The flow was visualized with a photoelasticity apparatus using an aqueous birefringent solution. We also studied the flow behavior at pulsatile flow in a dog aorta with a constriction of 71%. The flow through stenotic geometries depends on the Reynolds number of the flow generated in the tube and the constriction ratio d/D. At low d/D ratios, (with the increased constriction), the flow separation zones (recirculation zones, so-called reattachment length) and flow disturbances increased with larger Reynolds numbers. At lower values, eddies were generated. At high Re, eddies were observed in the pre-stenotic regions. The pressure drop is a function of the length and internal diameter of the stenosis, respective ratio of stenosis to the main vessel and the Reynolds numbers. At low Re-numbers and low d/D, distinct recirculation zones were found close to the stenosis. The flow is laminar in the distal areas. Further experiments under steady and unsteady flow conditions in a dog aorta model with a constriction of 71% showed similar effects. High velocity fluctuations downstream of the stenosis were found in the dog aorta. A videotape demonstrates these results.     

Particle flow behavior in models of branching vessels. II. Effects of branching angle and diameter ratio on flow patterns

To further elucidate the role of fluid mechanical factors in the localization of atherogenesis and thrombogenesis, we have studied the 3-dimensional flow patterns in square T-junctions with branching angles theta from 30 degrees to 150 degrees and diameter ratios d/D (side: main tube) from 1.05/3.0 to 1.0. Cine films of the motions of tracer microspheres in dilute suspensions were taken at inflow Reynolds numbers from 15 to 400 and flow ratios (main: side tube) from 0.1 to 4.0. Flow patterns with suspension entering through the main tube were similar to those previously described in uniform 3 mm diameter T-junctions: paired vortices (spiral secondary flows) symmetrical about the common median plane formed at the entrances of the main and side daughter tubes. Particles circulated through the main vortex, some crossing above and below the mainstream into and through the side vortex. At the geometrical flow ratio, the main vortex became smaller and smaller as the branching angle (theta less than 90 degrees) and diameter ratio decreased, and was confined to a thin side tube was a minimum. In obtuse angle T-junctions the stagnation point shifted from the flow divider into the side tube, enhancing the flow disturbance there. The velocity distributions in main and side tubes were skewed towards the inner walls close to the flow divider. When flow entered through the side tube, a pair of recirculation zones formed in the main tube at the inner wall of the bend with a sharper angle.     

An isolated upper airway preparation in conscious dogs

The purpose of this study was to develop an isolated upper airway preparation in conscious dogs. Each of the four dogs was trained to wear an individually fitted respiratory mask and surgically prepared with two side-hole tracheostomies. After full recovery, one endotracheal tube was inserted caudally into the lower tracheostomy hole and another tube cranially into the upper tracheostomy. When the two endotracheal tubes were connected to a breathing circuit including a box-balloon system, the magnitude and pattern of the inspiratory flow through the upper airway were identical to that inhaled spontaneously into the lungs by the dogs, but the gas medium inhaled into the upper airway could be independently controlled. Thus it allowed test gas mixtures to be inhaled spontaneously through an isolated upper airway. One limitation was that the inspired gas remained in the upper airway during expiration, but this can be corrected by a simple modification of the breathing circuit. This preparation was tested in studying the respiratory effects of upper airway exposure to CO2 gas mixtures. Our results showed small but significant reduction in both rate and volume of respiration when the concentration of CO2 gas mixture inhaled through the upper airway exceeded 5%. Irregular breathing patterns were frequently elicited in these dogs by higher concentrations (greater than 12%) of CO2.     

Experimental study of pulsatile and steady flow through a smooth tube and an atherosclerotic coronary artery casting of man

In vitro investigation of pulsatile and steady flows through a smooth, straight circular tube and a diseased human coronary artery cast was conducted with sugar-water solutions simulating the viscosity of blood. Time averaged pressure drops for pulsatile flows measured in the circular tube over a Reynolds number ranging from 50 to 1,000 were found to be identical to those for steady flows in the same tube, both of which were in excellent agreement with the Poiseuille flow prediction. For the polyurethane case (# 124) made from a human main coronary with significant but 'non obstructive' diffuse atherosclerotic disease, pressure drops for steady flows were found to be greater than Poiseuille flow predictions by a factor of 3-8 in the physiological Reynolds number range from about 100 to 400. Pulsatile flows in the same artery cast resulted in additional 30% increases in time averaged pressure drops, and thus flow resistance, compared to the steady flow data. Steady and pulsatile flow data measured in a straight, axisymmetric model of cast # 124 showed considerably smaller increases in flow resistance than those observed in # 124 casting.     

Mammalian cell damage in a novel membrane bioreactor

The experimental study has assessed a novel membrane bioreactor for mammalian cell culture. In the absence of a gas phase, the key features of cell damage associated with laminar and turbulent flow have been identified. The bioreactor employs a dimpled membrane in order to enhance transverse mixing in a narrow channel, but a fall in viable cell density has been observed at Reynolds numbers above Re = 83. In the laminar flow regime wall shear is the critical mechanism and an accurate calculation of shear rate in a complex channel has been achieved using the Reynolds analogy. Flow generating a wall shear rate in excess of 3000 s(-1) has been shown to cause damage. Power dissipation measurements have been used to distinguish between laminar and turbulent flow and also to predict Kolmogorov eddy lengths. An additional turbulent bulk stress damage mechanism at higher Reynolds numbers (Re > 250) results in a very rapid fall in viable cell density.     

Polyester and nylon powders used as pollen diluents preserve pollen germination and tube growth in controlled pollinations

Pollen acquisition for seed production, breeding programs and supplemental pollination can be costly and difficult. The identification of dry particulates for use as pollen diluents would facilitate the use of limited amounts of pollen and aid in accurate pollen application and dispersion. Four powders - Rilsan ES, polyester, wheat flour, and Lycopodium spores - were evaluated as pollen diluents using petunia as a model system. Diluents were combined with petunia pollen at a 5:1 (v/v) ratio. Two types of studies were conducted: (1) storage studies evaluated the viability of pollen combined and held with diluent for different durations; and (2) in vivo studies evaluated pollen tube growth in the styles of flowers pollinated with pollen-diluent mixtures. Pollen germination was not affected when stored as pollen-diluent mixtures for 4 days. Slight detrimental effects on pollen germination were observed after 6 days storage with Rilsan ES powders. Pollination with all the pollen-diluent mixtures resulted in fewer pollen tubes growing in the style compared to controls diluted with heat-killed pollen instead of diluent powders. Lycopodium-pollen mixtures were the most inhibitory, providing only 8% of the tube numbers observed in controls. Pollen mixed with polyester powders, Rilsan ES powders or wheat flour had tube numbers ranging from 47 to 61% of the control, but still had 175 or more pollen tubes per style, which would be sufficient for high rates of seed set in petunia. Wheat flour-pollen mixtures tended to clump and degrade pollen flow. Rilsan ES and polyester were identified as two promising pollen diluent powders that can facilitate accurate metering and distribution of pollen, produce large numbers of pollen tubes, and maintain pollen viability under storage.     

Estimation of inspiratory pressure drop in neonatal and pediatric endotracheal tubes.

Endotracheal tubes (ETTs) constitute a resistive extra load for intubated patients. The ETT pressure drop (DeltaP(ETT)) is usually described by empirical equations that are specific to one ETT only. Our laboratory previously showed that, in adult ETTs, DeltaP(ETT) is given by the Blasius formula (F. Lofaso, B. Louis, L. Brochard, A. Harf, and D. Isabey. Am. Rev. Respir. Dis. 146: 974-979, 1992). Here, we also propose a general formulation for neonatal and pediatric ETTs on the basis of adimensional analysis of the pressure-flow relationship. Pressure and flow were directly measured in seven ETTs (internal diameter: 2.5-7.0 mm). The measured pressure drop was compared with the predicted drop given by general laws for a curved tube. In neonatal ETTs (2.5-3.5 mm) the flow regime is laminar. The DeltaP(ETT) can be estimated by the Ito formula, which replaces Poiseuille's law for curved tubes. For pediatric ETTs (4.0-7.0 mm), DeltaP(ETT) depends on the following flow regime: for laminar flow, it must be calculated by the Ito formula, and for turbulent flow, by the Blasius formula. Both formulas allow for ETT geometry and gas properties.     

Low Reynolds number turbulence modeling of blood flow in arterial stenoses.

Moderate and severe arterial stenoses can produce highly disturbed flow regions with transitional and or turbulent flow characteristics. Neither laminar flow modeling nor standard two-equation models such as the kappa-epsilon turbulence ones are suitable for this kind of blood flow. In order to analyze the transitional or turbulent flow distal to an arterial stenosis, authors of this study have used the Wilcox low-Re turbulence model. Flow simulations were carried out on stenoses with 50, 75 and 86% reductions in cross-sectional area over a range of physiologically relevant Reynolds numbers. The results obtained with this low-Re turbulence model were compared with experimental measurements and with the results obtained by the standard kappa-epsilon model in terms of velocity profile, vortex length, wall shear stress, wall static pressure, and turbulence intensity. The comparisons show that results predicted by the low-Re model are in good agreement with the experimental measurements. This model accurately predicts the critical Reynolds number at which blood flow becomes transitional or turbulent distal an arterial stenosis. Most interestingly, over the Re range of laminar flow, the vortex length calculated with the low-Re model also closely matches the vortex length predicted by laminar flow modeling. In conclusion, the study strongly suggests that the proposed model is suitable for blood flow studies in certain areas of the arterial tree where both laminar and transitional/turbulent flows coexist.     

A numerical simulation of steady flow fields in a bypass tube.

Steady flow in a complete by-pass tube was simulated numerically. The study was to consider a complete flow field, which included both the by-pass and the host tubes. The changes of the hemodynamics were investigated with three parameters: the inlet flow Reynolds number (Re), anastomotic angle (alpha) and the position of the occlusion in the host tube. The baseline flow field was set up with Re=200, alpha=45 degrees and the centered position of occlusion. The parametric study was then conducted on combination of Re=100, 200, 400, alpha=35 degrees, 45 degrees, 60 degrees, 75 degrees, 90 degrees and three occlusion positions: left, center and right. It was found that in the baseline case, large slow/recirculation flows could be seen in the host tube both upstream and downstream of the occlusion. The separation points were on the opposite walls to the junctions. Recirculation zones were also found near the toe and in the proximal outer wall of the by-pass tube. Their sizes were about one diameter of the tube or smaller. In some cases, pairing vortices could be seen in the host tube upstream of the occlusion. The shear rate distribution associated with the flow fields was presented. The flow pattern obtained was agreeable to those observed experimentally by other investigators. The difference of the flow fields between a complete bypass and simple anastomosis was discussed. The present numerical code provides a preliminary simulation/design tool for bypass graft flows.     

Spatial velocity profile in mouse embryonic aorta and Doppler-derived volumetric flow: a preliminary model

Characterizing embryonic circulatory physiology requires accurate cardiac output and flow data. Despite recent applications of high-frequency ultrasound Doppler to the study of embryonic circulation, current Doppler analysis of volumetric flow is relatively crude. To improve Doppler derivation of volumetric flow, we sought a preliminary model of the spatial velocity profile in the mouse embryonic dorsal aorta using ultrasound biomicroscopy (UBM)-Doppler data. Embryonic hematocrit is 0.05-0.10 so rheologic properties must be insignificant. Low Reynolds numbers (<500) and Womersley parameters (<0.76) suggest laminar flow. UBM demonstrated a circular dorsal aortic cross section with no significant tapering. Low Dean numbers (<100) suggest the presence of minimal skewing of the spatial velocity profile. The inlet length allows for fully developed flow. There is no apparent aortic wall pulsatility. Extrapolation of prior studies to these vessel diameters (300-350 microm) and flow velocities (~50-200 mm/s) suggests parabolic spatial velocity profiles. Therefore, mouse embryonic dorsal aortic blood flow may correspond to Poiseuille flow in a straight rigid tube with parabolic spatial velocity profiles. As a first approximation, these results are an important step toward precise in utero ultrasound characterization of blood flow within the developing mammalian circulation.     

Flow and Oxygen Transfer Characteristics of an Intravenous Membrane Oxygenator: A Computational Study

Spectral element computational simulations of the conservation of mass, momentum and species equations are performed to investigate the flow and oxygen transfer characteristics of an Intravenous Membrane Oxygenator (IMO). The simulations consider a three-dimensional IMO computational model consisting of equally-spaced fibers, an elastic balloon with non-permeable walls positioned longitudinally within the vena cava, and a Newtonian and time-dependent incompressible flow. Flow characteristics and oxygen transfer parameters are determined for operating conditions of a stationary and a pulsating balloon. For the stationary balloon configuration the flow is two-dimensional, parallel, laminar and without secondary flows for the Reynolds number range of 5.7-455.2. Evaluations of the oxygen transfer characteristics for the stationary balloon indicate that the main transport mechanisms are diffusion and convection in the crosswise and streamwise directions, respectively. Additionally, evaluations of oxygen transfer rates and Sherwood numbers in this Reynolds number range indicate that the oxygen transfer rate reaches an asymptotic limit at relatively moderate Reynolds numbers. For the pulsating balloon, flow characteristic results demonstrate the existence of a strong secondary flow around the fiber, and between the balloon and the fiber. This secondary flow induces oscillatory crosswise and streamwise velocities and a seemingly random spanwise flow which enhances the flow mixing as well as the transport of oxygen from the fiber surface to the bulk flow.     

Vortex generation in pulsatile flow through arterial bifurcation models including the human carotid artery

Visualization experiments were performed to elucidate the complicated flow pattern in pulsatile flow through arterial bifurcations. Human common carotid arteries, which were made transparent, and glass-models simulating Y- and T-shaped bifurcations were used. Pulsatile flow with wave forms similar to those of arterial flow was generated with a piston pump, elastic tube, airchamber, and valves controlling the outflow resistance. Helically recirculating flow with a pattern similar to that of the horseshoe vortex produced around wall-based protuberances in circular tubes was observed in pulsatile flow through all the bifurcations used in the present study. This flow type, which we shall refer to as the horseshoe vortex, has also been demonstrated to occur at the human common carotid bifurcation in steady flow with Reynolds numbers above 100. Time-varying flows also produced the horseshoe vortex mostly during the decelerating phase. Fluid particles of dye solution approaching the bifurcation apex diverged, divided into two directions perpendicularly, and then showed helical motion representing the horseshoe vortex formation. While this helical flow was produced, the stagnation points appeared on the wall upstream of the apex. Their position was dependent upon the flow distribution ratio between the branches in the individual arteries. The region affected by the horseshoe vortex was smaller during pulsatile flow than during steady flow. Lowering the Reynolds number together with the Womersley number weakened the intensity of helical flow. A separation bubble, resulting from the divergence or wall roughness, was observed at the outer or inner wall of the branch vessels and made the flow more complicated.     

Measurement of steady-flow instability and turbulence levels in Dacron vascular grafts.

Fluid dynamic properties of Dacron vascular grafts were studied under controlled steady-flow conditions over a Reynolds number range of 800 to 4500. Knitted and woven grafts having nominal diameters of 6 mm and 10 mm were studied. Thermal anemometry was used to measure centerline velocity at the downstream end of the graft; pressure drop across the graft was also measured. Transition from laminar flow to turbulent flow was observed, and turbulence intensity and turbulent stresses (Reynolds normal stresses) were measured in the turbulent regime. Knitted grafts were found to have greater pressure drop than the woven grafts, and one sample was found to have a critical Reynolds number (Rc) of less than one-half the value of Rc for a smooth-walled tube.     

Flow patterns at the major T-junctions of the dog descending aorta

Using a novel technique developed in our own laboratory, an isolated transparent arterial segment containing the whole descending aorta and its four major branches was prepared from a dog. The flow patterns at each aortic T-junction were studied in detail under the conditions of steady flow by means of flow visualization and cinemicrographic techniques. It was found that a standing recirculation zone consisting of a pair of thin-layered spiral secondary flows located symmetrically about the common median plane of the aorta and side branches was formed at each T-junction over a wide range of flow conditions including the time-averaged estimated mean values of physiological flow rates and flow rate ratios. The results support the recent in vivo findings by other investigators that flow reversal occurs at some junctions of the dog abdominal aorta during each cardiac cycle. The flow patterns at the aortic T-junctions were very much similar to those previously observed in various glass model T-junctions. However, due to the particular anatomical structure of the vessel wall at each branching site (the curvature of the wall was very sharp at the flow divider, but gently rounded at the bend opposite to it) no recirculation zone was formed in the side branches. At a given flow rate ratio, the measured critical Reynolds numbers for the formation of spiral secondary flows and fully developed disturbed flows were much higher in aortic T-junctions than those in glass model T-junctions having equivalent branching angles and diameter ratios. These results indicate that, in the circulation, conditions at arterial T-junctions appear to be optimal for minimizing the formation of disturbed flows.     

Flow and Oxygen Transfer Characteristics of an Intravenous Membrane Oxygenator: A Computational Study

Abstract

Spectral element computational simulations of the conservation of mass, momentum and species equations are performed to investigate the flow and oxygen transfer characteristics of an Intravenous Membrane Oxygenator (IMO). The simulations consider a three-dimensional IMO computational model consisting of equally-spaced fibers, an elastic balloon with non-permeable walls positioned longitudinally within the vena cava, and a Newtonian and time-dependent incompressible flow. Flow characteristics and oxygen transfer parameters are determined for operating conditions of a stationary and a pulsating balloon. For the stationary balloon configuration the flow is two-dimensional, parallel, laminar and without secondary flows for the Reynolds number range of 5.7-455.2. Evaluations of the oxygen transfer characteristics for the stationary balloon indicate that the main transport mechanisms are diffusion and convection in the crosswise and streamwise directions, respectively. Additionally, evaluations of oxygen transfer rates and Sherwood numbers in this Reynolds number range indicate that the oxygen transfer rate reaches an asymptotic limit at relatively moderate Reynolds numbers. For the pulsating balloon, flow characteristic results demonstrate the existence of a strong secondary flow around the fiber, and between the balloon and the fiber. This secondary flow induces oscillatory crosswise and streamwise velocities and a seemingly random spanwise flow which enhances the flow mixing as well as the transport of oxygen from the fiber surface to the bulk flow.     

Liquid film bioreactors for cell mass production

In order to make heat and mass transfer processes in bioreactors more intensive, the turbulent liquid film flow which is proposed for realization in multitubular reactors has been developed. Experiments have been carried out in tubes with smooth and rough surfaces at cocurrent gas and liquid film downward flows with a view to determine the values of the mass transfer coefficients in turbulent liquid hold-up in contact tubes. The liquid viscosity and REYNOLDS number are changing in a wide range (from 2000 to 60000). The results show that the maximum values of the mass transfer coefficients and an acceptable hold-up can be obtained in tubes with rough surfaces at high REYNOLDS numbers of the liquid film. The results of culturing yeasts on hydrolyzate in a laboratory-size liquid film fermenter are also presented.     

Topological analysis of wall mass transport using a luminescent immobilized enzymatic system

A new technique of visualization of diffusion-convection phenomena at a solid-liquid interface using the luminol chemiluminescent reaction catalyzed by immobilized peroxidase has been previously described (Dimicoli, J.L., M. Nakache, and P. Peronneau, 1982, Biorheology, 19:281-300). We propose now a theoretical model that predicts quantitatively the light fluxes, JL, corresponding to the transfer J of the hydrogen peroxide substrate at the liquid-solid interface in a cylindrical tube for continuous flow experiments. A simple phenomenological relation, J alpha J1/mL (1 less than m less than 3) was first established for each point of the wall. Then, numerical integration showed that, independent of the laminar or turbulent character of the flow, J1/mL was proportional to (S1 Kideal)/(1 + Kideal/ET), where S1 is the bulk substrate concentration, Kideal is the ideal transport coefficient, and ET (in cm.S-1) a phenomenological first-order enzymatic rate constant per unit of wall surface. This relation proved to be satisfactory for all experimental conditions since a single mean value of ET takes into account the experimental data collected for a given enzymated tube in a large range of Reynolds number values (Re) (500 less than Re less than 9,000) and of distances from the entrance of the tube (chi greater than 0.3 cm). This quantitative analysis using a pseudo-first-order approximation interprets the observed great dependence of JL on Re(JL alpha Ren', with n' usually greater than 1/3 for laminar flows) and on S1 (JL alpha S1m). It predicts also that the laminar-to-turbulent transition can be evidenced for interfacial enzymatic activity, ET greater than 2.10(-4) cm.S-1, as observed with most of the tubes prepared by covalent binding of peroxidase on the acrylamide gel wall. The experiment had to be carried out at a pH value of 8, which corresponds to the fastest rate of the chemiluminescent reaction. The predicted entrance effects were also observed experimentally for the first time in an immobilized enzyme system. This technique appears therefore to be a valuable tool for the quantitative analysis of diffusion-convection phenomena at a liquid-solid interface with a good spatial resolution with a great range of flow rate.     

Numerical simulation of steady flow in a model of the aortic bifurcation.

The governing equations of steady flow of an incompressible viscous fluid through a 3-D model of the aortic bifurcation are solved with the finite element method. The effect of Reynolds number on the flow was studied for a range including the physiological values (200 < or = Re < or = 1600). The symmetrical bifurcation, with a branch angle of 70 degrees and an area ratio of 0.8, includes a tapered transition zone. Secondary flows induced by the tube curvature are observed in the daughter tubes. Transverse currents in the transition zone are generated by the combined effect of diverging and converging walls. Flow separation depends on both the Reynolds number and the inlet wall shear.