Effects of helium-oxygen mixtures on endotracheal tubes: an in vitro study

QUESTION: To determine flow pattern and critical Reynolds numbers in endotracheal tubes submitted to different helium-oxygen mixtures under laboratory conditions. MATERIALS AND METHODS: Flow-pressure relationships were performed for seven endotracheal tubes (rectilinear position, entry length applied) with distal end open to atmosphere (predicted internal diameters: 6-9 mm). Nine helium-oxygen mixtures were tested, with FIHe varying from zero to 0.78 (increment: 10%). Nine flows were tested, with rates varying from 0.25 to 1.60 l s(-1) (increment: 0.15 l s(-1)). Gas flow resistance was calculated, and for each endotracheal tube, a Moody diagram was realised. Flow regime and critical Reynolds numbers were then determined (fully established laminar, nonestablished laminar, smooth turbulent, or rough). RESULTS: Even low concentration of helium in inspiratory mixture reduces endotracheal tubes resistance. Effect is maximal for high flows, small tube and high FIHe. Critical Reynolds numbers are inversely correlated to tube diameter. ANSWER: Under laboratory conditions, flow pattern in endotracheal tubes varies from fully established laminar to rough. Knowledge of the critical Reynolds numbers allows correct application of fluid mechanic formula when studying tube or gaseous mixture effects on respiratory mechanisms.     

Low Reynolds number equi-bifurcation flow in a two-dimensional channel

The fluid flow in some physiological vessels such as the blood flow in blood vessels and the air flow through bronchi and bronchioles in the lungs undergoes a large number of bifurcations. The understanding of the bifurcation flow is of importance for a better comprehension of its effect in the blood and the air circulatory systems of the living body. The Reynolds number of flow in large blood vessels and bronchi is high and fluid inertia plays a dominant role in the bifurcation flow in such vessels. In small caliber blood vessels such as arterioles and capillaries, and bronchioles, the Reynolds number of flow is quite low and the effect of fluid inertia is negligible compared to the pressure and shear forces. In order to have a quantitative understanding of the bifurcation flow at low Reynolds numbers, the low Reynolds number equi-bifurcation flow in a two-dimensional channel at zero bifurcation angle is studied based on the Stokes approximation. The solution of the problem is posed as an infinite series, where the truncated version is used in numerical calculations. The results of this analysis is discussed in connection with the bifurcation flow of blood in small caliber blood vessels and that of the air in bronchioles in the lung.     

Finite element analysis of two dimensional steady flow in model arterial bifurcation

The purpose of the investigation reported in this paper is to determine theoretically the fluid dynamic field in models of common iliac arterial bifurcation and to identify the flow features which might influence the predominant occurrence of atherosclerotic lesions at such sites. This has been accomplished by numerically simulating fluid flow through 90 degrees symmetric bifurcations with branch-to-trunk area ratios of 0.8-1.414 and for Reynolds numbers ranging from 100 to 400. The analysis predicts flow reversal along the outer wall in models with area ratios over unity for high Reynolds number range, while no flow reversal occurred in models with area ratio below unity; a low shear zone along the outer wall and high shear stresses at the divider lip. Adverse pressure gradients are observed along the outer wall downstream of the corner point, the magnitudes increased with Reynolds number for a given branch to area ratio. Biological implication of the results is discussed with specific reference to the sites of atherosclerotic lesions found in man for these geometries.     

Flow disturbance measurements through a constricted tube at moderate Reynolds numbers

Instantaneous velocities in the field distal to contoured axisymmetric stenoses were measured with a laser Doppler anemometer. Upstream flow conditions were steady and spanned a range of Reynolds numbers from 500 to 2000. Autocorrelation functions and spectra of the velocity were employed to describe the nature of fluid dynamic disturbances. Depending upon the degree of stenosis and the Reynolds number, the flow field contained disturbances of a discrete oscillation frequency, of a turbulent nature, or both. If turbulence was detected in a given experiment, it was always preceded upstream by velocity oscillations at discrete frequency arising from vortex shedding. For mild degrees of stenosis (50% area reduction or less) the intensity of flow disturbances was relatively low until the Reynolds number exceeded 1000, thus highlighting difficulties to be expected in employing flow disturbance detection as a diagnostic tool in the recognition of early atherosclerosis in major arteries. In view of the relatively high noise levels inherent in noninvasive Doppler ultrasound systems employed clinically, it seems unlikely that detection of stenoses of less than 50% area reduction is feasible unless the Reynolds numbers exceed 1000 or unless pulsatility introduces new unsteady flow features beyond those studied here.     

Flow Visualization and Performance Measurements of a Flagellar Propeller

A new type of propeller that is optimized for low Reynolds numbers is required to propel a small object in a medium where the flow is dominated by viscous rather than inertial forces.A propeller in the shape of a bacterial flagellum seems an appropriate choice for driving a small object.Accordingly,in this study,we visualized the velocity field induced by a spring-like propeller inspired by the Escherichia coli flagellum,using a macroscopic model and applying stereoscopic particle image velocimetry.We also experimentally evaluated the effect of pitch and rotational speed on the performance of this flagellar propeller.Silicone oil,which has a kinematic viscosity 100,000 times that of water,was used as the working fluid to generate a low Reynolds number for the macroscopic model.Thrust,torque,and velocity were measured as functions of pitch and rotational speed,and the efficiency of the propeller was calculated from the measured results.We found that the flagellar propeller reached a maximum efficiency when the pitch angle was approximately 53°.Compared to pitch,rotational speed had a relatively small effect on the efficiency,and the pitch altered the flow pattern behind the rotating propeller.     

Flow within models of the vertebrate embryonic heart

Vertebrate cardiogenesis is believed to be partially regulated by fluid forces imposed by blood flow in addition to myocardial activity and other epigenetic factors. To understand the flow field within the embryonic heart, numerical simulations using the immersed boundary method were performed on a series of models that represent simplified versions of some of the early morphological stages of heart development. The results of the numerical study were validated using flow visualization experiments conducted on equivalent dynamically scaled physical models. The chamber and cardiac cushion (or valve) depths in the models were varied, and Reynolds numbers ranging from 0.01 to 1000 corresponding to the scale of the early heart tube to the adult heart were considered. The observed results showed that vortex formation within the chambers occurred for Reynolds numbers on the order of 1-10. This transition to vortical flow appears to be highly sensitive to the chamber and cushion depths within the model. These fluid dynamic events could be important to induce shear sensing at the endothelial surface layer which is thought to be a part of regulating the proper morphological development and functionality of the valves.     

Application of the synthetic jet concept to low Reynolds number biosensor microfluidic flows for enhanced mixing: a numerical study using the lattice Boltzmann method

The concept of macro scale synthetic jets has been applied to the low Reynolds number (Re=10), two-dimensional channel flows which may be found in biosensor microfluidic systems. The current numerical investigation utilizes a hybrid approach of the lattice Boltzmann (LB) method for flow field computations and a finite-difference, convection-diffusion equation for passive scalar transport. The study presents the modified main channel flow results for various wall jet geometries (derived from synthetic jets), jet inlet conditions, scaling issues and Reynolds numbers. The results indicate limited effects due to jet cavity-slot geometry, and that the forced jet imparts momentum to the channel flow thus enhancing fluid mixing.     

Steady flow through a double converging-diverging tube model for mild coronary stenoses

Velocity profiles and the pressure drop across two mild (62 percent) coronary stenoses in series have been investigated numerically and experimentally in a perspex-tube model. The mean flow rate was varied to correspond to a Reynolds number range of 50-400. The pressure drop across two identical (62 percent) stenoses show that for low Reynolds numbers the total effect of two stenoses equals that of two single stenoses. A reduction of 10 percent is found for the higher Reynolds numbers investigated. Numerical and experimental results obtained for the velocity profiles agree very well. The effect of varying the converging angle of a single mild (62 percent) coronary stenosis on the fluid flow has been determined numerically using a finite element method. Pressure-flow relation, especially with respect to relative short stenoses, is discussed.     

Numerical study of the impact of non-Newtonian blood behavior on flow over a two-dimensional backward facing step

Endothelial cell (EC) responsiveness to shear stress is essential for vasoregulation and plays a role in atherogenesis. Although blood is a non-Newtonian fluid, EC flow studies in vitro are typically performed using Newtonian fluids. The goal of the present study was to determine the impact of non-Newtonian behavior on the flow field within a model flow chamber capable of producing flow disturbance and whose dimensions permit Reynolds and Womersley numbers comparable to those present in vivo. We performed two-dimensional computational fluid dynamic simulations of steady and pulsatile laminar flow of Newtonian and non-Newtonian fluids over a backward facing step. In the non-Newtonian simulations, the fluid was modeled as a shear-thinning Carreau fluid. Steady flow results demonstrate that for Re in the range 50-400, the flow recirculation zone downstream of the step is 22-63% larger for the Newtonian fluid than for the non-Newtonian fluid, while spatial gradients of shear stress are larger for the non-Newtonian fluid. In pulsatile flow, the temporal gradients of shear stress within the flow recirculation zone are significantly larger for the Newtonian fluid than for the non-Newtonian fluid. These findings raise the possibility that in regions of flow disturbance, EC mechanotransduction pathways stimulated by Newtonian and non-Newtonian fluids may be different.     

Blood flow downstream of a two-dimensional bifurcation

Many cardiovascular lesions such as aneurysms, intimal cushions, and atherosclerotic plaques tend to occur near bifurcations. This suggests that hemodynamic factors may be involved. Since measuring devices (such as anemometers) are still too large to allow local measurements of flow disturbances, we have attempted to predict the nature of these factors mathematically. Biological variables include pulsatile flow of a nonNewtonian fluid in distensible branching vessels with different angles and flow rates. Our initial analysis considers the flow in a two-dimensional bifurcation with a symmetrical flow divider perfused with steady flow at variable Reynolds numbers. At all flows, high shear forces develop on either side of the flow divider (i.e. at the apex of the bifurcation). With high flows, regions of sluggish or reverse flow develop near the outer walls of the bifurcation. The analysis confirms that the flow at the apex is quite different from that at the outer angles and that the latter varies more with flow rate than the former.     

Biofilm formation in laminar flow usingPseudomonas fluorescens EX101

The relationship between biofilm formation and Reynolds number in laminar flow has been investigated usingPseudomonas fluorescens EX101. It was shown using a Modified Robbins Device that in laminar flow, numbers of viable cells in a developed biofilm increased with Reynolds number (Re 2, 17 and 51.5), as would be expected in a system where molecular transport to the wall is limited by diffusion. By monitoring fluorescent beads in a flowcell with a scanning confocal laser microscope at similar low Reynolds numbers, the velocity profile close to the solid surface was determined. It was shown that the presence of a thin bacterial film (up to 12 m) displaced the flow profile away from the wall by a distance equivalent to the film thickness. Total cell counts from the Modified Robbins Device samples were not significantly different at the different flow rates but were higher than viable counts. Interruption of the flow had no significant effect on colonisation by the bacteria through the Modified Robbins Device in the first few hours. However, viable numbers were reduced when the flow was stopped at 7 h after initial colonisation.     

Numerical simulations of the pulsating flow of cerebrospinal fluid flow in the cervical spinal canal of a Chiari patient

The flow of cerebrospinal fluid (CSF) in a patient-specific model of the subarachnoid space in a Chiari I patient was investigated using numerical simulations. The pulsating CSF flow was modeled using a time-varying velocity pulse based on peak velocity measurements (diastole and systole) derived from a selection of patients with Chiari I malformation. The present study introduces the general definition of the Reynolds number to provide a measure of CSF flow instability to give an estimate of the possibility of turbulence occurring in CSF flow. This was motivated by the fact that the combination of pulsating flow and the geometric complexity of the spinal canal may result in local Reynolds numbers that are significantly higher than the commonly used global measure such that flow instabilities may develop into turbulent flow in these regions. The local Reynolds number was used in combination with derived statistics to characterize the flow. The results revealed the existence of both local unstable regions and local regions with velocity fluctuations similar in magnitude to what is observed in fully turbulent flows. The results also indicated that the fluctuations were not self-sustained turbulence, but rather flow instabilities that may develop into turbulence. The case considered was therefore believed to represent a CSF flow close to transition.     

Measurement and prediction of flow through a replica segment of a mildly atherosclerotic coronary artery of man

Pressure distributions were measured along a hollow vascular axisymmetric replica of a segment of the left circumflex coronary artery of man with mildly atherosclerotic diffuse disease. A large range of physiological Reynolds numbers from about 60 to 500, including hyperemic response, was spanned in the flow investigation using a fluid simulating blood kinematic viscosity. Predicted pressure distributions from the numerical solution of the Navier-Stokes equations were similar in trend and magnitude to the measurements. Large variations in the predicted velocity profiles occurred along the lumen. The influence of the smaller scale multiple flow obstacles along the wall (lesion variations) led to sharp spikes in the predicted wall shear stresses. Reynolds number similarity was discussed, and estimates of what time averaged in vivo pressure drop and shear stress might be were given for a vessel segment.     

Numerical simulations of undulatory swimming at moderate Reynolds number

We perform numerical simulations of the swimming of a three-linkage articulated system in a moderately viscous regime. The computational methodology focuses on the creation, diffusion and transport of vorticity from the surface of the bodies into the fluid. The simulations are dynamically coupled, in that the motion of the three-linkage swimmer is computed simultaneously with the dynamics of the fluid. The novel coupling scheme presented in this work is the first to exploit the relationship between vorticity creation and body dynamics. The locomotion of the system, when subject to undulatory inputs of the hinges, is computed at Reynolds numbers of 200 and 1000. It is found that the forward swimming speed increases with the Reynolds number, and that in both cases the swimming is slower than in an inviscid medium. The vortex shedding is examined, and found to exhibit behavior consistent with experimental flow visualizations of fish.     

A numerical study of the shape of the surface separating flow into branches in microvascular bifurcations.

The shape of the separating surface formed by the streamlines entering the branches of microvascular bifurcations plays a major role in determining the distribution of red blood cells and other blood constituents downstream from the bifurcation. Using the finite element method, we determined the shape of the surface through numerical solution of three dimensional Navier-Stokes equations for fluid flow at low Reynolds numbers in a T-type bifurcation of circular tubes. Calculations were done for a wide range of daughter branch to parent vessel diameter ratios and flow ratios. The effect of Reynolds number was also studied. Our numerical results are in good agreement with previously reported experimental data of Rong and Carr (Microvascular Research, Vol. 39, pp. 186-202, 1990). The numerical results of this study will be used to predict the concentration of blood constituents downstream from microvascular bifurcations providing that the inlet concentration profile is known.     

Plug Effect of Erythrocytes in Capillary Blood Vessels

As an idealized problem of the motion of blood in small capillary blood vessels, the low Reynolds number flow of plasma (a newtonian fluid) in a circular cylindrical tube involving a series of circular disks is studied. It is assumed in this study that the suspended disks are equally spaced along the axis of the tube, and that their centers remain on the axis of the tube and that their faces are perpendicular to the tube axis. The inertial force of the fluid due to the convective acceleration is neglected on the basis of the smallness of the Reynolds number. The solution of the problem is derived for a quasi-steady flow involving infinitesimally thin disks. The numerical calculation is carried out for a set of different combinations of the interdisk distance and the ratio of the disk radius to the tube radius. The ratio of the velocity of the disk to the average velocity of the fluid is calculated. The different rates of transport of red blood cells and of plasma in capillary blood vessels are discussed. The average pressure gradient along the axis of the tube is computed, and the dependence of the effective viscosity of the blood on the hematocrit and the diameter of the capillary vessel is discussed.     

Phasic and spatial pressure measurements in a femoral artery branch model for pulsatile flow

Phasic and spatial time-averaged pressure distributions were measured in a 60-deg femoral artery branch model over a large range of branch flow ratios and at physiological Reynolds numbers of about 120 and 700. The results obtained with an in-vivo like flow wave form indicated spatial adverse time average pressure gradients in the branch vicinity which increased in magnitude with branch flow ratio, and the importance of the larger inertial effects at the higher Reynolds numbers. Pressure losses in the branch entrance region were relatively large, and corresponding flow resistances may limit branch flow, particularly at higher Reynolds numbers. The effect of branch flow was to reduce the pressure loss in the main lumen.     

Flush mounted hot film anemometer measurement of wall shear stress distal to a tri-leaflet valve for Newtonian and non-Newtonian blood analog fluids

Wall shear stress has been measured by flush-mounted hot film anemometry distal to an Ionescu-Shiley tri-leaflet valve under pulsatile flow conditions. Both Newtonian (aqueous glycerol) and non-Newtonian (aqueous polyacrylamide) blood analog fluids were investigated. Significant differences in the axial distribution of wall shear stress between the two fluids are apparent in flows having nearly identical Reynolds numbers. The Newtonian fluid exhibits a (peak) wall shear rate which is maximized near the valve seat (30 mm) and then decays to a fully developed flow value (by 106 mm). In contrast, the shear rate of the non-Newtonian fluid at 30 mm is less than half that of the Newtonian fluid and at 106 mm is more than twice that of the Newtonian fluid. It is suggested that non-Newtonian rheology influences valve flow patterns either through alterations in valve opening associated with low shear separation zones behind valve leaflets, or because of variations in the rate of jet spreading. More detailed studies are required to clarify the mechanisms. The Newtonian wall shear stresses for this valve are low. The highest value observed anywhere in the aortic chamber was 2.85 N/m2 at a peak Reynolds number of 3694.     

A Desktop Apparatus for Studying Interactions Between Microorganisms and Small-Scale Fluid Motion

Low levels of kinetic energy dissipation were successfully generated in a reactor using two submersible speakers. A software programme controlled the amplitude and frequency of the signal fed to each speaker and achieved good repeatability of flow conditions. The flow reactor had a near isotropic flow regime with a low mean flow, values were calculated from particle image velocimetry measurements. The flow characteristics compared well with grid turbulence reactors, though as no moving parts are present in this reactor design the strain rates were lower compared to oscillating grid set-ups. The low range of Reynolds numbers based on Taylor microscales (Re_λ~0.5–5.9) covered both turbulent and non-turbulent flow regimes. The small-scale fluid motion produced over the entire volume of this reactor makes it suitable for experiments examining the physiological responses of fluid motion on microorganisms.