Oxygen transport and cell viability in an annular flow bioreactor: comparison of laminar Couette and Taylor-vortex flow regimes

Rotating wall vessel bioreactors have been proposed as a means of controlling the fluid dynamic environment during long-term culture of mammalian cells and engineered tissues. In this study, we show how the delivery of oxygen to cells in an annular flow bioreactor is enhanced by the forced convective transport afforded by Taylor vortex flows. A fiberoptic oxygen probe with negligible lag time was used to measure the dissolved oxygen concentration in real time and under carefully controlled aeration conditions. From these data, the overall mass transfer coefficients were calculated and mass transport correlations determined under laminar Couette flow conditions and discrete Taylor vortex flow regimes, including laminar, wavy, and turbulent flows. While oxygen transport in Taylor vortex flows was significantly greater, and the available oxygen exceeded that consumed by murine fibroblasts in free suspension, the proportion of cells that remained viable decreased with increasing Reynolds number (101.8 < Rei < 1018), which we attribute to the action of fluid shear stresses on the cells as opposed to any limitation in mass transport. Nevertheless, the results of this study suggest that laminar Taylor-vortex flow regimes provide an effective means of maintaining the levels of oxygen transport required for long-term cell culture.     

Application of rotary microfiltration in debittering process of spent brewer's yeast

This study concerns the production of yeast extract from spent brewer's yeast using rotary microfiltration as a means to combine debittering and cell debris separation into a single step, without using a toxic alkali wash. The pH of yeast homogenate was found to affect protein yield and bitterness of the product. Rotary filtration of yeast homogenate at various pHs resulted in different percent protein transmissions. These were found to be 5.05%, 9.83%, and 30.83% for pH 5, 6, and 7.5, respectively. The bitterness concentration in the permeate was also found to be higher at higher pHs. Autolysis of the cell homogenate prior to filtration increased protein yield and decreased bitterness considerably. At pH 5.5, the protein transmission was increased to 60% and debittering efficiency was increased from 59% to 86%. The permeate flux and protein productivity could be further increased by increasing the rotational speed, but this resulted in a decrease in debittering efficiency. Thus, the rotational speed should be carefully selected to compromise between the yield and product quality. Furthermore, for the tested rotational speeds of 600 and 1000 rpm, the change in feed flow rate from 11 to 35 L h(-1) changes the flow behavior from turbulent vortex flow to laminar vortex flow, thus decreasing the flux and protein productivity.     

Homogeneous batch cultures of<Emphasis Type="Italic"> Aspergillus oryzae</Emphasis> by elimination of wall growth in the Variomixing bioreactor

A novel principle for mixing and aeration in stirred bioreactors, named Variomixing, was developed. Four baffles are rotated intermittently at a rotational speed slower or similar to the speed of a centrally placed axial flow impeller. Rotational speeds of the baffles and impeller of 5–10 and 500–600 rpm, respectively, results in the highly turbulent flow regime characteristic of conventional bioreactors with high mixing and mass transfer capacities. Stagnant zones around crevices and crannies in which wall growth may commence are avoided since the baffles are never completely at rest. Increasing the rotational speed of the baffles (5 s every 5 min), so that it follows the speed of the impeller (500–600 rpm), cancels the effect of the baffles and a deep vortex and high peripheral liquid flow rates at the reactor wall develop. The vortex ensures that also the head-space of the reactor wall is flushed and any deposits removed. The filamentous fungus Aspergillus oryzae has been grown in batch cultures in the Variomixing bioreactor. Compared to conventional laboratory-scale bioreactors, in which more than 30% of all biomass was found attached to walls, less than 2% of the total A. oryzae biomass was found on the walls in the Variomixing bioreactor.     

Studies on protein adsorption in a vortex flow reactor

The performance of a vortex flow reactor (VFR) with suspended particles for protein adsorption was studied under varying operating conditions, and resin volume fractions. The VFR behaved as an expanded bed in the regimen of laminar vortices flow. Streamline DEAE was used for bovine serum albumin (BSA) adsorption. Expanded bed VFR experiments were performed with varying geometric aspect ratios (14.6, 28.6 and 40.0) and axial superficial velocity (100–300 cm h⁻¹) to investigate their influence on productivity and dynamic capacity. The results are compared with literature data on an expanded bed column (EBC). Adsorption breakthrough curves were fitting to a simple two-parameter model.     

How to perform measurements in a hovering animal's wake: physical modelling of the vortex wake of the hawkmoth, Manduca sexta

The vortex wake structure of the hawkmoth, Manduca sexta, was investigated using a vortex ring generator. Based on existing kinematic and morphological data, a piston and tube apparatus was constructed to produce circular vortex rings with the same size and disc loading as a hovering hawkmoth. Results show that the artificial rings were initially laminar, but developed turbulence owing to azimuthal wave instability. The initial impulse and circulation were accurately estimated for laminar rings using particle image velocimetry; after the transition to turbulence, initial circulation was generally underestimated. The underestimate for turbulent rings can be corrected if the transition time and velocity profile are accurately known, but this correction will not be feasible for experiments on real animals. It is therefore crucial that the circulation and impulse be estimated while the wake vortices are still laminar. The scaling of the ring Reynolds number suggests that flying animals of about the size of hawkmoths may be the largest animals whose wakes stay laminar for long enough to perform such measurements during hovering. Thus, at low advance ratios, they may be the largest animals for which wake circulation and impulse can be accurately measured.     

Pulsed Doppler ultrasound system for the measurement of velocity distributions and flow disturbances in arterial prostheses

For the investigation of flow through prosthetic arteries a pulsed Doppler ultrasound system has been characterized. Preliminary in vitro experiments using this system are described; they verify its suitability for making velocity profile and flow disturbance measurements. The output from a frequency tracker is compared with spectral analysis of Doppler signals for both laminar and turbulent flow regimes and the root mean square fluctuations on the tracker output signal are used to identify transition from laminar to turbulent flow. In addition, the turbulent itensity of poststenotic flow is quantified at several axial locations and for different rates of flow. Finally, we present velocity profile measurements which were obtained using a deconvolution technique to account for the finite size of the sample volume.     

Experimental evaluation of laminar shear stress on the behaviour of hybridoma mass cell cultures,producing monoclonal antibodies against mitochondrial creatine kinase

In biotechnology, the interest in mass cultures of animal cells rises constantly; thus knowledge of the conditions influencing the cultures becomes important. Suspension cell cultures in bioreactors are subject to considerable shear forces, when stirring devices are employed. In order to get reliable data on the influence of shear forces on proliferation and antibody production of hybridoma cells, we tested cells, producing monoclonal antibodies against mitochondrial creatine kinase (Mi-CK), under laminar flow conditions in a rotating viscosimeter. Flow conditions in the annular gap were characterized by measuring the speed of revolution of the inner cylinder and the torque. From these data the shear stress could be determined. To confirm the laminar flow condition the velocity profile was determined by laser Doppler anemometry (LDA). After exposure to shear stress, cells were tested for viability, growth rate, antibody production as well as for the glucose uptake and lactate production rates. The data showed that cell death increases as a function of shear stress. The cells, remaining viable after exposure to shear stress showed growth and production rates similar to untreated cells.     

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.     

The shape of a membrane protein derived from rotational diffusion

Membrane proteins are modelled as cylinders with an elliptic cross-section in the plane of the membrane. The coefficient for rotational diffusion about the cylinder axis is calculated as a function of the axial ratio of the elliptic cross-section.     

A fluid dynamics approach to bioreactor design for cell and tissue culture

The problem of controlling cylindrical tank bioreactor conditions for cell and tissue culture purposes has been considered from a flow dynamics perspective. Simple laminar flows in the vortex breakdown region are proposed as being a suitable alternative to turbulent spinner flask flows and horizontally oriented rotational flows. Vortex breakdown flows have been measured using three-dimensional Stereoscopic particle image velocimetry, and non-dimensionalized velocity and stress distributions are presented. Regions of locally high principal stress occur in the vicinity of the impeller and the lower sidewall. Topological changes in the vortex breakdown region caused by an increase in Reynolds number are reflected in a redistribution of the peak stress regions. The inclusion of submerged scaffold models adds complexity to the flow, although vortex breakdown may still occur. Relatively large stresses occur along the edge of disks jutting into the boundary of the vortex breakdown region.     

Computational analysis of confined jet flow and mass transport in a blind tube.

A computational analysis of confined nonimpinging jet flow in a blind tube is performed as an initial investigation of the underlying fluid and mass transport mechanics of tracheal gas insufflation. A two-dimensional axisymmetric model of a laminar steady jet flow into a concentric blind-end tube is put forth and the governing continuity, momentum, and convection-diffusion equations are solved with a finite element code. The effects of the jet diameter based Reynolds number (Re(j)), the ratio of the jet-to-outer tube diameters (epsilon), and the Schmidt number (Sc) are evaluated with the determined velocity and contaminant concentration fields. The normalized penetration depth of the jet is found to increase linearly with increasing Re(j) for epsilon = O(0.1). For a given epsilon, a ring vortex that develops is observed to be displaced downstream and radially outward from the jet tip for increasing Re(j). The axial shear stress profile along the inside wall of the outer tube possesses regions of fixed shear stress in addition to a local minimum and maximum in the vicinity of the jet tip. Corresponding regions of axial shear stress gradients exist between the fixed shear stress regions and the local extrema. Contaminant concentration gradients develop across the ring vortex indicating the inward diffusion of contaminant into the jet flow. For fixed epsilon and Sc and Re(j) approximately 900, normalized contaminant flow rate is observed to be approximately twice that of simple diffusion. This model predicts modest net axial contaminant transport enhancement due to convection-diffusion interaction in the region of the ring vortex.     

Flow pattern and shear stress distribution of distal end-to-side anastomoses. A comparison of the instantaneous velocity fields obtained by particle image velocimetry

OBJECTIVE: To describe the local hemodynamics and pressure losses of crural bypass anastomoses using instantaneous velocity fields acquired by particle image velocimetry (PIV). METHODS: Silastic models of a Taylor patch, a Miller cuff and a femoro-crural patch prosthesis (FCPP) were attached to a circuit driven by a Berlin Heart, providing a pulsatile flow with an amplitude of 450 to 25 ml/min (mean 200 ml/min). An outflow resistance of 0.5 mmHg/ml/min (peripheral resistance units, PRU) was modeled using small silastic tubes providing a phase shift of -12 degrees between flow and pressure curves. The working fluid consisted of a glycerine/water mixture with a viscosity of 4 mPas. Hollow glass spheres with a mean size of 9-13 microm were used as tracer particles. Instantaneous velocity fields were obtained by means of PIV and shear rates as well as shear stresses were calculated. Triggered by the flowmeter signal, 10 measurements at 100 ms intervals per cardiac cycle were obtained. The pressures were measured on the inflow and at both distal outflows. The resulting mean pressure losses due to flow separation and distal fluid acceleration were calculated. RESULTS: Inside the Taylor patch anastomosis a large flow separation at the hood containing a clockwise rotating vortex was found. Additionally a smaller flow separation at the heel and a flow stagnation zone on the floor of the recipient artery were observed. Conversely, inside the Miller cuff a counterclockwise rotating vortex was seen inside a large heel flow separation. The FCPP also showed typical separation areas at the hood and heel of the anastomosis, although these were smaller compared to the other anastomoses. Inside the FCPP anastomosis no vortex creation was observed throughout the cardiac cycle. The mainstream velocities at the inlet levels were comparable for the three anastomoses. A significant fluid acceleration was present at the antegrade as well as the retrograde outlets of the Taylor and Miller cuff, while the fluid acceleration at the antegrade outflow of the FCPP was small, which was attributed to the end-to-end configuration of the antegrade FCPP leg. The calculated normalized antegrade and retrograde pressure losses for the Taylor form were 0.90 and 0.88, for the Miller cuff 0.89 and 0.86 and for the FCPP 0.94 and 0.86, respectively. The shear stresses inside the flow separations of the three anastomoses were significantly lower than normal wall shear stresses. High shear stress levels were found inside the transition zones between flow separation and high velocity mainstream. CONCLUSIONS: The flow pattern inside cuffed or funnel shaped anastomoses consists of large flow separation zones, which are thought to be associated with intimal hyperplasia development. In addition, fluid accelerations at the distal outlets result in pressure losses, which may contribute to impaired crural perfusion.     

Process development of starch hydrolysis using mixing characteristics of Taylor vortices

In food industries, enzymatic starch hydrolysis is an important process that consists of two steps: gelatinization and saccharification. One of the major difficulties in designing the starch hydrolysis process is the sharp change in its rheological properties. In this study, Taylor–Couette flow reactor was applied to continuous starch hydrolysis process. The concentration of reducing sugar produced via enzymatic hydrolysis was evaluated by varying operational variables: rotational speed of the inner cylinder, axial velocity (reaction time), amount of enzyme, and initial starch content in the slurry. When Taylor vortices were formed in the annular space, efficient hydrolysis occurred because Taylor vortices improved the mixing of gelatinized starch with enzyme. Furthermore, a modified inner cylinder was proposed, and its mixing performance was numerically investigated. The modified inner cylinder showed higher potential for enhanced mixing of gelatinized starch and the enzyme than the conventional cylinder.     

Photosynthetic efficiency of Chlorella sorokiniana in a turbulently mixed short light‐path photobioreactor

To be able to study the effect of mixing as well as any other parameter on productivity of algal cultures, we designed a lab‐scale photobioreactor in which a short light path (SLP) of (12 mm) is combined with controlled mixing and aeration. Mixing is provided by rotating an inner tube in the cylindrical cultivation vessel creating Taylor vortex flow and as such mixing can be uncoupled from aeration. Gas exchange is monitored on‐line to gain insight in growth and productivity. The maximal productivity, hence photosynthetic efficiency, of Chlorella sorokiniana cultures at high light intensities (1,500 μmol m^?1 s^?1) was investigated in this Taylor vortex flow SLP photobioreactor. We performed duplicate batch experiments at three different mixing rates: 70, 110, and 140 rpm, all in the turbulent Taylor vortex flow regime. For the mixing rate of 140 rpm, we calculated a quantum requirement for oxygen evolution of 21.2 mol PAR photons per mol O₂ and a yield of biomass on light energy of 0.8 g biomass per mol PAR photons. The maximal photosynthetic efficiency was found at relatively low biomass densities (2.3 g L^?1) at which light was just attenuated before reaching the rear of the culture. When increasing the mixing rate twofold, we only found a small increase in productivity. On the basis of these results, we conclude that the maximal productivity and photosynthetic efficiency for C. sorokiniana can be found at that biomass concentration where no significant dark zone can develop and that the influence of mixing‐induced light/dark fluctuations is marginal. © 2010 American Institute of Chemical Engineers Biotechnol. Prog., 2010     

Stability of elliptical cylinders in two-dimensional channel flow

The flow around rigid cylinders of elliptical cross section placed transverse to Poiseuille flow between parallel plates was simulated to investigate issues related to the tumbling of red blood cells and other particles of moderate aspect ratio in the similar flow in a Field Flow Fractionation (FFF) channel. The torque and transverse force on the cylinder were calculated with the cylinder freely translating, but prevented from rotating, in the flow. The aspect ratios (long axis to short axis) of the elliptical cylinders were 2, 3, 4, and 5. The cylinder was placed transversely at locations of y0/H = 0.1, 0.2, 0.3, and 0.4, where y0 is the distance from the bottom of the channel and H is the height of the channel, and the orientation of the cylinder was varied from 0 to 10 deg with respect to the axis of the channel for a channel Reynolds number of 20. The results showed that equilibrium orientations (indicated by a zero net torque on the cylinder) were possible for high-aspect-ratio cylinders at transverse locations y0/H < 0.2. Otherwise, the net torque on the cylinder was positive, indicating that the cylinder would rotate. For cylinders with a stable orientation, however, a transverse lift forced existed up to about y0/H = 0.25. Thus, a cylinder of neutral or low buoyancy might be lifted with a stable orientation from an initial position near the wall until it reached y0/H < 0.2, whereupon it would begin to tumble or oscillate. The dependence of lift and torque on cylinder orientation suggested that neutral or low-buoyancy cylinders may oscillate in both transverse location and angular velocity. Cylinders more dense than the carrier fluid could be in equilibrium both in terms of orientation and transverse location if their sedimentation force matched their lift force for a location y0/H < 0.2.     

Pulsatile flow effects on the hemodynamics of intracranial aneurysms

High-resolution numerical simulations are carried out to systematically investigate the effect of the incoming flow waveform on the hemodynamics and wall shear stress patterns of an anatomic sidewall intracranial aneurysm model. Various wave forms are constructed by appropriately scaling a typical human waveform such that the waveform maximum and time-averaged Reynolds numbers, the Womersley number (α), and the pulsatility index (PI) are systematically varied within the human physiologic range. We show that the waveform PI is the key parameter that governs the vortex dynamics across the aneurysm neck and the flow patterns within the dome. At low PI, the flow in the dome is similar to a driven cavity flow and is characterized by a quasi-stationary shear layer that delineates the parent artery flow from the recirculating flow within the dome. At high PI, on the other hand, the flow is dominated by vortex ring formation, transport across the neck, and impingement and breakdown at the distal wall of the aneurysm dome. We further show that the spatial and temporal characteristics of the wall shear stress field on the aneurysm dome are strongly correlated with the vortex dynamics across the neck. We finally argue that the ratio between the characteristic time scale of transport by the mean flow across the neck and the time scale of vortex ring formation can be used to predict for a given sidewall aneurysm model the critical value of the waveform PI for which the hemodynamics will transition from the cavity mode to the vortex ring mode.     

The vortex wake of a 'hovering' model hawkmoth

Visualization experiments with Manduca sexta have revealed the presence of a leading-edge vortex and a highly three-dimensional flow pattern. To further investigate this important discovery, a scaled-up robotic insect was built (the ''flapper'') which could mimic the complex movements of the wings of a hovering hawkmoth. Smoke released from the leading edge of the flapper wing revealed a small but strong leading-edge vortex on the downstroke. This vortex had a high axial flow velocity and was stable, separating from the wing at approximately 75 per cent of the wing length. It connected to a large, tangled tip vortex, extending back to a combining stopping and starting vortex from pronation. At the end of the downstroke, the wake could be approximated as one vortex ring per wing. Based on the size and velocity of the vortex rings, the mean lift force during the downstroke was estimated to be about 1.5 times the body weight of a hawkmoth, confirming that the downstroke is the main provider of lift force.     

Motion of cells sedimenting on a solid surface in a laminar shear flow.

Cell adhesion often occurs under dynamic conditions, as in flowing blood. A quantitative understanding of this process requires accurate knowledge of the topographical relationships between the cell membrane and potentially adhesive surfaces. This report describes an experimental study made on both the translational and rotational velocities of leukocytes sedimenting of a flat surface under laminar shear flow. The main conclusions are as follows: (a) Cells move close to the wall with constant velocity for several tens of seconds. (b) The numerical values of translational and rotational velocities are inconsistent with Goldman's model of a neutrally buoyant sphere in a laminar shear flow, unless a drag force corresponding to contact friction between cells and the chamber floor is added. The phenomenological friction coefficient was 7.4 millinewton.s/m. (c) Using a modified Goldman's theory, the width of the gap separating cells (6 microns radius) from the chamber floor was estimated at 1.4 micron. (d) It is shown that a high value of the cell-to-substrate gap may be accounted for by the presence of cell surface protrusions of a few micrometer length, in accordance with electron microscope observations performed on the same cell population. (e) In association with previously reported data (Tissot, O., C. Foa, C. Capo, H. Brailly, M. Delaage, and P. Bongrand. 1991. Biocolloids and Biosurfaces. In press), these results are consistent with the possibility that cell-substrate attachment be initiated by the formation of a single molecular bond, which might be considered as the rate limiting step.     

Two-equation turbulence modeling of pulsatile flow in a stenosed tube

The study of pulsatile flow in stenosed vessels is of particular importance because of its significance in relation to blood flow in human pathophysiology. To date, however, there have been few comprehensive publications detailing systematic numerical simulations of turbulent pulsatile flow through stenotic tubes evaluated against comparable experiments. In this paper, two-equation turbulence modeling has been explored for sinusoidally pulsatile flow in 75% and 90% area reduction stenosed vessels, which undergoes a transition from laminar to turbulent flow as well as relaminarization. Wilcox's standard k-omega model and a transitional variant of the same model are employed for the numerical simulations. Steady flow through the stenosed tubes was considered first to establish the grid resolution and the correct inlet conditions on the basis of comprehensive comparisons of the detailed velocity and turbulence fields to experimental data. Inlet conditions based on Womersley flow were imposed at the inlet for all pulsatile cases and the results were compared to experimental data from the literature. In general, the transitional version of the k-omega model is shown to give a better overall representation of both steady and pulsatile flow. The standard model consistently over predicts turbulence at and downstream of the stenosis, which leads to premature recovery of the flow. While the transitional model often under-predicts the magnitude of the turbulence, the trends are well-described and the velocity field is superior to that predicted using the standard model. On the basis of this study, there appears to be some promise for simulating physiological pulsatile flows using a relatively simple two-equation turbulence model.     

The three-dimensional leading-edge vortex of a 'hovering' model hawkmoth

Recent flow visualisation experiments with the hawkmoth, Manduca sexta, revealed small but clear leading-edge vortex and a pronounced three-dimensional flow. Details of this flow pattern were studied with a scaled-up, robotic insect (''the flapper'') that accurately mimicked the wing movements of a hovering hawkmoth. Smoke released from the leading edge of the flapper wing confirmed the existence of a small, strong and stable leading-edge vortex, increasing in size from wingbase to wingtip. Between 25 and 75 per cent of the wing length, its diameter increased approximately from 10 to 50 per cent of the wing chord. The leading-edge vortex had a strong axial flow veolocity, which stabilized it and reduced its diamater. The vortex separated from the wing at approximately 75 per cent of the wing length and thus fed vorticity into a large, tangled tip vortex. If the circulation of the leading-edge vortex were fully used for lift generation, it could support up to two-thirds of the hawkmoth''s weight during the downstroke. The growth of this circulation with time and spanwise position clearly identify dynamic stall as the unsteady aerodynamic mechanism responsible for high lift production by hovering hawkmoths and possibly also by many other insect species.