Relationship between mass transfer coefficient and liquid flow velocity in heterogenous biofilms using microelectrodes and confocal microscopy

The relationship between local mass transfer coefficient and fluid velocity in heterogenous biofilms was investigated by combining microelectrodes and confocal scanning laser microscopy (CSLM). The biofilms were grown for up to 7 days and consisted of cell clusters separated by interstitial channels. Mass transfer coefficient depth profiles were measured at specific locations in the cell clusters and channels at average flow velocities of 2.3 and 4.0 cm/s. Liquid flow velocity profiles were measured in the same locations using a particle tracking technique. The velocity profiles showed that flow in the open channel was laminar. There was no flow at the top surface of the biofilm cell clusters but the mass transfer coefficient was 0.01 cm/s. At the same depth in a biofilm channel, the flow velocity was 0.3 cm/s and the mass transfer coefficient was 0.017 cm/s. The mass transfer coefficient profiles in the channels were not influenced by the surrounding cell clusters. Local flow velocities were correlated with local mass transfer coefficients using a semi-theoretical mass transfer equation. The relationship between the Sherwood number (Sh,) the Reynolds number (Re,) and the Schmidt number (Sc) was found using the experimental data to find the dimensionless empirical constants (n1, n2, and m) in the equation Sh = n(1) + n(2)Re(m) Sc(1/3). The values of the constants ranged from 1.45 to 2.0 for n(1), 0.22 to 0.28 for n(2), and 0.21 to 0.60 for m. These values were similar to literature values for mass transfer in porous media. The Sherwood number for the entire flow cell was 10 when the bulk flow velocity was 2.3 cm/s and 11 when the bulk flow velocity was 4.0 cm/s. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 681-688, 1997.     

Measurement of local mass transfer coefficients in a cast model of the human upper respiratory tract

Local mass transfer coefficients measured using the naphthalene sublimation technique in an acrylic cast model of the human upper respiratory tract are reported as the Sherwood numbers for the corresponding regions. A steady air flow rate of 12 L per min was used for all measurements. Values of the Sherwood number are seen to be highest in the nasal cavity and proximal nasopharynx while a minimum value occurs just downstream from the larynx. Local values of the Nusselt number obtained in the trachea and proximal nasal cavity assuming a complete heat and mass transfer analogy agree well with in-vivo physiological measurements. The mass transfer coefficients found can be incorporated into an analytical model of respiratory heat and water vapor transfer or into a model of pollutant gas uptake in the respiratory tract.     

Effect of inlet velocity profiles on patient-specific computational fluid dynamics simulations of the carotid bifurcation

Patient-specific computational fluid dynamics (CFD) is a powerful tool for researching the role of blood flow in disease processes. Modern clinical imaging technology such as MRI and CT can provide high resolution information about vessel geometry, but in many situations, patient-specific inlet velocity information is not available. In these situations, a simplified velocity profile must be selected. We studied how idealized inlet velocity profiles (blunt, parabolic, and Womersley flow) affect patient-specific CFD results when compared to simulations employing a "reference standard" of the patient's own measured velocity profile in the carotid bifurcation. To place the magnitude of these effects in context, we also investigated the effect of geometry and the use of subject-specific flow waveform on the CFD results. We quantified these differences by examining the pointwise percent error of the mean wall shear stress (WSS) and the oscillatory shear index (OSI) and by computing the intra-class correlation coefficient (ICC) between axial profiles of the mean WSS and OSI in the internal carotid artery bulb. The parabolic inlet velocity profile produced the most similar mean WSS and OSI to simulations employing the real patient-specific inlet velocity profile. However, anatomic variation in vessel geometry and the use of a nonpatient-specific flow waveform both affected the WSS and OSI results more than did the choice of inlet velocity profile. Although careful selection of boundary conditions is essential for all CFD analysis, accurate patient-specific geometry reconstruction and measurement of vessel flow rate waveform are more important than the choice of velocity profile. A parabolic velocity profile provided results most similar to the patient-specific velocity profile.     

Microbial growth rates and local external mass transfer coefficients in a porous bed biofilm system measured by 19F magnetic resonance imaging of structure,oxygen concentration,and flow velocity

¹⁹F nuclear magnetic resonance (NMR) oximetry and ¹H NMR velocimetry were used to noninvasively map oxygen concentrations and hydrodynamics in space and time in a model packed bed biofilm system in the presence and absence of flow. The development of a local oxygen sink associated with a single gel bead inoculated with respiring Escherichia coli was analyzed with a phenomenological model to determine the specific growth rate of the bacteria in situ, returning a value (0.66 hr⁻¹) that was close to that measured independently in planktonic culture (0.62 hr⁻¹). The decay of oxygen concentration in and around the microbiologically active bead was delayed and slower in experiments conducted under continuous flow in comparison to no-flow experiments. Concentration boundary layer thicknesses were determined and Sherwood numbers calculated to quantify external mass transfer resistance. Boundary layers were thicker in no-flow experiments compared to experiments with flow. Whereas the oxygen concentration profile across a reactive biofilm particle was symmetric in no-flow experiments, it was asymmetric with respect to flow direction in flow experiments with Sherwood numbers on the leading edge (Sh = 7) being larger than the trailing edge (Sh = 3.5). The magnitude of the experimental Sh was comparable to values predicted by a variety of correlations. These spatially resolved measurements of oxygen distribution in a geometrically complex model reveal in innovative detail the local coupling between microbial growth, oxygen consumption, and external mass transfer.     

Variations in mass transfer to single endothelial cells

Mass transfer between flowing blood and arterial mural cells (including vascular endothelial cells) may play an important role in atherogenesis. Endothelial cells are known to have an apical surface topography that is not flat, and hence mass transfer patterns to individual endothelial cells are likely affected by the local cellular topography. The purpose of this paper is to investigate the relationship between vascular endothelial cell surface topography and cellular level mass transfer. Confluent porcine endothelial monolayers were cultured under both shear and static conditions and atomic force microscopy was used to measure endothelial cell topography. Using finite element methods and the measured cell topography, flow and concentration fields were calculated for a typical, small, blood-borne solute. A relative Sherwood number was defined as the difference between the computed Sherwood number and that predicted by the Leveque solution for mass transfer over a flat surface: this eliminates the effects of axial location on mass transfer efficiency. The average intracellular relative Sherwood number range was found to be dependent on cell height and not dependent on cell elongation due to shear stress in culture. The mass flux to individual cells reached a maximum at the highest point on the endothelial cell surface, typically corresponding to the nucleus of the cell. Therefore, for small receptor-mediated solutes, increased solute uptake efficiency can be achieved by concentrating receptors near the nucleus. The main conclusion of the work is that although the rate of mass transfer varies greatly over an individual cell, the average mass transfer rate to a cell is close to that predicted for a flat cell. In comparison to other hemodynamic factors, the topography of endothelial cells therefore seems to have little effect on mass transfer rates and is likely physiologically insignificant.     

Methodology for predicting oxygen transport on an intravenous membrane oxygenator combining computational and analytical models

A computational methodology for accurately predicting flow and oxygen-transport characteristics and performance of an intravenous membrane oxygenator (IMO) device is developed, tested, and validated. This methodology uses extensive numerical simulations of three-dimensional computational models to determine flow-mixing characteristics and oxygen-transfer performance, and analytical models to indirectly validate numerical predictions with experimental data, using both blood and water as working fluids. Direct numerical simulations for IMO stationary and pulsating balloons predict flow field and oxygen transport performance in response to changes in the device length, number of and balloon pulsation frequency. Multifiber models are used to investigate interfiber interference and length effects for a stationary balloon whereas a single fiber model is used to analyze the effect of balloon pulsations on velocity and oxygen concentration fields and to evaluate oxygen transfer rates. An analytical lumped model is developed and validated by comparing its numerical predictions with experimental data. Numerical results demonstrate that oxygen transfer rates for a stationary balloon regime decrease with increasing number of fibers, independent of the fluid type. The oxygen transfer rate ratio obtained with blood and water is approximately two. Balloon pulsations show an effective and enhanced flow mixing, with time-dependent recirculating flows around the fibers regions which induce higher oxygen transfer rates. The mass transfer rates increase approximately 100% and 80%, with water and blood, respectively, compared with stationary balloon operation. Calculations with combinations of frequency, number of fibers, fiber length and diameter, and inlet volumetric flow rates, agree well with the reported experimental results, and provide a solid comparative base for analysis, predictions, and comparisons with numerical and experimental data.     

Packed bed dynamics during microbial treatment of wastewater: modelling and simulation

A mathematical model consisting of mass balance equations and accounting for bioreaction and mass transfer is presented to describe both unsteady and steady-state degradation of phenol in a biofilter. The model has been validated for the steady-state situation with literature work. The model has been able to predict the dynamics of the biofiltration process with variations in system and operating conditions as inlet substrate concentration, liquid phase mass transfer coefficients, particle size, Henry's constant, inlet velocity, growth and half saturation constants and bed void fraction. The results show that inlet substrate concentration, inlet velocity, growth and half saturation constants and liquid phase mass transfer coefficients significantly control the operational dynamics. It is also shown that inhibition effects can be neglected for low concentrations (<0.5 kg m(-3)) of phenol. Thus, the model can be used as a design tool for a biofilter.     

Effect of common carotid artery inlet length on normal carotid bifurcation hemodynamics

Controversy exists regarding the suitability of fully developed versus measured inlet velocity profiles for image-based computational fluid dynamics (CFD) studies of carotid bifurcation hemodynamics. Here, we attempt to resolve this by investigating the impact of the reconstructed common carotid artery (CCA) inlet length on computed metrics of "disturbed" flow. Twelve normal carotid bifurcation geometries were reconstructed from contrast-enhanced angiograms acquired as part of the Vascular Aging--The Link That Bridges Age to Atherosclerosis study (VALIDATE). The right carotid artery lumen geometry was reconstructed from its brachiocephalic origin to well above the bifurcation, and the CCA was truncated objectively at locations one, three, five, and seven diameters proximal to where it flares into the bifurcation. Relative to the simulations carried out using the full CCA, models truncated at one CCA diameter strongly overestimated the amount of disturbed flow. Substantial improvement was offered by using three CCA diameters, with only minor further improvement using five CCA diameters. With seven CCA diameters, the amounts of disturbed flow agreed unambiguously with those predicted by the corresponding full-length models. Based on these findings, we recommend that image-based CFD models of the carotid bifurcation should incorporate at least three diameters of CCA length if fully developed velocity profiles are to be imposed at the inlet. The need for imposing measured inlet velocity profiles would seem to be relevant only for those cases where the CCA is severely truncated.     

Microelectrode measurements of local mass transport rates in heterogeneous biofilms

Microelectrodes were used to measure oxygen profiles and local mass transfer coefficient profiles in biofilm clusters and interstitial voids. Both profiles were measured at the same location in the biofilm. From the oxygen profile, the effective diffusive boundary layer thickness (DBL) was determined. The local mass transfer coefficient profiles provided information about the nature of mass transport near and within the biofilm. All profiles were measured at three different average flow velocities, 0.62, 1.53, and 2.60 cm sec-1, to determine the influence of flow velocity on mass transport. Convective mass transport was active near the biofilm/liquid interface and in the upper layers of the biofilm, independent of biofilm thickness and flow velocity. The DBL varied strongly between locations for the same flow velocities. Oxygen and local mass transfer coefficient profiles collected through a 70 micrometer thick cluster revealed that a cluster of that thickness did not present any significant mass transport resistance. In a 350 micrometer thick biofilm cluster, however, the local mass transfer coefficient decreased gradually to very low values near the substratum. This was hypothetically attributed to the decreasing effective diffusivity in deeper layers of biofilms. Interstitial voids between clusters did not seem to influence the local mass transfer coefficients significantly for flow velocities of 1.53 and 2.60 cm sec-1. At a flow velocity of 0.62 cm sec-1, interstitial voids visibly decreased the local mass transfer coefficient near the bottom.     

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.     

Double Diffusive Magnetohydrodynamic (MHD) Mixed Convective Slip Flow along a Radiating Moving Vertical Flat Plate with Convective Boundary Condition

In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, , local Nusselt number, , and local Sherwood number are shown and explained through tables.     

Characteristics of airflow in a CT-based ovine lung: a numerical study.

The transient airflow in a rigid, asymmetric monopodial sheep (ovine) tracheobronchial tree of up to 13 generations was investigated numerically. The lung geometry was segmented and reconstructed from computed-tomographic (CT) images. The flow characteristics in the image-based sheep airway were compared with the flow patterns produced by a Weibel-based model at prime locations. Boundary conditions were prescribed 1) a velocity profile from experimental data at the inlet and 2) zero pressure at the bronchial outlets. A mesh convergence study was carried out to establish confidence in the model predictions, and gross left-right ventilation was validated against experimental xenon wash-in-washout data. Detailed flow characteristics were investigated at three points in the breathing cycle: 1) peak inhalation, 2) peak exhalation, and 3) transition. Simulation results revealed fundamental differences between airflow in monopodial and bipodial branching airways. Compared with idealized bipodial flow, the flow in the sheep airway was asymmetric and highly vortical, especially during exhalation and transition. The streak lines during the inhalation phase suggest that the left and right upper lobes are ventilated by airflow in the peripheral region of the trachea. This work may contribute to understanding the interplay between structure and function in the lung.     

Inlet conditions for image-based CFD models of the carotid bifurcation: is it reasonable to assume fully developed flow?

BACKGROUND: Computational fluid dynamics tools are useful for their ability to model patient specific data relevant to the genesis and progression of atherosclerosis, but unavailable to measurement tools. The sensitivity of the physiologically relevant parameters of wall shear stress (WSS) and the oscillatory shear index (OSI) to secondary flow in the inlet velocity profiles was investigated in three realistic models of the carotid bifurcation. METHOD OF APPROACH: Secondary flow profiles were generated using sufficiently long entrance lengths, to which curvature and helical pitch were added. The differences observed were contextualized with respect to effect of the uncertainty of the models' geometry on the same parameters. RESULTS: The effects of secondary velocities in the inlet profile on WSS and OSI break down within a few diameters of the inlet. Overall, the effect of secondary inlet flow on these models was on average more than 3.5 times smaller than the effect of geometric variability, with 13% and 48% WSS variability induced by inlet secondary flow and geometric differences, respectively. CONCLUSIONS: The degree of variation is demonstrated to be within the range of the other computational assumptions, and we conclude that given a sufficient entrance length of realistic geometry, simplification to fully developed axial (i.e., Womersley) flow may be made without penalty. Thus, given a choice between measuring three components of inlet velocity or a greater geometric extent, we recommend effort be given to more accurate and detailed geometric reconstructions, as being of primary influence on physiologically significant indicators.     

A theoretical study on the effect of surface roughness on mass transport and transformation in biofilms

This modeling study evaluates the influence of biofilm geometrical characteristics on substrate mass transfer and conversion rates. A spatially two-dimensional model was used to compute laminar fluid flow, substrate mass transport, and conversion in irregularly shaped biofilms. The flow velocity above the biofilm surface was varied over 3 orders of magnitude. Numerical results show that increased biofilm roughness does not necessarily lead to an enhancement of either conversion rates or external mass transfer. The average mass transfer coefficient and Sherwood numbers were found to decrease almost linearly with biofilm area enlargement in the flow regime tested. The influence of flow, biofilm geometry and biofilm activity on external mass transfer could be quantified by Sh-Re correlations. The effect of biofilm surface roughness was incorporated in this correlation via area enlargement. Conversion rates could be best correlated to biofilm compactness. The more compact the biofilm, the higher the global conversion rate of substrate. Although an increase of bulk fluid velocity showed a large effect on mass transfer coefficients, the global substrate conversion rate per carrier area was less affected. If only diffusion occurs in pores and channels, then rough biofilms behave as if they were compact but having less biomass activity. In spite of the fact that the real biofilm area is increased due to roughness, the effective mass transfer area is actually decreased because only biofilm peaks receive substrate. This can be explained by the fact that in the absence of normal convection in the biofilm valleys, the substrate gradients are still largely perpendicular to the carrier. Even in the cases where convective transport dominates the external mass transfer process, roughness could lead to decreased conversion rates. The results of this study clearly indicate that only evaluation of overall conversion rates or mass fluxes can describe the correct biofilm conversion, whereas interpretation of local concentration or flow measurements as such might easily lead to erroneous conclusions.     

Flow mixing enhancement from balloon pulsations in an intravenous oxygenator

Computational investigations of flow mixing and oxygen transfer characteristics in an intravenous membrane oxygenator (IMO) are performed by direct numerical simulations of the conservation of mass, momentum, and species equations. Three-dimensional computational models are developed to investigate flow-mixing and oxygen-transfer characteristics for stationary and pulsating balloons, using the spectral element method. For a stationary balloon, the effect of the fiber placement within the fiber bundle and the number of fiber rings is investigated. In a pulsating balloon, the flow mixing characteristics are determined and the oxygen transfer rate is evaluated. For a stationary balloon, numerical simulations show two well-defined flow patterns that depend on the region of the IMO device. Successive increases of the Reynolds number raise the longitudinal velocity without creating secondary flow. This characteristic is not affected by staggered or non-staggered fiber placement within the fiber bundle. For a pulsating balloon, the flow mixing is enhanced by generating a three-dimensional time-dependent flow characterized by oscillatory radial, pulsatile longitudinal, and both oscillatory and random tangential velocities. This three-dimensional flow increases the flow mixing due to an active time-dependent secondary flow, particularly around the fibers. Analytical models show the fiber bundle placement effect on the pressure gradient and flow pattern. The oxygen transport from the fiber surface to the mean flow is due to a dominant radial diffusion mechanism, for the stationary balloon. The oxygen transfer rate reaches an asymptotic behavior at relatively low Reynolds numbers. For a pulsating balloon, the time-dependent oxygen-concentration field resembles the oscillatory and wavy nature of the time-dependent flow. Sherwood number evaluations demonstrate that balloon pulsations enhance the oxygen transfer rate, even for smaller flow rates.     

Conjugate Effects of Heat and Mass Transfer on MHD Free Convection Flow over an Inclined Plate Embedded in a Porous Medium

The aim of this study is to present an exact analysis of combined effects of radiation and chemical reaction on the magnetohydrodynamic (MHD) free convection flow of an electrically conducting incompressible viscous fluid over an inclined plate embedded in a porous medium. The impulsively started plate with variable temperature and mass diffusion is considered. The dimensionless momentum equation coupled with the energy and mass diffusion equations are analytically solved using the Laplace transform method. Expressions for velocity, temperature and concentration fields are obtained. They satisfy all imposed initial and boundary conditions and can be reduced, as special cases, to some known solutions from the literature. Expressions for skin friction, Nusselt number and Sherwood number are also obtained. Finally, the effects of pertinent parameters on velocity, temperature and concentration profiles are graphically displayed whereas the variations in skin friction, Nusselt number and Sherwood number are shown through tables.     

Influence of model boundary conditions on blood flow patterns in a patient specific stenotic right coronary artery

Background

In literature, the effect of the inflow boundary condition was investigated by examining the impact of the waveform and the shape of the spatial profile of the inlet velocity on the cardiac hemodynamics. However, not much work has been reported on comparing the effect of the different combinations of the inlet/outlet boundary conditions on the quantification of the pressure field and flow distribution patterns in stenotic right coronary arteries.

Method

Non-Newtonian models were used to simulate blood flow in a patient-specific stenotic right coronary artery and investigate the influence of different boundary conditions on the phasic variation and the spatial distribution patterns of blood flow. The 3D geometry of a diseased artery segment was reconstructed from a series of IVUS slices. Five different combinations of the inlet and the outlet boundary conditions were tested and compared.

Results

The temporal distribution patterns and the magnitudes of the velocity, the wall shear stress (WSS), the pressure, the pressure drop (PD), and the spatial gradient of wall pressure (WPG) were different when boundary conditions were imposed using different pressure/velocity combinations at inlet/outlet. The maximum velocity magnitude in a cardiac cycle at the center of the inlet from models with imposed inlet pressure conditions was about 29% lower than that from models using fully developed inlet velocity data. Due to the fact that models with imposed pressure conditions led to blunt velocity profile, the maximum wall shear stress at inlet in a cardiac cycle from models with imposed inlet pressure conditions was about 29% higher than that from models with imposed inlet velocity boundary conditions. When the inlet boundary was imposed by a velocity waveform, the models with different outlet boundary conditions resulted in different temporal distribution patterns and magnitudes of the phasic variation of pressure. On the other hand, the type of different boundary conditions imposed at the inlet and the outlet did not have significant effect on the spatial distribution patterns of the PD, the WPG and the WSS on the lumen surface, regarding the locations of the maximum and the minimum of each quantity.

Conclusions

The observations from this study indicated that the ways how pressure and velocity boundary conditions are imposed in computational models have considerable impact on flow velocity and shear stress predictions. Accuracy of in vivo measurements of blood pressure and velocity is of great importance for reliable model predictions.

     

Quantitative comparison of CFD predicted and MRI measured velocity fields in a carotid bifurcation phantom

Steady flow of a blood mimicking fluid in a physiologically realistic model of the human carotid bifurcation was studied using both magnetic resonance imaging (MRI) and computational fluid dynamics (CFD) modelling techniques. Quantitative comparisons of the 3D velocity field in the bifurcation phantom were made between phase contrast MRI measurements and CFD predictions. The geometry for the CFD model was reconstructed from T(1) weighted MR imaging of the test phantom. It was found that the predicted velocity fields were in fair agreement with MR measured velocities. In both the internal and external carotid arteries, the agreement between CFD predictions and MRI measurements was better along the inner-outer wall axis with a correlation factor C>0.897 (average 0.939) where the velocity profiles were skewed, than along the anterior-posterior axis (average correlation factor 0.876) where the velocity profiles were in M-shape.     

LDA measurements and numerical prediction of pulsatile laminar flow in a plane 90-degree bifurcation

An experimental and numerical study of pulsatile laminar flow in a plane 90-degree bifurcation is presented. Detailed LDA velocity measurements of the oscillatory flow field have been carried out. The numerical predictions, which are based on an iterative, finite-difference numerical procedure using primitive dependent variables, are in good agreement with the measurements. The results show that one separation zone is established near the bottom wall of the main duct and another near the upstream wall of the branch. The location and size of the separation zones vary within the cycle and are influenced by the Reynolds number, the flow rate ratio, and the Stokes number.