Showing papers on "Shear stress published in 2002"

Biofilm material properties as related to shear-induced deformation and detachment phenomena.

Abstract: Biofilms of various Pseudomonas aeruginosa strains were grown in glass flow cells under laminar and turbulent flows. By relating the physical deformation of biofilms to variations in fluid shear, we found that the biofilms were viscoelastic fluids which behaved like elastic solids over periods of a few seconds but like linear viscous fluids over longer times. These data can be explained using concepts of associated polymeric systems, suggesting that the extracellular polymeric slime matrix determines the cohesive strength. Biofilms grown under high shear tended to form filamentous streamers while those grown under low shear formed an isotropic pattern of mound-shaped microcolonies. In some cases, sustained creep and necking in response to elevated shear resulted in a time-dependent fracture failure of the "tail" of the streamer from the attached upstream "head." In addition to structural differences, our data suggest that biofilms grown under higher shear were more strongly attached and were cohesively stronger than those grown under lower shears.

A study of compressibility effects in the high-speed turbulent shear layer using direct simulation

Abstract: Direct simulations of the turbulent shear layer are performed for subsonic to supersonic Mach numbers. Fully developed turbulence is achieved with profiles of mean velocity and turbulence intensities that agree well with laboratory experiments. The thickness growth rate of the shear layer exhibits a large reduction with increasing values of the convective Mach number, Mc. In agreement with previous investigations, it is found that the normalized pressure–strain term decreases with increasing Mc, which leads to inhibited energy transfer from the streamwise to cross-stream fluctuations, to the reduced turbulence production observed in DNS, and, finally, to reduced turbulence levels as well as reduced growth rate of the shear layer. An analysis, based on the wave equation for pressure, with supporting DNS is performed with the result that the pressure–strain term decreases monotonically with increasing Mach number. The gradient Mach number, which is the ratio of the acoustic time scale to the flow distortion time scale, is shown explicitly by the analysis to be the key quantity that determines the reduction of the pressure–strain term in compressible shear flows. The physical explanation is that the finite speed of sound in compressible flow introduces a finite time delay in the transmission of pressure signals from one point to an adjacent point and the resultant increase in decorrelation leads to a reduction in the pressure–strain correlation.The dependence of turbulence intensities on the convective Mach number is investigated. It is found that all components decrease with increasing Mc and so does the shear stress.DNS is also used to study the effect of different free-stream densities parameterized by the density ratio, s = ρ2/ρ1, in the high-speed case. It is found that changes in the temporal growth rate of the vorticity thickness are smaller than the changes observed in momentum thickness growth rate. The momentum thickness growth rate decreases substantially with increasing departure from the reference case, s = 1. The peak value of the shear stress, uv, shows only small changes as a function of s. The dividing streamline of the shear layer is observed to move into the low-density stream. An analysis is performed to explain this shift and the consequent reduction in momentum thickness growth rate.

Grain-size-sensitive seismic wave attenuation in polycrystalline olivine

Abstract: [1] In order to investigate the processes responsible for the attenuation of seismic shear waves in the Earth's upper mantle, four olivine polycrystals ranging in mean grain size d from 3 to 23 μm have been fabricated, characterized, and mechanically tested in torsion at high temperatures and seismic frequencies. Both the shear modulus, which governs the shear wave speed VS, and the dissipation of shear strain energy Q−1 have been measured as functions of oscillation period To, temperature T, and, for the first time, grain size. At sufficiently high T all four specimens display similar absorption band viscoelastic behavior, adequately represented for 1000 < T < 1200 or 1300°C and 1 < To < 100 s, by the expression Q−1 = A [Tod−1 exp (−E/RT)]α with A = 7.5 × 102 s−α μmα, α = 0.26 and E = 424 kJ mol−1. This mildly grain-size-sensitive viscoelastic behavior of melt-free polycrystalline olivine is attributed to a combination of elastically and diffusionally accommodated grain boundary sliding, the latter becoming progressively more important with increasing T and/or To. Extrapolation to the larger (mm-cm) grain sizes expected in the Earth's upper mantle yields levels of dissipation comparable with those observed seismologically, implying that the same grain-size-sensitive processes might be responsible for much of the observed seismic wave attenuation. The temperature sensitivity of VS is increased substantially by the viscoelastic relaxation allowing the lateral variability of wave speeds to be associated with relatively small temperature perturbations.

Shear properties of passive ventricular myocardium

Abstract: We examined the shear properties of passive ventricular myocardium in six pig hearts. Samples (3 × 3 × 3 mm) were cut from adjacent regions of the lateral left ventricular midwall, with sides align...

Rheology and microstructure in concentrated noncolloidal suspensions

Abstract: The rheological behavior of a monodisperse suspension of non-Brownian particles undergoing simple shear flow in the presence of a weak interparticle force is studied using accelerated Stokesian dynamics. The availability of a faster numerical algorithm permits the investigation of larger systems (typically of 512 particles), and accurate results for the suspension viscosity, first and second normal stress differences, and the particle pressure are determined as a function of the volume fraction. The system microstructure, expressed through the pair-distribution function, is also studied and it is demonstrated how the resulting anisotropy in the pair-distribution function is correlated with the suspension non-Newtonian behavior. The ratio of the normal to excess shear stress is found to be an increasing function of the volume fraction, suggesting different volume fraction scalings for different elements of the stress tensor. The relative strength and range of the interparticle force is varied and its effec...

Severe plastic deformation: simple shear versus pure shear

Abstract: The paper analyzes an effect of deformation mode on structure evolution under severe plastic deformation. From a continuum standpoint, all possible strain states range from pure shear to simple shear and can be described by a single parameter. The microstructure evolution at large strains is linked with successive steps of continuous flow and flow localization. It is shown that simple shear conforms to the optimal deformation mode for development of spatial networks of high angle boundaries and fine grains during flow localization both for monotonic loading and cross loading. Using this approach, different deformation techniques for simple shear processing are considered with the emphasis on equal channel angular extrusion.

Flow-small angle neutron scattering measurements of colloidal dispersion microstructure evolution through the shear thickening transition

Abstract: The shear induced microstructure for electrostatic and Brownian suspensions are compared using in situ small angle neutron scattering (SANS). The dispersions consist of 75 nm Stober silica coated with 3-(trimethoxysilyl) propyl methacrylate (TPM) and have a zeta potential of −42.6±4.7 mV. Neutralizing the surface charge with 0.066 M¯ nitric acid yields stable hard-sphere dispersions. SANS is conducted over a range of shear rates on the charge-stabilized and Brownian suspensions to test the order–disorder transition and hydrocluster mechanisms for shear thickening, and demonstrate the influence of stabilizing forces on the shear induced microstructure evolution. Through treatment of the colloidal micromechanics, shear induced changes in the microstructure are correlated to the hydrodynamic component of the shear stress and the thermodynamic component of the normal stress, i.e., the method of “Rheo-SANS” is developed. The results demonstrate that hydrocluster formation accompanies the shear thickening trans...

Frictional-viscous flow of phyllosilicate-bearing fault rock: Microphysical model and implications for crustal strength profiles

Abstract: It is widely believed that around the brittle-ductile transition, crustal faults can be significantly weaker than predicted by conventional two-mechanism brittle-ductile strength envelopes. Factors contributing to this weakness include the polyphase nature of natural rocks, foliation development, and the action of fluid-assisted processes such as pressure solution. Recently, ring shear experiments using halite/kaolinite mixtures as an analogue for phyllosilicaterich rocks for the first time showed frictional-viscous behavior (i.e., both normal stress and strain rate sensitive behavior) involving the combined effects of pressure solution and phyllosilicates. This behavior was accompanied by the development of a mylonitic microstructure. A quantitative assessment of the implications of this for the strength of natural faults has hitherto been hampered by the absence of a microphysical model. In this paper, a microphysical model for shear deformation of foliated, phyllosilicate-bearing fault rock by pressure solution-accommodated sliding along phyllosilicate foliae is developed. The model predicts purely frictional behavior at low and high shear strain rates and frictional-viscous behavior at intermediate shear strain rates. The mechanical data on wet halite + kaolinite gouge compare favorably with the model. When applied to crustal materials, the model predicts major weakening with respect to conventional brittle-ductile strength envelopes, in particular, around the brittle-ductile transition. The predicted strength profiles suggest that in numerical models of crustal deformation the strength of high-strain regions could be approximated by an apparent friction coefficient of 0.25-0.35 down to depths of 15-20 km.

Hydraulic characteristics of rough fractures in linear flow under normal and shear load

Abstract: A hydro-mechanical testing system, which is capable of measuring both the flow rates and the normal and shear displacement of a rock fracture, was built to investigate the hydraulic behaviour of rough tension fractures. Laboratory hydraulic tests in linear flow were conducted on rough rock fractures, artificially created using a splitter under various normal and shear loading. Prior to the tests, aperture distributions were determined by measuring the topography of upper and lower fracture surfaces using a laser profilometer. Experimental variograms of the initial aperture distributions were classified into four groups of geostatistical model, though the overall experimental variograms could be well fitted to the exponential model. The permeability of the rough rock fractures decayed exponentially with respect to the normal stress increase up to 5 MPa. Hydraulic behaviours during monotonic shear loading were significantly affected by the dilation occurring until the shear stress reached the peak strength. With the further dilation, the permeability of the rough fracture specimens increased more. However, beyond shear displacement of about 7 to 8 mm, permeability gradually reached a maximum threshold value. The combined effects of both asperity degradation and gouge production, which prohibited the subsequent enlargement of mean fracture aperture, mainly caused this phenomenon. Permeability changes during cyclic shear loading showed somewhat irregular variations, especially after the first shear loading cycle, due to the complex interaction from asperity degradations and production of gouge materials. The relation between hydraulic and mechanical apertures was analyzed to investigate the valid range of mechanical apertures to be applied to the cubic law.

A new in vitro model to evaluate differential responses of endothelial cells to simulated arterial shear stress waveforms.

Abstract: In the circulation, flow-responsive endothelial cells (ECs) lining the lumen of blood vessels are continuously exposed to complex hemodynamic forces. To increase our understanding of EC response to these dynamic shearing forces, a novel in vitro flow model was developed to simulate pulsatile shear stress waveforms encountered by the endothelium in the arterial circulation. A modified waveform modeled after flow patterns in the human abdominal aorta was used to evaluate the biological responsiveness of human umbilical vein ECs to this new type of stimulus. Arterial pulsatile flow for 24 hours was compared to an equivalent time-average steady laminar shear stress, using no flow (static) culture conditions as a baseline. While both flow stimuli induced comparable changes in cell shape and alignment, distinct patterns of responses were observed in the distribution of actin stress fibers and vinculin-associated adhesion complexes, intrinsic migratory characteristics, and the expression of eNOS mRNA and protein. These results thus reveal a unique responsiveness of ECs to an arterial waveform and begin to elucidate the complex sensing capabilities of the endothelium to the dynamic characteristics of flows throughout the human vascular tree.

Drag reduction in wall-bounded turbulence via a transverse travelling wave

Abstract: Computational experiments based on direct numerical simulation of wall-bounded flow reveal that turbulence production can be suppressed by the action of a transverse travelling wave. Flow visualizations show that the near-wall flow structure is altered substantially, compared to other turbulence control techniques, leading to a large amount of shear stress reduction (i.e., more than 30%). The travelling wave can be induced by a spanwise force that is confined within the viscous sublayer, it has its maximum at the wall, and decays exponentially away from it. We demonstrate the robustness of this approach, and its application in salt water using arrays of electro-magnetic tiles that can produce the required travelling wave excitation. We also study corresponding results from spanwise oscillations using a similar force, which also leads to large drag reduction. Although the turbulence statistics for the two approaches are similar, the near-wall structures appear to be different: in the spanwise oscillatory excitation there is a clear presence of wall-streaks whereas in the travelling wave excitation these streaks have disappeared. From the fundamental point of view, the new finding of this work is that appropriate enhancement of the streamwise vortices leads to weakening of the streak intensity, as measured by the normal vorticity component, and correspondingly substantial suppression of turbulence production. From the practical point of view, our findings provide guidance for designing different surface-based actuation techniques including piezoelectric materials, shape memory alloys, and electro-magnetic tiles.

The low frequency reflection characteristics of the fundamental antisymmetric Lamb wave a0 from a rectangular notch in a plate.

Abstract: An analysis of the reflection of the fundamental Lamb mode a0 from surface-breaking rectangular notches in isotropic plates is presented. The results are obtained from finite element time domain simulations together with experimental measurements. Good agreement is found between the simulations and the measurements. Results are shown for a range of notch widths and depths, including the special case of a crack, defined as a zero-width notch. The reflection coefficient, when plotted as a function of the notch width, exhibits a cosinusoidal periodic shape, and this is explained by interference between the separate reflections from the start and the end of the notch. The reflection coefficient, when plotted as a function of notch depth, shows that in general the reflection increases with both frequency and notch depth, but the shapes of the functions are complex and there are some surprising features. An analysis of the reflection from cracks using the S-parameter scattering approach and some simplified descriptions of the crack-opening behavior yields physical explanations of the nature of these reflection functions. It is found that opening of the crack can be described adequately by a quasistatic assumption only when the crack is small, and in other cases a ray theory approach is more representative. The reflection function is shown to be a result of contributions from both the axial stress and the shear stress in the wave, and the relative importance of these varies with the crack depth and the frequency.

Numerical Analysis of Flow Through a Severely Stenotic Carotid Artery Bifurcation

Abstract: The results of computational simulations may supplement MR and other in vivo diagnostic techniques to provide an accurate picture of the hemodynamics in particular vessels, which may help demonstrate the risks of embolism or plaque rupture posed by particular plaque deposits. In this study, a model based on an endarterectomy specimen of the plaque in a carotid bifurcation was examined. The flow conditions include steady flow at Reynolds numbers of 300, 600, and 900 as well as unsteady, pulsatile flow. Both dynamic pressure and wall shear stress are very high, with shear values up to 70 N/m 2 , proximal to the stenosis throat in the internal carotid artery, and both vary significantly through the flow cycle. The wall shear stress gradient is also strong along the throat. Vortex shedding is observed downstream of the most severe occlusion. Two turbulence models, the Chien and Goldberg varieties of k-«, are tested and evaluated for their relevance in this geometry. The Chien model better captures phenomena such as vortex shedding. The flow distal to stenosis is likely transitional, so a model that captures both laminar and turbulent behavior is needed. @DOI: @10.1115/1.1427042#

Dynamics of Izmit Earthquake Postseismic Deformation and Loading of the Duzce Earthquake Hypocenter

Abstract: We have developed dynamic finite-element models of Izmit earthquake postseismic deformation to evaluate whether this deformation is better explained by afterslip (via either velocity-strengthening frictional slip or linear viscous creep) or by distributed linear viscoelastic relaxation of the lower crust. We find that velocity-strengthening frictional afterslip driven by coseismic shear stress loading can reproduce time-dependent Global Positioning System data better than either linear viscous creep on a vertical shear zone below the rupture or lower crustal viscoelastic relaxation. Our best frictional afterslip model fits the main features of postseismic slip inversions, in particular, high slip patches at (and below) the hypocenter and on the western Karadere segment, and limited afterslip west of the Hersek Delta (Burgmann et al., 2002). The model requires a weakly velocity-strengthening fault, that is, either low effective normal stress in the slipping regions or a smaller value for the parameter describing rate-dependence of friction ( a - b ) than is indicated by laboratory experiments. Our best afterslip model suggests that the Coulomb stress at the Duzce hypocenter increased by 0.14 MPa (1.4 bars) during the Izmit earthquake (assuming right-lateral slip on a surface dipping 50° to the north), and by another 0.1 MPa during the 87 days between the Izmit and Duzce earthquakes. In the Marmara Sea region (within about 160 km of the Izmit earthquake rupture), this model indicates that the Coulomb stresses increased by 15%-25% of the coseismic amount during the first 300 days after the earthquake. Three hundred days after the earthquake, postseismic contributions to Coulomb stressing rate on the Maramara region faults had fallen to values equal to or less than the inferred secular stress accumulation rate. Our estimates of postseismic Coulomb stress are highly model dependent: in the Marmara region, the linear viscous shear zone and viscoelastic lower crust models predict greater postseismic Coulomb stresses than the frictional afterslip model. Near-field stress and fault-zone rheology estimates are sensitive to the Earth9s elastic structure. When a layered elastic structure is incorporated in our model, it yields a Coulomb stress of 0.24 MPa at the Duzce hypocenter, significantly more than the 0.14 MPa estimated from the uniform elastic model. Because of the higher near-field coseismic stresses, the layered elastic model requires a higher value of velocity-strengthening parameter ( A - B ) ([ a - b ] times effective normal stress r ′) to produce comparable postseismic slip. ( A - B ) is estimated at 0.4 and 0.2 MPa, respectively, for the layered and uniform elastic models. These results highlight the importance of understanding the Earth9s elastic structure and the mechanism for postseismic deformation if we wish to accurately model coseismic and postseismic crustal stresses.

Slip at polymer–polymer interfaces: Rheological measurements on coextruded multilayers

Abstract: Polypropylene (PP) and polystyrene (PS), with closely matched viscosity, were coextruded into 8, 32, and 64 alternating layers. The apparent steady shear viscosity of these multilayer samples was measured with an in-line slit rheometer and with a parallel-plate rheometer. In both cases the apparent viscosity decreased with the number of layers providing strong evidence for interfacial slip. The velocity difference across the interface (interfacial slip velocity) versus shear stress, ΔVI(τ) was calculated from the apparent viscosity measurements. ΔVI(τ) showed sigmoidal behavior: a region of very low slip ( 103 Pa followed by a linear region ΔVI=τ/β∞. These data could be fit with a modified Ellis model. The same function fit the different number of layers and both slit and parallel-plate data indicating ΔVI(τ) is a material property of the PP/PS pair. Slip was also observed in PS/PMMA (polymethyl methacrylate) and PP/aPA (amorphous nylon) p...

Detached-eddy simulation with compressibility corrections applied to a supersonic axisymmetric base flow

Abstract: Detached-eddy simulation is applied to an axisymmetric base flow at supersonic conditions. Detached-eddy simulation is a hybrid approach to modeling turbulence that combines the best features of the Reynolds-averaged Navier-Stokes and large-eddy simulation approaches. In the Reynolds-averaged mode, the model is currently based on either the Spalart-Allmaras turbulence model or Menter’s shear stress transport model; in the largeeddy simulation mode, it is based on the Smagorinski subgrid scale model. The intended application of detached-eddy simulation is the treatment of massively separated, highReynolds number flows over complex configurations (entire aircraft, automobiles, etc.). Because of the intented future application of the methods to complex configurations, Cobalt, an unstructured grid Navier-Stokes solver, is used. The current work incorporates compressible shear layer corrections in both the Spalart-Allmaras and shear stress transport-based detached-eddy simulation models. The effect of these corrections on both detached-eddy simulation and Reynolds-averaged Navier-Stokes models is examined, and comparisons are made to the experiments of Herrin and Dutton. Solutions are obtained on several grids—both structured and unstructured—to test the sensitivity of the models and code to grid refinement and grid type. The results show that predictions of base flows using detached-eddy simulation compare very well with available experimental data, including turbulence quantities in the wake of the axisymmetric body. @DOI: 10.1115/1.1517572#

On the applicability of cross-anisotropic elasticity to granular materials at very small strains

Abstract: The paper examines the validity of assuming that granular material behaviour can be considered as cross-anisotropic, linear elastic, within a kinematic ‘kernel’ yield surface that is dragged through stress space with the current effective stress point. Data from more than 300 high-resolution triaxial probing and bender element tests performed on 15 samples are reported in which both small stress cycles and shear wave measurements in both the vertical and horizontal directions were conducted on sand and glass ballotini specimens under various effective stress states. It was found that behaviour is not fully elastic. However, provided the effective stress ratio, R, was kept below around 2·2, most features of the very small-strain behaviour could be described in terms of strongly anisotropic compliance terms that varied with void ratio and current effective stress state, apparently independently of the specimen's stress history. The anisotropy depended on the effective stress states. Specimens loaded to R va...

A shear-compression specimen for large strain testing

Abstract: A new specimen geometry, the shear-compression specimen (SCS), has been developed for large strain testing of materials. The specimen consists of a cylinder in which two diametrically opposed slots are machined at 45° with respect to the longitudinal axis, thus forming the test gage section. The specimen was analyzed numerically for two representative material models, and various gage geometries. This study shows that the stress (strain) state in the gage, is three-dimensional rather than simple shear as would be commonly assumed. Yet, the dominant deformation mode in the gage section is shear, and the stresses and strains are rather uniform. Simple relations were developed and assessed to relate the equivalent true stress and equivalent true plastic strain to the applied loads and displacements. The specimen was further validated through experiments carried out on OFHC copper, by comparing results obtained with the SCS to those obtained with compression cylinders. The SCS allows to investigate a large range of strain rates, from the quasi-static regime, through intermediate strain rates (1–100 s−1), up to very high strain rates (2×104s−1 in the present case).

Global Omori law decay of triggered earthquakes: Large aftershocks outside the classical aftershock zone

Abstract: [1] Triggered earthquakes can be large, damaging, and lethal as evidenced by the1999 shocks in Turkey and the 2001 earthquakes in El Salvador. In this study, earthquakes with Ms ≥ 7.0 from the Harvard centroid moment tensor (CMT) catalog are modeled as dislocations to calculate shear stress changes on subsequent earthquake rupture planes near enough to be affected. About 61% of earthquakes that occurred near (defined as having shear stress change ∣Δτ∣ ≥ 0.01 MPa) the Ms ≥ 7.0 shocks are associated with calculated shear stress increases, while ∼39% are associated with shear stress decreases. If earthquakes associated with calculated shear stress increases are interpreted as triggered, then such events make up at least 8% of the CMT catalog. Globally, these triggered earthquakes obey an Omori law rate decay that lasts between ∼7–11 years after the main shock. Earthquakes associated with calculated shear stress increases occur at higher rates than background up to 240 km away from the main shock centroid. Omori's law is one of the few time-predictable patterns evident in the global occurrence of earthquakes. If large triggered earthquakes habitually obey Omori's law, then their hazard can be more readily assessed. The characteristic rate change with time and spatial distribution can be used to rapidly assess the likelihood of triggered earthquakes following events of Ms ≥ 7.0. I show an example application to the M = 7.7 13 January 2001 El Salvador earthquake where use of global statistics appears to provide a better rapid hazard estimate than Coulomb stress change calculations.

On thermoplastic shear instability in the machining of a titanium alloy (Ti-6Al-4V)

Abstract: A thermal model for the thermoplastic shear instability in the machining of a titanium alloy (Ti-6Al-4V) is developed It is based on the analysis of the shear-localized chip formation process and the temperature generated in the shear band due to various heat sources (primary, preheating, and image) in machining The temperature in the shear band was determined analytically using the Jeager’s classical stationary- and moving-heat-source methods Using Recht’s classical model of catastrophic shear instability (thermal softening vs strain hardening), the onset of shear localization was determined The shear stress in the shear band is calculated at the shear-band temperature and compared with the value of the shear strength of the bulk material at the preheating temperature If the shear stress in the shear band is less than or equal to the shear strength of the bulk material, then shear localization is imminent The cutting speed at which this occurs is taken as the critical speed for the onset of shear localization, which continues at all speeds above this value In the case of titanium alloys, this speed is rather low, indicating shear localization practically at all conventional cutting speeds The effect of the depth of the cut on the onset of shear localization was also considered, as it may affect the heat transfer from the shear-localized region, ie, between the segments in the chip, to the rest of the chip and preheating of the segment For example, there can be a significant difference in the thermal aspects of shear localization in ultraprecision machining (where the depths of cuts are a few micrometers or less) compared to conventional machining (where the depths of cuts are several hundred micrometers) This is because of the differences in the distances between the segments as well as the energy inputs in each case

Theoretical study on shear stress generated by microstreaming surrounding contrast agents attached to living cells.

Abstract: Numerical calculations have shown that shear stress associated with microstreaming surrounding encapsulated stable bubbles of contrast agents, near living cells driven by 0.12-MPa acoustic pressure amplitude ultrasound (US) at 1 MHz or 2 MHz, may be large enough to generate reparable sonoporation of the cells. Some encapsulated bubbles that have mechanically weak shells may break into free bubbles under the above-mentioned sound field. When that happens, the shear stress caused by microstreaming surrounding the free bubble increases dramatically and may play an important role in lethal sonoporation and fragmentation of cells during the early stage of US exposure. (E-mail: jwu@zoo.uvm.edu)

Computational Fluid Dynamics Modeling of Steady-State Momentum and Mass Transport in a Bioreactor for Cartilage Tissue Engineering

Abstract: Computational fluid dynamics (CFD) models to quantify momentum and mass transport under conditions of tissue growth will aid bioreactor design for development of tissue-engineered cartilage constructs. Fluent CFD models are used to calculate flow fields, shear stresses, and oxygen profiles around nonporous constructs simulating cartilage development in our concentric cylinder bioreactor. The shear stress distribution ranges from 1.5 to 12 dyn/cm2 across the construct surfaces exposed to fluid flow and varies little with the relative number or placement of constructs in the bioreactor. Approximately 80% of the construct surface exposed to flow experiences shear stresses between 1.5 and 4 dyn/cm2, validating the assumption that the concentric cylinder bioreactor provides a relatively homogeneous hydrodynamic environment for construct growth. Species mass transport modeling for oxygen demonstrates that fluid-phase oxygen transport to constructs is uniform. Some O2 depletion near the down stream edge of constructs is noted with minimum pO2 values near the constructs of 35 mmHg (23% O2 saturation). These values are above oxygen concentrations in cartilage in vivo, suggesting that bioreactor oxygen concentrations likely do not affect chondrocyte growth. Scale-up studies demonstrate the utility and flexibility of CFD models to design and characterize bioreactors for growth of tissue-engineered cartilage.

Internal and External Mass Transfer in Biofilms Grown at Various Flow Velocities

Abstract: It appears that biofilms arrange their internal structure according to the flow velocity at which they are grown, which affects the internal mass transfer rate and microbial activity. In biofilms grown at various flow velocities we determined the vertical profiles of the local relative effective diffusivity (termed D(l)) at several locations within each biofilm. From these profiles we calculated the surface-averaged relative effective diffusivity (termed D(sa)) at various distances from the bottom and plotted it against these distances. The D(sa) decreased linearly toward the bottom, forming well-defined profiles that were different for each biofilm. The gradients of these profiles were multiplied by the diffusivity of oxygen, zeta = D(w) dD(sa)/dz, and plotted versus the flow velocity at which each biofilm was grown. The gradients were low at flow velocities below 10 cm/s, reached a maximum at a flow velocity of 10 cm/s, and decreased again at flow velocities exceeding 10 cm/s. The existence of a maximum indicates a possibility that two opposing forces were affecting the slope of the profiles. To explain these observations we hypothesized that biofilms, depending on the flow velocity at which they are grown, arrange their internal architecture to control (1) the nutrient transport rate and (2) the mechanical pliability needed to resist the shear stress of the water flowing past them. It appears that biofilms attempt to satisfy the second goal first, to increase their mechanical strength, and that they do so at the expense of the nutrient transfer rate to deeper layers. This strength increase is associated with an increase in biofilm density, which slows down the internal mass transport rate. Biofilms grown at low flow velocities exhibit low density and high effective diffusivity but cannot resist higher shear stress, whereas biofilms grown at higher flow velocities are denser and can resist higher shear stress but have a lower effective diffusivity.