It is well documented that physiological and morphological properties of anchored cells are influenced by fluid shear stress. Common orbital shakers provide a means of simultaneously applying shear stress to cells for tens to hundreds of cases by loading the shaker with multiple dishes. However, the complex flow in orbiting dishes is amenable to analytical solution for resolving shear created by the fluid motion only for simplified conditions. The only existing quantification of shear in this flow is an equation that estimates a constant scalar value of shear for the entire surface of the dish. In practice, wall shear stress (WSS) will be oscillatory rather than steady due to the travelling waveform and will vary across the surface of the dish at any instant in time. This article presents a computational model that provides complete spatial and temporal resolution of WSS over the bottom surface of a dish throughout the orbital cycle. The model is reasonably well validated by the analytical solution, with resultant WSS magnitudes that are within 0.99 ± 0.42 dyne/cm(2) . The model results were compared to tangential WSS magnitudes obtained using one-dimensional optical velocimetry at discreet locations on the bottom of an orbiting dish. The experimental minimum and maximum WSS at 1 mm from the center of the dish were 6 and 7 dyne/cm(2) , respectively, whereas WSS generated from the computational model ranged from 0.5 to 8.5 dyne/cm(2) . The experimental minimum and maximum WSS at 12 mm from the center of the dish were 6 and 16 dyne/cm(2) , respectively, whereas WSS generated from the computational model ranged from 0.5 to 14 dyne/cm(2) . Discrepancies between the experimental and computational data may be attributed to a sparse sampling rate for the experimental probe, a sharp gradient at the sample area which could cause the unidirectional probe to be inaccurate if its location were not precise, and too few particles to track and a scattering of the signal by the free surface when the liquid is shallow.

Particle image velocimetry (PIV) and an extended solution of Stokes’ second problem were used to validate a computational fluid dynamics (CFD) model of flow in an orbiting dish. Velocity vector components throughout one complete orbit differed between CFD and PIV by less than 5%. Computational velocity magnitudes averaged over the interior 20% radius, the region where the analytical solution is most applicable, were 0.3% higher than the analytical values, while the experimental values in the same region were 2.4% higher. Velocity profiles in the center of the dish across normalized heights that most influence wall shear stress varied on average by ∼–0.00046 for the normalized radial component and by ∼0.0038 for the normalized tangential component compared to the analytical solution. These results represent the most comprehensive validation to date for computational models of the orbiting dish system. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4233–4242, 2017

Electrical impedance techniques have been used to characterize endothelium morphology, permeability, and motility in vitro. However, these impedance platforms have been limited to either static endothelium studies and/or induced laminar fluid flow at a constant, single shear stress value. In this work, we present a microfabricated impedance sensor for real-time, in vitro characterization of human umbilical vein endothelial cells (HUVECs) undergoing oscillatory hydrodynamic shear. Oscillatory shear was applied with an orbital shaker and the electrical impedance was measured by a microfabricated impedance chip with discrete electrodes positioned at radial locations of 0, 2.5, 5.0, 7.5, 10.0, and 12.5 mm from the center of the chip. Depending on their radial position within the circular orbital platform, HUVECs were exposed to shear values ranging between 0.6 and 6.71 dyne/cm(2) (according to numerical simulations) for 22 h. Impedance spectra were fit to an equivalent circuit model and the trans-endothelial resistance and monolayer's capacitance were extracted. Results demonstrated that, compared to measurements acquired before the onset of shear, cells at the center of the platform that experienced low steady shear stress (∼2.2 dyne/cm(2) ) had an average change in trans-endothelial resistance of 6.99 ± 4.06% and 1.78 ± 2.40% change in cell capacitance after 22 hours of shear exposure; cells near the periphery of the well (r = 12.5 mm) experienced transient shears (2.5-6.7 dyne/cm(2) ) and exhibited a greater change in trans-endothelial resistance (24.2 ± 10.8%) and cell capacitance (4.57 ± 5.39%). This study, demonstrates that the orbital shear platform provides a simple system that can capture and quantify the real-time cellular morphology as a result of induced shear stress. The orbital shear platform presented in this work, compared to traditional laminar platforms, subjects cells to more physiologically relevant oscillatory shear as well as exposes the sample to several shear values simultaneously. Biotechnol. Bioeng. 2016;113: 1336-1344. © 2015 Wiley Periodicals, Inc.

This study demonstrated the effects of the directionality of oscillatory wall shear stress (WSS) on proliferation and proatherogenic gene expression (I-CAM, E-Selectin, and IL-6) in the presence of inflammatory mediators leukotriene B4 (LTB4) and bacterial lipopolysaccharide (LPS) from endothelial cells grown in an orbiting culture dish. Computational fluid dynamics (CFD) was applied to quantify the flow in the dish, while an analytical solution representing an extension of Stokes second problem was used for validation. Results indicated that WSS magnitude was relatively constant near the center of the dish and oscillated significantly (0-0.9 Pa) near the side walls. Experiments showed that LTB4 dominated the shear effects on cell proliferation and area. Addition of LPS didn't change proliferation, but significantly affected cell area. The expression of I-CAM1, E-Selectin and IL-6 were altered by directional oscillatory shear index (DOSI, a measure of the biaxiality of oscillatory shear), but not shear magnitude. The significance of DOSI was further reinforced by the strength of its interactions with other atherogenic factors. Hence, directionality of shear appears to be an important factor in regulating gene expression and provides a potential explanation of the propensity for increased vascular lesions in regions in the arteries with oscillating biaxial flow.

High-solids biomass slurries exhibit non-Newtonian behavior with a yield stress and require high power input for mixing. The goals were to determine the effect of scale and geometry on power number P 0 , and estimate the power for mixing a pretreated biomass slurry in a 3.8 million L hydrolysis reactor of conventional design. A lab-scale computational fluid dynamics model was validated against experimental data and then scaled up. A pitched-blade turbine and A310 hydrofoil were tested for various geometric arrangements. Flow was transitional; laminar and turbulence models resulted in equivalent P 0 which increased with scale. The ratio of impeller diameter to tank diameter affected P 0 for both impellers, but impeller clearance to tank diameter affected P 0 only for the A310. At least 2 MW is required to operate at this scale.