Spatial and temporal resolution of shear in an orbiting petri dish

Abstract

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.