(421b) Comparison of Computed and Measured Wall Shear Stress in An Orbiting Cell Culture Dish

Authors: 
Berson, R. E., University of Louisville
Thomas, J., University of Louisville


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 mixing the fluid containing nutrients while 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 generally not amenable to analytical solution for resolving shear created by the fluid motion. 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. Here we present a computational model that for the first time 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 both the analytical solution (resultant WSS magnitudes that are within 0.99 ± 0.42 dyne/cm2) and comparison to tangential WSS magnitudes obtained using one-dimensional optical velocimetry at discreet locations on the bottom of an orbiting dish. The experimental maximum WSS varied by about 12% from the computational model at both locations that were measured.

Neglecting surface tension, flow in the dish is influenced by Reynolds, Froude and Stokes numbers and a slope parameter [ratio of steady-state acceleration-induced free surface slope and static fluid aspect ratio (fluid height to dish radius)]. Conditions on a shaker table are typically low Reynolds and low slope. The existing analytical result is an extension of Stokes 2nd problem to orbital plate motion for low Froude and high Stokes, and is valid for flow not too close to the vertical walls of the dish, which was confirmed by CFD results. These results help explain why cellular responses depend on location in the dish.