Fluid dynamics of orbitally shaken shallow fluid layers

Abstract

Motivated by the pathological effect of blood flow on endothelial cells and its relevance in the progress of atherosclerosis, this thesis investigates the fluid dynamics of orbitally shaken shal- low fluid layers in cylindrical containers. The study uses computational and analytical models to characterise flow in 33 case studies, which map the parameter space of the dimensionless numbers that govern the physics. A travelling wave characterises the flow and wave breaking and wall boundaries determine the multidirectional character of the shear stress field. A novel shear stress metric (transWSSmin) has been investigated by combining numerical simulations with laboratory experiments, and evidence is presented that transWSSmin correlates with en- dothelial permeability changes, implying that cells align close to the direction that minimises the transverse shear stresses instead of the mean flow direction, as widely accepted. A potential flow theory has been shown to be a powerful tool to predict the surface amplitude up to the onset of the wave breaking, which allows for classification in non-breaking/breaking regimes based on an amplitude breaking threshold identified in the simulations. An improved analytical model for the prediction of the shear stress, the PT-Stokes WSS model, has been developed, which is a generalisation of the classic Stokes solution. The model consists of a Stokes boundary layer coupled with the potential flow, and thus takes into account the free surface and side walls. Even in highly nonlinear cases, the PT-Stokes model predicts shear stress within 50% accuracy except at resonant conditions. A strong correlation has been found between the bottom wall shear stress and the surface velocity, showing that the largest source of error is the surface velocity predictions by the potential flow model due to the omission of viscous effects. Finally, results are translated into recommendations and tools for the investigation of endothelial cells in orbital shakers.