We develop a simple mathematical model for forced flow of culture medium through a porous scaffold in a tissue engineering bioreactor. Porous-walled hollow fibres penetrate the scaffold and act as additional sources of culture medium. The model, based on Darcy's law, is used to examine the nutrient and shear stress distributions throughout the scaffold. We consider several configurations of fibres and inlet and outlet pipes. Compared with a numerical solution of the full Navier-Stokes equations within the complex scaffold geometry, the modelling approach is cheap, and does not require knowledge of the detailed microstructure of the particular scaffold being used. The potential of this approach is demonstrated through quantification of the effect the additional flow from the fibres has on the nutrient and shear-stress distribution.

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The simulation of dilute emulsions in a model ACIP2 Sonolator is investigated using computational fluid dynamics and population balance methods. Two breakage frequency models are used that differ in the expression of the drop breakage time. Drop breakage modeling based on homogenous isotropic turbulence (HIT) shows poor agreement of the Sauter mean diameter when compared to the experiments; simulations with the empirical model from Alopaeus et al. yield better agreement. By perturbing the classical HIT spectrum, it is shown that the breakage time in the empirical model corresponds to a non-isotropic energy spectrum. Such spectra have been observed in the non-isotropic near field in a model A Sonolator, which provides a plausible explanation of why the empirical model performs better than the HIT-based model.

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