Optimisation of Fluid Mixing in a Hydrosac Growing Module

A mathematical model is proposed for the flow of nutrients in an inflatable hydroponics module being developed by Phytoponics. Simple experiments were performed via the injection of dye into the system enabling a basic understanding of the time and length scales of nutrient flow and mixing. Four different flow regimes are identified. At the scale of a single root, a Stokes-flow approximation may be used. Brinkman flow operates at the individual plant scale which homogenises into a 1D model for macro-scale flow of nutrients. A shear flow model is used to predict the flow in regions dominated by plant roots. Finally, simplified two-phase flow equations are derived for the more turbulent bubble flow during aeration. These are solved within the software COMSOL. The overall conclusion is that both the periodic flow of nutrients and the aeration are required to enable even nutrient spread.