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A common way to replace body tissue is via donors, but as the world population is ageing at an unprecedented rate there will be an even smaller supply to demand ratio for replacement parts than currently exists. Tissue engineering is a process in which damaged body tissue is repaired or replaced via the engineering of artificial tissues. We consider one type of this; a two-phase flow through a rotating high-aspect ratio vessel (HARV) bioreactor that contains a porous tissue construct. We extend the work of Cummings and Waters [2007], who considered a solid tissue construct, by considering flow through the porous construct described by a rotating form of Darcy's equations. By simplifying the equations and changing to bipolar variables, we can produce analytic results for the fluid flow through the system for a given construct trajectory. It is possible to calculate the trajectory numerically and couple this with the fluid flow to produce a full description of the flow behaviour. Finally, coupling with the numerical result for the tissue trajectory, we can also analytically calculate the particle paths for the flow which will lead to being able to calculate the spatial and temporal nutrient density.