At the scale of the pores (the microscopic scale in this case), however, a distinction exists in that the fluid is exactly (or nearly) incompressible, while the porous solid network is not obviously incompressible.

-   In @growthpaper, the acceleration of the solid phase was included as a driving force in the constitutive relation for the flux of other phases. However, acceleration is not frame-invariant and its use in constitutive relations is inappropriate.

-   Chemical solutes in the extra-cellular fluid are advected by the fluid velocity and additionally undergo transport under a chemical potential gradient relative to the fluid. In the hyperbolic limit, where advection dominates, spatial instabilities emerge in numerical solutions of these transport equations [@Brooks:82; @Paper6]. Numerical stabilisation of the equations is intimately tied to the mathematical representation of fluid incompressibility.

-   The modelling of solid-fluid mechanical coupling carries strong implications for the stiffness of tissue response, the nature of fluid transport, and since nutrients are dissolved in the fluid, ultimately for growth. We present upper and lower bounds for this problem and computations of coupled boundary value problems with these bounds.

These issues are treated in detail in relevant sections of the paper, which is laid out as 