The transport of liquids in softwood: timber as a model porous medium

Timber is the only widely used construction material we can grow. The wood from which it comes has evolved to provide structural support for the tree and to act as a conduit for fluid flow. These flow paths are crucial for engineers to exploit the full potential of timber, by allowing impregnation with liquids that modify the properties or resilience of this natural material. Accurately predicting the transport of these liquids enables more efficient industrial timber treatment processes to be developed, thereby extending the scope to use this sustainable construction material; moreover, it is of fundamental scientific value — as a fluid flow within a natural porous medium. Both structural and transport properties of wood depend on its micro-structure but, while a substantial body of research relates the structural performance of wood to its detailed architecture, no such knowledge exists for the transport properties. We present a model, based on increasingly refined geometric parameters, that accurately predicts the time-dependent ingress of liquids within softwood timber, thereby addressing this long-standing scientific challenge. Moreover, we show that for the minimalistic parameterisation the model predicts ingress with a square-root-of-time behaviour. However, experimental data show a potentially significant departure from this $$\sqrt{{\boldsymbol{t}}}$$t behaviour — a departure which is successfully predicted by our more advanced parametrisation. Our parameterisation of the timber microstructure was informed by computed tomographic measurements; model predictions were validated by comparison with experimental data. We show that accurate predictions require statistical representation of the variability in the timber pore space. The collapse of our dimensionless experimental data demonstrates clear potential for our results to be up-scaled to industrial treatment processes.