Partially-Filled Macropores in Swelling and Nonswelling Media: Flow Modes Requiring Supplementation of Darcy’s Law

Abstract:

A traditional assumption for unsaturated flow is that the pores are either water-filled and conducting or empty and nonconducting. Evidence from lab and field investigations, however, shows that substantial preferential flow can occur in macropores that are partially filled. Such flow can transmit large fluxes of water. Rates of transport can exceed the saturated hydraulic conductivity, because of possible reductions of friction and buoyancy effects. These conditions reduce the influence of capillarity on energy state, driving force, and the configuration of water-filled space. Influences such as gravity, inertia, and chaotic liquid-phase irregularities then take on increased importance. Perhaps most important is that with partial filling, the flux of water entering the pore is a determining influence on the configuration of air and water phases. Hence the incoming flux itself influences the pore’s conductance, and Darcy’s law cannot be expected to apply.

Flow through partially-filled macropores thus requires new or revised concepts of flow pathways in unsaturated soil, and new ways of quantifying their effect. Flow modes can include free-surface films, rivulets that are not fully confined by capillarity, pulse flow, and sliding drops. Gravity dominates the driving force. Because capillarity does not establish complete geometrical confinement for these modes of flow, the mathematical relation between flux and force is not the direct Darcian proportionality, but rather a mode-specific relation involving incoming flux and flow-stream dimensions. In swelling soils there is the further complication that flow may switch from one mode to another because macropore size, shape, and connectedness vary dynamically with changing water content.

This presentation evaluates commonalities and divergences among different partially-filled flow modes and compares them with commonly-assumed Poiseuille flow modes. Mathematical relations for the physical processes of these flow modes provide a basis for developing an improved model for the preferential component of unsaturated flow.