Partially-Filled Macropores: Preferential Flow Modes That Require Supplementation of Darcy's Law.

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. Flow modes can include free-surface films and rivulets, capillary rivulets, pulse flow, and sliding drops. Such flow may transmit large amounts of water, and, because of possible reductions of friction and buoyancy effects, at rates exceeding the saturated hydraulic conductivity. With water and air each occupying a significant fraction of a pore’s internal volume, pore aperture has much less influence on pore conductance than for pores that toggle between full and empty states. Similarly, capillarity may have much less influence on energy state, driving force, and the configuration of water-filled space. Other influences have increased importance in partially filled pores—for example gravity, inertia, and possible chaotic irregularities of the liquid phase. 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 should not be expected to apply.

Partial filling of macropores requires new or revised concepts of flow pathways in unsaturated soil, and new ways of quantifying their effect. Many scientists have introduced concepts and quantitative models appropriate for flow in a specific partially-filled mode such as films or pulses.  If one particular mode is chosen as the basis of a quantitative model, that one must serve also as an analog for any others. This presentation evaluates commonalities and divergences among different partially-filled flow modes along with their quantitative formulations, providing a basis for an improved preferential flow model that can supplement Darcy’s law.