Contribution of dynamic capillary pressure to rainfall infiltration in thin homogeneous growth substrates

Journal article, 2021

The use of green roofs to help mitigate storm water contributions to urban flooding has been gaining popularity but is hindered by the limited data on the performance of such roofs with regard to storm water runoff mitigation. The underlying issue stems from the inherent complexity of modeling subsurface multiphase flow. Modeling of this phenomena requires calculating the contributions of substrate microstructure characteristics, the influence of the wetting and non-wetting phases upon each other, and the effect of the microstructure on the wetting phase. Previously we have observed how the microstructure can affect detention, however the quantification of this relationship is still missing. In the present paper we present numerical simulations of wetting phase infiltration of a thin monodisperse packed bed in order to understand and quantify the impact of microstructure geometry on storm water infiltration of a green roof substrate. For a slightly hydrophilic case, (θ=82°), we find that a dominant mechanism underlying this relationship is the microstructure-induced dynamic behavior of the capillary pressure. We determine that at larger packing ratios (ratio of packed bed depth to particle size), the influence of hydraulic head diminishes and behaves conversely for thinner layers, particularly when larger pores are present. Indeed, thin beds composed of large particles can exhibit high flow velocities that in turn affect the capillary pressure within the substrate. We observe that the capillary pressure can shift from negative values denoting capillary suction to positive ones which cause valve-like blocking effects on the flow; dependent upon the flow velocity as determined by the microstructure. In particular, we find that the capillary pressure depends on the value of the pore-scale gravity-induced flow velocity, quantified through a characteristic Capillary number. The provided quantification of this relationship can be invaluable from a design perspective to understand the behavior of capillary pressure of different substrates under a variety of flow rates prior to testing substrate candidates. In addition, a comparison of the behavior of the dynamic component of capillary pressure to other works is undertaken. Flow homogeneity is also found to be linked to the flow velocity, and consequently to the microstructure.