Forces governing the dynamics of liquid spreading in packed beds

Abstract

Liquid spreading through a randomly packed particle-resolved bed influenced by capillary or inertial ($AB_s \sim 1$), and gravitational force (moderately ($AB_s \sim 0.1$) and strongly ($AB_s \sim 0.01$)) is investigated using the volume-of-fluid simulations. The relative contribution of governing forces at different stages of spreading is analysed using the time evolution of Weber ($We_I$) and$AB_I$numbers. We show that the dynamics of liquid spreading at$AB_s \sim 1$is primarily governed by the inertial force in the beginning ($AB_I > 1$,$We_I > 1$) followed by the capillary force at$t/t^* \sim 1$. This interplay of governing forces leads to inertia- and capillary-induced bubble entrapments at the void scale and promote lateral liquid spreading. When the$AB_s \sim 0.1$, the$t/t^*$for which the flow is governed by inertial ($AB_I > 1$,$We_I > 1$) and capillary forces ($AB_I > 1$,$We_I < 1$) decreases and the relative contribution of gravitational force is substantial at large$t/t^*$($AB_I < 1$). This force balance leads to unified-void filling characterised by negligible bubble trapping and results in a decrease in the lateral spreading. Further decrease in the$AB_s$to${\sim } 0.01$results in liquid spreading primarily governed by gravitational force ($AB_I < 1$) with small contribution of inertial and capillary forces at the very beginning leading to trickling flow and a further decrease in lateral spreading. Finally, a regime map is proposed, which provides the relationship between different forces, void-scale events, and the resultant liquid spreading at$t/t^* \sim 1$.