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 (ABs ∼ 1), and gravitational force (moderately (ABs ∼ 0.1) and strongly (ABs ∼ 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 (WeI) and ABI numbers. We show that the dynamics of liquid spreading at ABs ∼ 1 is primarily governed by the inertial force in the beginning (ABI < 1, WeI < 1) followed by the capillary force at t/t∗ ∼ 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 ABs ∼ 0.1, the t/t∗ for which the flow is governed by inertial (ABI < 1, WeI < 1) and capillary forces (ABI < 1, WeI < 1) decreases and the relative contribution of gravitational force is substantial at large t/t∗ (ABI < 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 ABs to ∼0.01 results in liquid spreading primarily governed by gravitational force (ABI < 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∗ ∼ 1.