Forces governing the dynamics of liquid spreading in packed beds

Liquid spreading through a randomly packed particle-resolved bed influenced by capillary or inertial (AB(S) similar to 1), and gravitational force (moderately (AB(S) similar to 0.1) and strongly (AB(S) similar to 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 N 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* similar to 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) similar to 0.1, the t/t* for which the flow is governed by inertial (AB(I) > 1, Wei > 1) and capillary forces (AB(I) > 1, Wei < 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 similar to 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* similar to 1.

Automated summary

This study investigates the spreading of liquid in a randomly packed particle bed influenced by capillary, inertial, and gravitational forces using volume-of-fluid simulations. The relative contributions of these forces at different stages of spreading are analyzed through the time evolution of Weber and AB numbers. The results show that the initial spreading is primarily governed by inertial force, followed by capillary force at a later stage. The interplay of these forces leads to bubble entrapment and lateral liquid spreading. As the gravitational force increases, the contribution of inertial and capillary forces decreases, resulting in unified void filling and reduced lateral spreading. When the gravitational force is dominant, liquid spreading is primarily controlled by gravity, resulting in trickling flow and further decreased lateral spreading.