Water-based fire extinguishing agent is the main means to deal with smoldering fires. However

due to the hydrophobic properties of the particle surface

the porous medium channel provide resistance and slow down the extinguishing agent flow during the downward permeation process. To promote the liquid permeation process in such porous media

this work studied liquid imbibition process and analyzed the oscillating and attenuating process of liquid level in capillary channel by theoretical

experimental

and numerical methods. An empirical mathematical equation was proposed to describe the oscillating process

and the effects of the capillary diameter and contact angle parameters on the transportation process were analyzed. Based on this

the "relay-mode" was proposed to promote the liquid transportation forward. Finally

the transient simulation results of liquid permeation in coal stacks showed when the liquid flowed through the channel with changed diameter from large to small ones

the transportation distance was several times longer than that through the unidiameter ones. The trend of liquid "relay-mode" in capillaries can be used to promote the permeation in granular materials porous media stacks. The relevant results also provide new thoughts to develop the water-based fire extinguishing agents and then improve the firefighting efficiency of deep-seated fire in porous media stacks.