Hydrodynamics of liquid imbibition in porous media

Abstract

Liquid imbibition in a porous structure is mundanely observed in our daily lives, including such phenomena as water absorption into a sponge, ink imbibition in fibrous paper, a water cleaning process by towel or tissue, etc. In this thesis, we combine experimental observation and theoretical analysis to understand the hydrodynamics of liquid imbibition in porous media. We start with relatively simple two-dimensional (2-D) flows on rough porous surfaces, and then increase the complexity of the structure to eventually understand flows in three-dimensional (3-D) multiscale porous media. We first consider one of the most representative 2-D wicking flows, ink writing, i.e. liquid spreading into porous plates from moving point source. We use hydrophilic microtextured silicon wafers (superhydrophilic substrate) as model paper, capillary tubes as model pens, and various liquids as model inks. We start by focusing on liquid spreading when the source is stationary. Balancing surface tension force and viscous shear force, scaling law of blot spreading with time is derived. We then concentrate on the behaviors of the liquid when the source moves in a constant speed. Employing a simplified schematics delineating the frontal liquid flow from the moving source, geometrical analysis is coupled with aforementioned force balance. The front profile predicted by the scaling analysis shows good agreement with experimental results. Also, considering volume conservation, the line thickness is quantified by parametric analysis and verified by experiments. Next, we focus on the role of pore structure in the dynamics of liquid wicking on 2-D substrate. In experiments, we prepare arrays of pillars of varying height, pitches, diameter, and skewness. Through the macroscopic model, deducing average capillary force and resisting shear force, we derive a scaling law of the liquid propagation, which applies for wide range of structural conditions. Through the microscopic model, we approach the dynamics more rigorously by considering the local pressure drop between consecutive pillars. Separating the microscopic propagation by climbing and sweeping, we derive scaling laws of the spreading dynamics. Comparing results of the macroscopic model and microscopic model, we derive the validation limit of the scaling law of macroscopic model. We then consider flows within the dual sized porous media, the simplest form of multi-porous media. The employed structure consists of parallel substrates with micropillar arrays, separated by a millimetric gap. The flow involves the bulk flow at the millimetric gap and the film flow in the micrometric pores above the bulk. The bulk flow between the superhydrophilic surfaces shows identical behavior to what is observed on smooth substrates, meaning that the bulk flow is independent of the microstructures. The flow of the film emanating from the bulk is affected by the bulk in the beginning, but becomes independent of the bulk flow in the late stages. The entire flow regimes are investigated by scaling analysis and verified by experiments. Also, the moment of the film emanating from the bulk is quantitatively estimated by comparing the rising speeds of bulk and film. Finally, we investigate the flows in porous material of practical importance, cellulose sponge, containing various sized pores. We construct a simple model, delineating unit structure of sponge pores by introducing large void and wall pores of the sponge. We first study the horizontal flow in sponge to understand the flow without gravitational effects. The horizontal liquid propagation distance is found to obey the Washburns rule. We turn to the vertical flow, which shows different flow behaviors depending on the rise height. When the rise height is small so that the large void can be completely saturated, liquid flow behavior is identical to the horizontal flow. Whereas, when the rise height is so large that the large void is saturated but partially. The rise height grows like time to the 1/4. This unusual phenomenon is caused by the non-uniformity of permeability, which is inversely proportional to the square of rise height. The scaling laws for the entire flow dynamics show good agreement with experimental results.