Rodrigo Rosati

Continuum-Scale Modeling of Liquid Redistribution in a Stack of Thin Hydrophilic Fibrous Layers

Macroscale three-dimensional modeling of fluid flow in a thin porous layer under unsaturated conditions is a challenging task. One major issue is that such layers do not satisfy the representative elementary volume length-scale requirement. Recently, a new approach, called reduced continua model (RCM), has been developed to describe multiphase fluid flow in a stack of thin porous layers. In that approach, flow equations are formulated in terms of thickness-averaged variables and properties. In this work, we have performed a set of experiments, where a wet

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260\hbox {-}\upmu \hbox {m}

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260-μm-thin porous layer was placed on top of a dry layer of the same material. We measured the change of average saturation with time using a single-sided low-field nuclear magnetic resonance device known as NMR-MOUSE. We have employed both RCM and the traditional Richards equation-based models to simulate our experimental results. We found that the traditional unsaturated flow model cannot simulate experimental results satisfactorily. Very close agreement was obtained by including the dynamic capillary term as postulated by Hassanizadeh and Gray in the traditional equations. The reduced continua model was found to be in good agreement with the experimental result without adding dynamic capillarity term. Moreover, the computational effort needed for RCM simulations was one order of magnitude less than that of traditional models.

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Offering multifaceted applications, thin fibrous porous materials are mostly used in stacks of layers, each layer having a defined functionality. Since only a few pores exist across a layer a couple of hundred microns thick, the interface between layers may significantly affect liquid ingress. Thus, the main objective of the study is to substantiate that an interface layer is present during liquid infiltration between stacked thin fibrous layers and that it affects the fluid transport properties. A compact single-sided NMR device with a low static gradient of about 2 T/m perpendicular to the sensor surface and a uniform magnetic field in lateral directions was used to profile a 2-mm thick slice in one shot. The liquid ingress into the thin fibrous layers and their interfaces was visualized by Fourier-transforming the NMR signal and processing the time-dependent 1D profiles with a newly developed mathematical method. The flow characteristics and liquid distribution profiles of a 400-µm thick layer were compared with those of two stacked 200-µm thick layers from the same material but with an interface between them. The results show major differences in distributions and flow dynamics for the single and dual layer cases, which reveal the importance of the interface in fluid flow.