Evaluation of different approaches to modelling dynamic unsaturated fluid flow conditions in hydrophilic nonwoven fibrous layers

Abstract

This study investigates the applicability of statically measured hydraulic properties of a compressed thin nonwoven fibrous layer, to predict unsaturated dynamic fluid flow conditions. The autoporosimetry technique was used to perform both quasi-static and dynamic inflow and outflow experiments. In the quasi-static experiments, air pressure is increased or decreased in small increments to identify static water retention curve parameters. During dynamic experiments, one large pressure step was applied, after which the saturation of the fabric sample through time was recorded. Three different types of models to simulate the dynamic experiments have been examined: a Richards equation-based model, a two-phase flow Darcy-based model, and a Reduced Continua Model (RCM). Traditional continuumscale Richards and Darcy based models are in good agreement with laboratory data for fabric layers without surficial bonding patterns. However, the initial moment of inflow experiments had a clear time delay comparing to continuum-scale modeling results for materials with bonding patterns. Including the effect of dynamic capillarity and modification of the relative permeability function, within the 2D axisymmetric Darcy model, yields satisfactory results. However, these modifications to the model are arbitrary and inconsistent. A recently developed model for modeling multiphase flow through a stack of thin porous layers, called the RCM, is employed to account for the effect of interlayer pore space between the thin fabric and membrane. The interlayer space effect is accounted for within the mass transfer function of the RCM. It was found that the interlayer space effect can explain the mentioned delay of initial wetting. Perfect match between experimental and modeling results are obtained, after considering a low interface transfer rate coefficient in the RCM simulations of the fabric layers with surficial bonding patterns. The dynamic outflow experiments are modeled with the same mass transfer functions as the inflow experiments, also yielding results that are in good agreement with experimental outflow data. This study shows that the RCM is more accurate and computationally more affordable compared to traditional continuum-scale models, when it comes to modeling flow through a stack of thin porous layers.