Study of Hydraulic Properties of Uncoated Paper: Image Analysis and Pore-Scale Modeling

Measuring Open Porosity of Porous Materials Using THz-TDS and an Index-Matching Medium

The porosity of porous materials is a critical quality attribute of many products ranging from catalysis and separation technologies to porous paper and pharmaceutical tablets. The open porosity in particular, which reflects the pore space accessible from the surface, is crucial for applications where a fluid needs to access the pores in order to fulfil the functionality of the product. This study presents a methodology that uses terahertz time-domain spectroscopy (THz-TDS) coupled with an index-matching medium to measure the open porosity and analyze scattering losses of powder compacts. The open porosity can be evaluated without the knowledge of the refractive index of the fully dense material. This method is demonstrated for pellets compressed of pharmaceutical-grade lactose powder. Powder was compressed at four different pressures and measured by THz-TDS before and after they were soaked in an index-matching medium, i.e., paraffin. Determining the change in refractive index of the dry and soaked samples enabled the calculation of the open porosity. The results reveal that the open porosity is consistently lower than the total porosity and it decreases with increasing compression pressure. The scattering losses reduce significantly for the soaked samples and the scattering centers (particle and/or pore sizes) are of the order of or somewhat smaller than the terahertz wavelength. This new method facilitates the development of a better understanding of the links between material properties (particles size), pellet properties (open porosity) and performance-related properties, e.g., disintegration and dissolution performance of pharmaceutical tablets.

Characterization of the Interface Between Coating and Fibrous Layers of Paper

Coated paper is an example of a multi-layer porous medium, involving a coating layer along the two surfaces of the paper and a fibrous layer in the interior of the paper. The interface between these two media needs to be characterized in order to develop relevant modeling tools. After careful cutting of the paper, a cross section was imaged using focused ion beam scanning electron microscopy. The resulting image was analyzed to characterize the coating layer and its transition to the fibrous layer. Such image analysis showed that the coating layer thickness is highly variable, with a significant fraction of it being thinner than a minimum thickness required to keep ink from invading into the fibrous layer. The overall structure of the coating and fibrous layers observed in this analysis provide insights into how the system should be modeled, with the resulting conclusion pointing to a specific kind of multi-scale modeling approach.

Stick-slip motion and controlled filling speed by the geometric design of soft micro-channels

HYPOTHESIS

Liquid can move by capillary action through interconnected porous materials, as in fabric or paper towels. Today mass transport is controlled by chemical modification. It is, however, possible to direct mass transport by geometrical modifications. It is here proposed that it is possible to tailor capillary flow speed in a model system of micro-channels by the angle, size and position of attached side channels.

EXPERIMENTS

A flexible, rapid, and cost-effective method is used to produce micro-channels in gels. It involves 3D-printed moulds in which gels are cast. Open channels of micrometre size with several side channels on either one or two sides are produced with tilting angles of 10-170°. On a horizontal plane the meniscus of water driven by surface tension is tracked in the main channel.

FINDINGS

The presence of side channels on one side slowed down the speed of the meniscus in the main channel least. Channels having side channels on both sides with tilting angles of up to 30° indicated tremendously slower flow, and the liquid exhibited a stick-slip motion. Broader side channels decreased the speed more than thinner ones, as suggested by the hypothesis. Inertial forces are suggested to be important in branched channel systems studied here.

Pore space extraction and characterization of sack paper using μ-CT

We show that attenuation X-ray microcomputed tomography (μ-CT) offers a route to extract the three-dimensional pore space of paper reliably enough to distinguish samples of the same kind of paper. Here, we consider two sack kraft papers for cement bags with different basis weights and thicknesses. Sample areas of approximately 5 mm² with a resolution of 1.5 μm are considered, i.e. sizes that exceed sample areas of 2 mm² for which the pore structure was previously studied in the literature. The image segmentation is based on indicator kriging as a local method that removes ambiguities in assigning voxels as pore or as fibre. The microstructures of the two samples are statistically compared in terms of descriptors such as sheet thickness, porosity, fractions of externally accessible pores and mean geodesic tortuosity. We demonstrate that a quantitative comparison of samples in terms of porosity and thickness requires a common definition of the sheet surfaces. Finally, the statistical pore space analysis based on the μ-CT scans reliably reveals structural differences between the two paper samples, but only when several descriptors are used.

LAY DESCRIPTION

This paper is a seemingly abundant material. Its intrinsic porosity enables a vast number of commercial applications. Particularly packing products, e.g. cement bags, often incorporate sack kraft paper due to its high porosity and its additional mechanical strength. A direct quantification of the porosity of sack kraft papers is, hence, particularly desirable. However, experimental quantification of paper porosity or its pore network properties is difficult and often highly indirect. A nondestructive statistical analysis of the 3D microstructure holds the promise to directly assess the pores. In particular, X-ray microcomputed tomography (μ-CT), frequently with sub-μm resolution, has been established as a method to study the fibre and pore structure of paper. The question arises, whether statistical analysis of the microstructure based on μ-CT imaging is sufficient to reliably distinguish between different sack kraft papers. Here, we explore whether the pore structure of paper can be extracted and statistically analysed for larger sample areas despite the fact that a larger sample size directly translates into a lower resolution of the μ-CT scan. We expect that a large sample size increases the region of interest on the basis of which samples can be better distinguished. A lowered resolution poses a severe challenge for the reliable identification of voxel data as pores or as fibres, because the contrast between paper fibres (made of cellulose) and air, which is established due to X-ray absorption, is weak. We show that we can reliably assign each voxel by using an indicator kriging as a two-step method. This method performs an initial voxel identification based on the overall distribution of measured grey values and refines the identification by inspecting the local environment of each voxel. For the pore space extracted in such a way, we can then compute quantities that are related to the geometry and connectivity properties of the pores. Furthermore, we address a paper-born challenge for such an analysis, i.e. we cannot always unambiguously tell whether a pore is located inside the paper sheet or at the surface of the paper. The way the paper surfaces are extracted from the microstructure decisively determines the final specifications of the predicted properties. A significant distinction of the samples is only possible when comparing the properties of the pore network.

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 260 - μ m -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.