3D imaging and analysis of fibrous filter sheets using X-ray microtomography and image analysis.

G. van Dalen1, M. van Ginkel2, G. Hay1

1 Unilever Research & Development, Imaging & Spectroscopy, Olivier van Noortlaan 120, 3133AT Vlaardingen, the Netherlands Gerard-van.Dalen@unilever.com 2 Eikomagos e.U., 1040 Vienna, Austria

Introduction Filter material is used in many applications such as filtration of air, fuel, chemicals and beverages. For each application specific properties are needed such as wet strength, porosity, particle retention, volumetric flow rate, compatibility, efficiency and capacity. Filter material is composed of a broad range of natural or synthetic fibres (e.g. cellulose, polypropylene and polyethylene). The filter properties depend on the three-dimensional (3D) fibre network and the interconnected pores. Therefore, methods are needed to characterise this 3D microstructure. X-ray computed microtomography (micro-CT) can be used for the non-invasive visualisation and quantitative analysis of the pore space. Micro-CT is widely used for studying the porosity of cellular and fibrous material. These include food productsi, cancellous boneii, paperiii,ivv, textile fabricsvi,vii,viii and membranesix. In this study micro-CT is used for the 3D visualisation and analysis of fibrous filter sheets with a thickness ranging from different processes. Fibres with different densities are visible in micro-CT images as gradients of grey levels or intensities, and can be straightforwardly segmented using thresholding. Image analysis is used to quantify the pore morphology. Specifically, in this study the presented methodology offers a way to determine the true thickness of thin fibrous filters, and obtain quantitative information on porosity, pore size distribution, and pore interconnectedness. The thickness of the fibres is close to the resolution of the laboratory micro-CT scanner and was not analysed within this study. For this, higher resolution/contrast is needed which can be obtained using synchrotron micro-CTx. Method X-ray microtomography Samples were imaged using a Skyscan 1172 desktop micro-CT system with a 100kV X-ray source (10W, 20-100kV, 0- -ray detector (4000 * 2664

mages were acquired using a step size

made. The total scanning time (1800 images) was about 6 hours. A stack of ~2500 horizontal cross sections with a pixel size of 4000*4000 was obtained after tomographic reconstruction of the projection images. A beam hardening correction of 40%, ring artefact correction of 20 and smoothing of 4 were selected. Small pieces were cut from each sample and were fixed on a sample rod with clip (Figure 2). The sample rod with a piece of filter sheet was mounted on a micro-positioning stage which helps to achieve exact positioning of the tube in the middle of the scanning field. Usually, double-sided adhesive is used tape to fix the sample on a sample rodvi. However, this will result in blending of the tape with the very thin fibre material, making segmentation of the fibres quite difficult (no clean boundary between the tape and the filter material).

Figure 2 Micro-CT set-up used for imaging filter papers. Image analysis The stacks of 2D micro-CT images of the paper samples were converted to a 3D image using the AvizoFire software (v. 9.2.0, Thermo Scientific), rotated in 3D space and cropped. Resulting in typically size of 4000 x 2500 x 300 pixels. The actual thickness of the samples is considerably

quired to capture the entire sample. For 3D visualisation, volume rendering was used. All subsequent steps were performed using the image analysis toolbox (DIPlib 2.8 from Delft University of Technology, NL, http://www.diplib.org/) running under MATlab (version R2016a from MathWorks). Binary images of the fibre materials were made using thresholding. Masks Image analysis was performed on masked regions. Two masks were created (Figure 3). The most significant of these is the mask that captures the material as a whole: the sheet. It is computed in two steps. First, any loose fibres jutting out from the main structure are removed. A local averaging filter produces distinct values in the bulk of the material versus in the region around an isolated fibre that can be predicted and used to discriminate between the two. Next, the sheet is found by applying a distance transform based on a closing operation to the bulk material as used by Wernerssonv

more open structure at the top and bottom of the sheet, the core mask is defined: a fixed width core of the sheet (except where the sheet is thinner than the target width).

Figure 3 Schematic cross section of the sheet and core masks. Measurements To estimate the variability of the measurements the volume was divided into equal-sized sub-volumes (a grid of columns). Only for the connectivity the total volume was used. For the porosity a 5x5 grid was used and for the sheet thickness a 20x20 grid. The sheet thickness is measured using the distance transform. First the distance trans-form is computed, and then within each of the 20×20 measurement columns the maximum value is taken and multiplied by two. These are averaged to produce the final sheet thickness

measurement. Any artefacts due to e.g. the incomplete removal of a protruding fibre are corrected by this procedure. The porosity is a simple measure to quantify the pore space. It is the ratio of empty space in the sample against the total space occupied by the sample, as given by the sheet image. For the connectivity analysis, we consider all the paths that a sphere of diameter can take through the sample. This was done for a range of possible values of . Our task lies not so much in finding the paths through the sample for a given diameter , this is in fact a straightforward task, but in finding some features that can capture some of the path structure. How do we find the paths? The distance transform of the pore space gives us all the pixels which lie at least ½ from the fibres. These pixels are grouped into separate subvolumes of the pore space that represent all allowed positions for the centre of the sphere. Only subvolumes that connect the top and the bottom of the sheet are of interest. Any given subvolume can have multiple entry and exit points at the top and bottom surfaces. Also, the size of the subvolume can vary substantially, corresponding from a very narrow path that just allows a sphere of diameter to pass through to very large pores. Here, we focus solely on the existence of the paths. What can we expect to happen when varying ? At the smallest sizes, there will generally be a single connected travel space. As this travel space will simply equate the pore space. As increases, the volume of the travel space will decrease. As increases, the travel space will break up into ever more multiple disjoint paths. A second effect also occurs: each path allows a maximum sphere diameter to pass through. Therefore, as soon as exceeds

that path is no longer part of the travel space. As grows further and further this effect starts to dominate over the break up process and the number of paths decreases until there are no paths left ( > max). The process just sketched is taken to be characteristic for the connectivity properties of a sample.

Results An example of a cross section through a 3D micro-CT image of a filter sheet is shown in Figure 4. The grey levels in the image range from black (low grey level = low X-ray absorption) to white (high grey level = high X-ray absorption). The filter sheet was made of cellulose and polypropylene (PP) fibres. Figure 5 shows a 3D view of the fibres using volume rendering of the 3D micro-CT image. The fibres can be identified by their shape. The PP fibres are smooth tube shaped whereas the cellulose fibres are rough flat, or ribbon shaped. The fibres are entangled forming a porous network.

Figure 4 Cropped micro-CT image of a horizontal cross section (top) of a filter sheet with enlarged view (bottom).

Figure 5 3D volume rendering of a micro-CT image of a filter sheet sample with enlarged view.

An example of the result of the binarization of the fibres in a micro-CT image of a filter sheet sample is shown in Figure 6. Included is the calculated sheet. At the edges of the sheet, it can be observed how tight the sheet fits to the fibres.

Figure 6 Surface renderings of a micro-CT image of a filter sheet sample showing the fibres in red and the outline of the calculated sheet in transparent blue (box size = 4.0mmx2.5mmx0.4mm).

The relation of the micro-CT image-based sheet thickness measurement and the physical thickness measurement of filter sheet samples is shown in Figure 7A. The micro-CT results are about 23% higher. The variability of the micro-CT results is much lower than observed for the physical measurements (see error bars). The thickness should depend on the physical sheet density, expressed in grams per square meter (gsm), for fibres with comparable densities. The sheet thickness measured from the micro-CT images correlates better to the physical gsm (Figure 7B) than the physical sheet thickness to the physical gsm (correlation coefficient of 0.72

and 0.52, respectively). The measured thickness using physical measurements can be

accurately defined.

Figure 7 Thickness of filter sheets measured from micro-CT images compared to physical measurements.

The measured porosity of the investigated filter sheet samples ranges from to 0.80 to 0.95. The results using a sheet or core mask were not significantly different. The key investigated connectivity property is the number of paths connecting the top and bottom of a sheet sample as a function of sphere diameter and normalised per unit area. An example of a connectivity curve is given in Figure 8. Key points are identified in this figure which can be used to capture the main characteristics of the connectivity curves. Some of these features are correlated to each other. Tail10 and the maximum sphere diameter, are correlated with the tail parameter (correlation coefficient of 0.81 and 0.532, respectively). The tail, mode and count have a strong discriminatory power between different types of samples, and are good candidates to correlate physical measurements against (not included in this paper). The count correlates with the sheet thickness (Figure 9A) and the mode correlates with the porosity (Figure 9b). The thicker the sheet, the fewer paths are available and a higher porosity results generally in larger diameters of the paths. Examples of 3D micro-CT images of filter sheet samples with some measured parameters are shown in Figure 10. A sample size of approximately 4.0mm x 2.5mm is in most cases sufficient to capture a representative sample view. However, for some filter sheet sample larger sample sizes are needed to be representative for the non-homogenous material (for example, sample 3 in Figure 10). A larger sample can be imaged by stitching several micro-CT images (Figure 11).

Figure 8 Connectivity parameters with graph showing the number of paths connecting top and bottom of the sample per square millimetre as a function of the diameter of the probing sphere.

Figure 9 Connectivity parameters count as function of the sheet thickness and mode as

function of the porosity measured from the micro-CT images of filter sheet samples.

Figure 10 3D surface views of micro-CT images of filter sheet samples with measured parameters (T=thickness, P=porosity, M=mode, C=count). Image size = 3.1mm x 2.5mm.

Figure 11 3D surface view of a micro-CT image (11.9mm x 7.2mm) of an inhomogeneous filter sheet sample with enlarged views (1mm x 1mm).

Conclusion X-ray microtomography combined with 3D image analysis is a powerful tool for the characterisation of the 3D microstructure of thin fibrous filter material. It provides quantitative information about the pore system (e.g. porosity and connectivity). Also, it offers a more accurate and precise determination of the sheet thickness than using traditional physical methods. This information can be used as input for simulation models or the complete 3D microstructure can provide a mesh as input for finite element modelling to predict filtration properties. References:

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