Cellular Ceramics / p3

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3.1.2.2.4Capillary Flow Porometry

The structure of porous materials is often very complex because of the nature of the porosity (closed porosity, blind pores, and through-pores), the pore shape, the surface area, and the isotropy. For applications like filter media, the fluid or gas flow characteristics, the barrier properties, and the efficiency of the process are governed by the combination of all aspects of the pore structure.

Capillary flow porometry, also known as extrusion flow porometry, can be applied to determine some important characteristics of porous materials [38, 39]:

Principle

The sample is placed in a wetting liquid to fill the pores of the sample. As the liquid/solid surface free energy cls is lower than the solid/gas surface free energy csg, pores are spontaneously filled by the liquid. When a nonreacting gas increasingly pressurises the sample, the liquid is removed from the pores and a gas flow through the pores results. To displace the liquid from the pores, the work done by the gas must be equal to the increase in surface free energy. This can be expressed by the following equation:

where p is differential pressure, dV the increase in volume of gas in the pore, and dS the increase in solid/gas surface area (or the corresponding decrease in solid/ liquid interfacial area).

The pore cross section can be quite complex. The diameter of a pore at any location along the pore path can be defined as the diameter of a cylindrical opening that has the same dS/dV ratio as the actual pore. This is illustrated in Fig. 20.

Figure 20 Schematic representation of pore cross section and the definition of pore diameter in capillary flow analysis.

Taking into account the relation between the contact angle h and surface tension c, the relation between the pore diameter D and the differential pressure needed to displace the liquid from the pore can be expressed as:

250 Part 3 Structure

where fw and fd are the flow rates through wet and dry samples, respectively, at the same differential pressure. The area under the curve in a certain pore range is the percentage flow through that pore size range. A typical result of a capillary flow analysis of a ceramic foam is presented in Fig. 23.

Pore

Liquid

D2

Figure 22 Schematic view of a through-pore channel and the pore diameter measured by capillary flow analysis (in comparison with liquid extrusion and mercury intrusion porosimetry).

Figure 23 Capillary flow analysis of sample 1, showing the dry flow curve, the wet flow curve, and the half-dry flow curve.

2) The gas flow curve through the dry sample permits the calculation of the gas permeability using Darcy’s law [40]:

where F is the volume flow rate at the average pressure per unit time, k the permeability, l the viscosity of the fluid, A the cross-sectional area of the porous sample, l the thickness of the porous sample, pi the inlet pressure, and po the outlet pressure.

Analogously, liquid permeability for a variety of liquids and solutions can be measured by using the corresponding wet flow curve.

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3) The flow rate data enable calculation of the surface area by using the Kozeny– Carman relation [41, 42]. Accurate measurements are possible when the specific surface area is less than 10 m2 g–1 and the distribution of pore diameters is relatively narrow. The agreement with gas adsorption measurements is reasonably good if the sample is free of blind pores.

Specifications

In this study, a PMI Capillary flow porometer, type CFP-1200-A was used (Porous Materials Inc., USA). The specifications according to the manufacturer are summarized in Tab. 3. The measurable pore size stretches over a broad range from 13 nm to 500 mm. The low pressure needed to remove the liquid enables the characterization of mechanically weaker structures (e.g., polymer foams) and avoids distortion of the pore structures.

Table 3 Specification of the capillary flow analysis equipment.

Results

Figure 24a presents pore diameter and filter flow (ratio of the wet and dry flow curves) as a function of the applied pressure for sample 4. From these raw data, the bubble point can easily be identified as the pore diameter that corresponds to the

Figure 24 a) Relation between pore diameter and filter flow as a function of differential pressure and b) size distribution of the most restricted part in the pore channels for sample 4.

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lowest pressure needed to initiate flow through the wet sample. For this sample, the bubble point is 338 mm, and 90 % of the filter flow occurs for pores larger than 49 mm. A pore size distribution is obtained by the differentiation of the filter flow as a function of the pore diameter (Fig. 24b).

Figure 25 presents an overview of the filter flow curves for the eight samples. Although the pore diameters of the different samples vary over a relatively broad range (from 200 to 1700 mm), the pore sizes as measured by capillary flow analysis are distributed over a much smaller range (ca. 20 to 700 mm). This can be explained by the presence of semiclosed windows and other restricted pore channels that cannot be detected by image analysis or other techniques based on microscopy.

Diameter / µm

Figure 25 Filter flow curves measured by capillary flow analysis for the eight samples.

Comparing the information of the capillary flow analysis with the pore diameter determined by the Visiocell measurements clearly shows the difference between the two techniques regarding the measured property (Fig. 26). As capillary flow analysis only measures the most restricted part of the pore channel, mean pore flow diameter and the bubble point are lower than the average diameter of the pore size determined by the Visiocell technique.

Although a general increase in the restricted pore diameter is seen with increasing cell size of the polyurethane foam, this trend is not followed to the same degree. When coating with more viscous suspensions, the formation of semiclosed cell windows cannot be avoided, as exemplified by the lowering of the restricted pore channel diameter for samples 6 and 8 compared to samples 5 and 7, respectively.

The mean flow pore diameter and the bubble point are critical parameters of porous materials that are used in applications such as filtration or porous bone replacements. For the latter, bone ingrowth requires a minimum pore channel diameter that enables migrating biological material like cells or veins to penetrate the porous implant. The combination of the mean pore diameter and the most restricted part of the pore channel play a critical role in the ability for complete ingrowth.

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Figure 26 Comparison of the pore diameter by the Visiocell method, bubble point, and mean flow pore diameter measured by capillary flow analysis.

3.1.2.2.5Micro Computer Tomography

Knowledge of the structure and morphology of highly porous ceramic materials is essential for various applications. Structural properties such as fractional density, which corresponds to the overall porosity, the mean size and size distribution of the foam cells and the surrounding struts, the shape of the cells, and the isotropy of the individual cells influence many properties. For example, gas permeability is increased by large windows interconnecting cells and decreased by small cell diameters.

Several approaches have been used to evaluate the structure, such as magnetic resonance imaging and optical analysis. Tomography facilitates three-dimensional imaging of complex structures. Optical tomography was used to evaluate transparent aqueous foams: light was transmitted through a sample and detected by a camera with a plane detector [43, 44]. The drawback of light optical analysis is that it cannot be used for nondestructive evaluation of the three-dimensional structure of nontransparent ceramics. However, X rays transmit through most ceramic materials, and thus X-ray tomography can be used to characterize porous ceramic materials [45].

Principle

X-ray micro tomography is based on the evaluation of stacked two-dimensional layers of the sample that are scanned sequentially [46] (Fig. 27a). An X-ray source, usually a microfocus X-ray tube, emits a fan-shaped beam of intensity I0 that passes through the specimen. The intensity I is detected by a line array of length x. The relative intensity I/I0 of the transmitted beam depends on the amount and nature of the material being analyzed. Between two recordings the sample is slightly rotated. After a full rotation up to several hundred recordings have been taken. The intensity data can be displayed as a sinugram (Fig. 27b).