In-plane permeability

Although in-plane permeability is critical in order to understand in detail the transport mechanisms of fluids inside diffusion layers, it has not been as commonly used (and measured) as through-plane permeability. The following are a few examples of how in-plane permeability can be determined... 

Experimental apparatus used to measure in-plane permeability (a) assembled view (b) exploded view (c) sectioned view. (Reprinted from J. T. Gostick et al. Journal of Power Sources 162 (2006) 228-238. With permission from Elsevier.)... 

Gostick et al. [212] designed an apparatus in which the in-plane permeability was measured as a function of the DL thickness with different compression pressures (see Figure 4.25). The DL specimen was compressed between plates, which had spacers of different thicknesses in order to control the total thickness in each test. The sample was located between two grooves or channels, one of which corresponded to the inlet of the air and the other to the air outlet. Therefore, the air had to flow in plane through the sample in order to... 

For each thickness, at least 10 different flow rate measurements were obtained in order to cover the range of flow rates that a DL experiences during normal fuel cell operation. To obfain fhe corresponding permeabilify, fhe pressure drop resulfs were ploffed as a function of the mass flow rate. After this, the Forchheimer equation was fitted to the plotted data to determine the viscous and inertial permeabilities. As expected, the in-plane permeabilities of each sample DL maferial decreased when the compression pressure was increased. It is also important to mention that these tests were performed in two perpendicular directions for each sample in order to determine whether any anisotropy existed due to fiber orienfation. 

Feser et al. [214] used a radial flow apparatus to determine the viscous in-plane permeability of differenf DLs af various levels of compression (see Figure 4.26). A stack of round-shaped samples, wifh each layer of material separated with a brass shim, was placed inside two plates. Thicker shim stock was also used in order to control the total thickness of the stack of samples. Compressed air entered fhe apparafus fhrough the upper plate and was forced through the samples in the in-plane direction. After this, the air left the system and flowed through a pressure gage and a rotameter in order to measure the pressure drop and the air flow rate. The whole apparatus was compressed using a hydraulic press for each compression pressure, 10 different flow rates were used. 

Gurau ef al. [129] presented another apparatus used to measure the in-plane viscous and inertial permeability coefficients. In their method, an annular DL sample was placed between an upper and lower fixture. The gas entered the upper fixture and was then forced fhrough fhe DL info fhe ouflef porfs (open to the atmosphere). A strain sensor was located in the upper fixture in order to determine the thickness of fhe DL (i.e., deformation) because fhe whole assembly was compressed to a determined pressure. In fhis mefhod, the flow rate, temperatures in both fixtures, and pressures were monitored in each test. Once the data were collected, the in-plane permeability was determined from the Forchheimer equation by application of fhe leasf squares fit analysis method. 

Chang et al. [183] presented a similar design in which two discs (with orifices in the middle) were used to compress the sample material. Pressurized air (without any moisture) was then passed through the orifices of fhe discs toward the sample DL, which then flowed peripherally to the atmosphere. The two discs were compressed in order to see how the permeability of the DL changed as a function of the clamping pressure. The permeability coefficient was solved using Darcy s law thus, only the viscous in-plane permeability was taken into account. Other, similar techniques can be found in the literature [215-217]. 

Park, Lee, and Popov [136] used a similar technique to determine the liquid permeation in different diffusion layers. Feser, Prasad, and Advani [214] used the same method explained in Section 4.4.S.2 to measure the liquid in-plane permeability of DLs. When water was used, flow was forced from a pressurized tank (0-200 kPa) through the apparatus (and the sample), and the outlet water was then collected with a graduated cylinder. 

Ariadurai SA, Potluri P. Modeling the in-plane permeability of woven geotextiles. Textile Research J 1999 69 345-51. 

Mekic S, Akhatov I, Ulven C (2009) Analysis of a radial infusion model for in-plane permeability measurements of fiber reinforcement in composite materials. Polym Compos 30(12) 1788-1799... 

C. Lekakou, M.A.K. Johari, Norman, and G. Bader. Measurement techniques and effects on in-plane permeability of woven cloths in resin transfer molding. Compos. A 27, 401-408 (1996). 

One of two standard test methods may be used to measure the in-plane permeability of materials BSEN ISO 12958 Determination of in-plane water flow capacity and ASTM D4716 Determining the in-plane flow rate per unit width and the hydraulic transmissivity of a geosynthetic using a constant head . As stated above, a series of loads is applied to the test specimen. At each applied load o " is determined... 

It was shown above that the cover factor is directly related to the POA, and it is therefore reasonable to assume that the relation extends to the fabric permeability normal to the plane of the fabric. However, the in-plane permeability is more complex, as it concerns the cross-section area of the fabric. 

Thus for separation, filtration, and drainage applications the cross-plane and in-plane permeability values obtained by index testing would be moderated according to ... 

A parameter for in-plane permeability of a geotextile or drainage geocomposite. 

Heardmann, E., Lekakou, C., Bader, M., 2001. In plane permeability of sheared fabrics. Compos. Part A 32, 933-940. 

For GDL carbon materials, Gaston et al. [66] showed using MIP on hand-made woven fabrics that a relationship exists between the amount of macropores and the through-plane gas permeability. They also showed that woven materials can exhibit high in-plane permeability, which means also a low pressure drop. For a non-woven carbon paper, Hiramitsu et al. [67] showed that even small amounts of hydrophobized carbon black introduced in the GDL reduce flooding significantly. 

In that case, significant transverse flow develops, and macrovoids may be entrapped as illustrated in Rg. 9.20. From the solution procedure point of view, fully three-dimensional flow modeling and simulations are not much more difficult than the two-dimensional version however, one needs (1) to discretize the solution domain in 3D instead of 2D (which takes much longer CPU time to solve the pressure distributions and advance the flow front in a time marching scheme) and (2) to measure the transverse permeability of the preform which is much more difficult than measuring in-plane permeability components. ... 

Experimental procedures formeasurmg the in-plane permeability of a porous preform are summarized in this section. The schematics of the experimental setups are shown in Figs. 9.27-9.30 for four different approaches. Table 9.2 summarizes the boundary conditions, required data to be collected during the experiments and the formulas used to calculate the permeability. 

A single radial injection experiment allows one to measure both principal in-plane permeability components (A n and /C22). One does not have to address the issue of racetracking during radial injection. These are the major advantages of the radial injection compared to the ID linear injection. 

Figure 9.31 shows some samples of experimentally measured permeability values for mats and fabrics published in the literature. Eleven institutions and companies participated in calculating in-plane permeabilities of two fabrics using different experiment types (ID linear and radial),... 

For composite parts which are relatively thin and saturated through the thickness, one can reasonably neglect fluid-flow in the thickness direction, particularly when the transverse permeability is very much smaller than the in-plane permeability. For this case, one can derive the fluid mass conservation equation in general three-dimensional form and then specialise it to... 

Gantois R, Jourdain E, Dusserre G. Recent patents on in-plane permeability measurement of LCM composite reinforcements. Recent Patents on Engineering,... 

Heardman E, Lekakou C, Bader MG. In-plane permeability of sheared fabrics. Composites Part A Applied Science and Manufacturing, 2001 32(7) 933-940. DOI 10.1016/S1359-835X(01)00006-9. 

Bickerton S, Gan JM, Zhang F, Cosson B, Comas-Cardona S, Binetruy C. An optically based inverse method to measure in-plane permeability fields, in Proceedings of the 10th International Conference on Flow Processes in Composite Materials, Monte-Verita, Switzerland, 2010. 

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