presents the time usage for the flow front at the edges of the fibre fabrics. Predicted time refers to the ideal saturated flow, and actual time corresponds to the experimental data. shows that the filling time for the unsaturated flow was faster than that for the saturated flow, and the lead time could be obtained for the unsaturated flow. Samples 1 and 2 are both triaxially stitched fibre fabrics but with different injection flow rates. The lead time for sample 1 was 6.1 s and that for sample 2 was 5.7 s. Samples 2 and 3 were both injected with 150 ml/min of oil but have different geometric structures. The lead time for sample 3 was 2.8 s. Samples 3 and 4 are both biaxially woven fibre fabrics injected with oil at 120 ml/min. The lead time for sample 4 was 2.5 s. The varying lead times show that geometric structure is an essential factor that affects unsaturated flow. Sample 5 was injected with resin, and its lead time was 9.8 s. Based on the results of sample 4, we found that viscosity would promote the formation of an unsaturated area, considering that the surface tension of the fibre tows is not changed. The higher the viscosity, the bigger is the capillary number. This would hinder the flow impregnating to the tows. Viscosity may be another essential factor that affects unsaturated flow. These results elucidate the unsaturated flow behaviour of dual-scale fabrics.

Table 2 Filling times for flow fronts.

According to Darcy’s law, a 1D flowing can be expressed as

$$v=\text{-}\frac{K}{\eta}\frac{dP}{dx}$$(5)

However, inlet flow has a constant flow rate,

$$v=\frac{Q}{A}$$(6)

From Equations (5) and (6), we obtain

$$dP=\text{-}\frac{Q\eta}{AK}dx$$(7)

After integrating Equation (7), we obtain

$${\int}_{P0}^{0}dP}=\text{-}\frac{Q\eta}{AK}{\displaystyle {\int}_{0}^{x}dx$$(8)

Based on the constant flow rate, we obtain

$${v}^{t}=\frac{x}{t}=\frac{v}{\varphi}=\frac{Q}{\varphi A}$$(9)

where *v*^{t} is the actual velocity of the flow front. From Equations (8) and (9), we obtain

$$P0=\frac{Q\eta}{AK}x=\frac{\eta}{\varphi K}{\mathrm{(}\frac{Q}{A}\mathrm{)}}^{2}t$$(10)

where *P*_{0} is the inlet pressure. We found that *P*_{0} against time shows linear relation. When the unsaturated flow front arrived at the edge of the fibre fabrics, we continued injecting oil until the fibre fabric was completely infiltrated. Therefore, a final pressure was obtained through our sensor, and the value of this pressure was equal to the ideal saturated flow under the same experimental conditions. The ideal filling time for different samples was also identified. Hence, the diagram of pressure for ideal saturated flow could be illustrated. The inlet pressure data for real experiment were collected by the sensor, and then, the experimental and ideal saturated data were collected. Figure 5 shows the plot of the inlet pressure against time for the different experimental samples. Diagrams a to e represent samples 1–5 in . The triangular line segment represents the saturated flow, and the curve with squares corresponds to the data collected in the experiment. These figures show two significant characteristics. First is that the unsaturated flowing front is faster than the saturated flow when it reaches the fabric edge. Second is that the inlet pressure of the unsaturated flow is always higher than the saturated flow until they both maximally increase.

Figure 5: Plot of inlet pressure against time for different cases.

To verify the mechanism of this unsaturated flow, the filling process was divided into three parts according to their pressure characteristics. The unsaturated area was rapidly generated in the first stage (Section A). The resistance of the inside tows was higher than that of the macropore between tows because the scale of the macropore was significantly higher than that of the micropore. The fluid only filled the macropore, and only macro flow was observed. Thus, the true porosity was smaller than the theoretical porosity listed in . This finding is the main factor causing the inlet pressure to be higher than the theoretical value. In the present section, the unsaturated flow and length of the unsaturated area rapidly increased in a short period. The inlet pressure plotted in Figure 5C and D against time exhibited linear relation. This result was caused by the geometric structure of the fibre fabrics. Samples 3 and 4 were biaxially woven; their gaps were homogeneously distributed, and both have high densities. In addition, sample 5 was biaxially woven, but the pressure nonlinearly increased because the injection medium was resin, which is more viscous. Comparing samples 1 and 2, triaxially stitched fabrics have low densities and evident large gaps between the fabrics. These gaps appear disordered. Therefore, Figure 5A and B shows a nonlinear increase.

As the fluid continued to fill the cavity, it gradually impregnated the fibre tows in Section B. True porosity was lower than that in the initial phases of Section A, but still higher than theoretical porosity. Therefore, the inlet pressure was still higher than the theoretical value. In the present section, the flow front velocity gradually decreased. This event can be reviewed in the video. The inlet pressure slowly increased, and the length of the unsaturated flow was shorter, as presented in Figure 5. This section shows nonlinear relation.

The unsaturated area was stable in Section C. In this section, the formation rate of the new unsaturated area was equal to the disappearance of the previous unsaturated area, which was observed to be filled by fluid. In this stage, the length of the unsaturated area maintained the balance, as shown in Figure 6. This balance represented the position of the unsaturated flow front against time. The figure shows that the last stage exhibited linear relation, indicating that the unsaturated flow was balanced and had no changes. In this section, the pressure maximally increased until the unsaturated front reached the fabric edges. When the unsaturated front reached the fabric edges, the inlet pressure no longer increased until the fibre fabrics were fully infiltrated. This phenomenon is consistent with the observations of Kuentzer et al. [16], [23]. The pressure was equal to the final theoretical pressure. The inlet pressure with a constant flow rate increased from start to end. Therefore, the pressure in Section C was higher than the theoretical value.

Figure 6: Position of unsaturated flow front against time.

One of the conclusions in this study is that the inlet pressure of the unsaturated flow for dual-scale fibre fabrics is always higher than the saturated flow, but this finding is different from the results of previous studies [24], [25]. These studies indicated that the inlet pressure of the unsaturated flow is lower than the saturated flow. Based on our results and discussion, we concluded that the pressure exceeds the saturated flow. This divergence is important for the mould design and industrial production. Otherwise, the unsaturated flow front will be faster than the saturated flow front.

We modified the injection rate for similar samples, and the results show that a higher velocity leads to a more rapid unsaturated flow front (Figure 7). The screenshot corresponds to samples 1 and 2 with the flow front at the same place and with the length of 500 mm for the mould. The flow rate for A was 120 ml/min and that for B was 150 ml/min. In these images, an evident unsaturated area was observed. However, the zone length for A was smaller than that for B, and the time usage for B was 37 s while that for A was 47 s. A high injection flow rate also promoted the unsaturated flow.

Figure 7: Flow fronts at the same location.

Figure 8 shows the scheme of the pressure with different fabric structures (samples 1 and 4) but with the same injection rate of 120 ml/min. The triangular line segment represents the triaxially stitched fabrics, and the square line segment represents the biaxially woven fabrics. These segments reached the fabric edge almost at the same time. Moreover, the inlet pressure of the biaxially woven fabrics was significantly higher than that of the triaxially stitched fabrics. After observing the structure of two fabrics, the gap of the fibre tow in the biaxial woven fabrics was evidently more compact than that in the triaxially stitched fabrics.

Figure 8: Schematic of pressure for different structure fabrics.

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