# Dynamic void content prediction during radial injection in liquid composite molding

Boris Gourichon, Mylene Deleglise, Christophe Binetruy, Patricia Krawczak

► To cite this version:

Boris Gourichon, Mylene Deleglise, Christophe Binetruy, Patricia Krawczak. Dynamic void content prediction during radial injection in liquid composite molding. Composites Part A: Applied Science and Manufacturing, 2008, 39 (1), pp.46 - 55. 10.1016/j.compositesa.2007.09.008. hal-01773125

HAL Id: hal-01773125

https://hal.science/hal-01773125v1

Submitted on 2 Feb 2026

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
# Dynamic void content prediction during radial injection in liquid composite molding

Boris Gourichon, Mylène Deléglise, Christophe Binetruy*, Patricia Krawczak

Ecole des Mines de Douai, Polymer and Composites Technology and Mechanical Engineering Department, Douai, France

In liquid composite manufacturing, a resin is injected through a dry porous media previously placed in a closed mold. To reach aeronautic requirements or for short injection cycles in the automotive industry, entrapped air in the final part before curing has to remain as low as possible. Air entrapment will depend on the fibrous structure, such as fiber content or tow and preform architecture, and on the injection parameters, or more precisely on the fluid pressure and the flow front orientation with respect to the fibrous direction. Void content prediction during unidirectional flow in liquid composite molding processes was presented in a previous article [Gouri chon B, Binetruy C, Krawczak P. A new numerical procedure to predict dynamic void content in liquid composite molding. Composites Part A 2006;37(11):1961 9]. In that article, it was shown that microvoids creation, evolution and elimination could be numerically predicted. Good agreement was obtained with experimental measurements of entrapped air volume for 1D flow. Usually, during injection of real parts, flow orientation is not constant, according to the part shape or to the injection scheme employed. The aim of this paper is to evaluate the importance of fiber orientation with respect to the flow front direction by taking as a reference a radial flow where any flow direction can be studied. A bidirectional model was thus developed based on the comparison of the direction of the flow front to the fiber orientation during radial injection by defining an entrapment angle. An experimental analysis of radial flow is conducted in order to analyze the voids creation process regarding fiber orientation by comparing experimental and numerical fluid pressure profiles during injection. Good agreement between numerical and experimental pressure profiles were obtained, thus validating the developed numerical code. However, the change in pressure level due to the presence of microvoids is not significant. In our case, pressure is thus not a reliable parameter to testify for microvoids creation.

**Keywords:** E. Resin transfer molding (RTM); C. Computational modelling; B. Porosity

## 1. Introduction

Resin transfer molding (RTM) is one of the most cost competitive processing technology for composite part manufacturing. A low viscosity thermoset or reactive thermoplastic resin is injected to impregnate a preform made of glass or carbon fabrics placed in a closed mold. The possibility of producing high fiber content, complex shape and large parts in a closed mold with limited volatile organic

compounds (VOC) emission is among its many advantages on other processes such as autoclave curing or hand lay-up. Recent efforts on process modeling have made efficient simulation tools available, thus reducing the expensive and time consuming prototyping phase. A key parameter for production of structural composite parts is air entrapment, since residual high void content could lead to mechanical softening, early failure, or part rejection. In a dual scale porous medium, woven fabric for instance, the difference in length scale between micropores (pores inside a fiber tow) and macropores (pores between fiber tows) is usually 1 or 2 orders of magnitude. During impregnation driven by viscous forces, the resin flows first between fiber tows

<footnote>* Corresponding author. Tel.: +33 3 27 71 21 75; fax: +33 3 27 71 29 81.
E-mail address: binetruy@ensm douai.fr (C. Binetruy).</footnote>
(macropores) and then impregnates the fiber tow (micropores) transversally, the global flow front position matching the macropores flow front [2, 5]. The direct consequence of this delayed impregnation is the presence of air bubbles trapped within the fabric when resin starts exiting the mold. For example, Jinlian et al. [6] showed that air entrapment is facilitated for fabrics presenting warp and weft fiber tows with different permeabilities resulting in a higher resin velocity along the weft tow than along the warp tow, causing air entrapment. Creation and evolution of air bubbles during injection can be simulated using Lattice Boltzmann method. Spaid et al. specifically studied the influence of fiber diameter and local fiber volume content on the impregnation of fiber tows [7]. Since the tow saturation time scale can be of the same order of magnitude than the whole part impregnation and resin gel times for fast injections of highly reactive resins, it is critical to include saturation models and void content prediction in future simulation tools. Then the model for generation, evolution and elimination of air bubbles need to be understood. Pars eval et al. [8] developed a model for permeability variation with saturation in dual scale porous medium and good agreement was found with experiments. Although the study did not address the problem of void formation and bubble elimination, it demonstrated the necessity to account for saturation effects when modeling flow through a dual scale porous medium. Other authors [9,10] devel oped an analytical model to determine the permeability of the fiber tows and of the bulk preform. Breard et al. [11,12] proposed a numerical model for void formation in LCM where a ratio characterizing the difference between saturated and unsaturated permeabilities was identified. Good agreement was found for saturation between the numerical model and experimental measurements using the liquid electrical conductivity technique. Pillai et al. pro posed to add a sink term in the continuity equation to account for the delayed impregnation of fiber tow

$$ \nabla \cdot v = -S \qquad (1) $$

where v is the fluid velocity and S is the sink term and represents liquid absorption velocity per unit volume [13]. The study of the dual flow simulation lead Pillai et al. to consider a sink effect index $\psi$ that depends on the tow and channel permeabilities ratio (the channels being the free space between fiber tows), and on the characteristic mold and tow lengths [13,14]. It was then observed numerically and experimentally that inlet pressure does not follow the pressure profile of an injection without considering sink effects, the greater the $\psi$ parameter is, the stronger the discrepancy. According to Lundstrom [15,16], the voids are mobilized depending on their size and a critical pressure which is a function of the radii of the constriction and flow channel and the surface forces. A high resin pressure and a high flow rate are important for void removal during bleeding.

The sink term can also be implemented in a simulation tool by including additional elements that would represent

the volume accessible to the resin inside the fiber tows, while regular mesh elements only represent the free volume between fiber tows. This model has been developed and implemented into the simulation package LIMS to predict fiber tow saturation [17]. Flow within a woven or stitched fabric is driven both by viscous forces on the macroscale and capillary forces on the microscale and the formation of micro or macrovoids is the result of the competition between those two phenomena. Patel et al. [18, 21] carried out experiments to investigate the process of void formation. They showed that macrovoids were formed at low flow rate and microvoids within transverse tows at high flow rate. A critical pressure $P_c$ that allows air bubbles to mobilize through the preform is to be considered as well [22, 24].

In a previous work [24], a new experimental method to measure saturation kinetics throughout the injection process was developed and the final void content was measured for various flow rates. Those results helped validating a saturation module implemented in the LIMS simulation tool and determining the distribution of entrapped air in the preform as a function of the fluid pressure locally applied [1]. Since those previous results only dealt with unidirectional flow, investigation of void formation for complex flow front shapes was to be conducted. Therefore, central injections were performed in an instrumented mold and the implemented saturation module was enhanced to model void formation during radial injection schemes.

## 2. Experimental set-up

As pressure is the governing parameter during void formation and evolution, the experimental set-up designed to track void content for a radial injection case is based on the fluid pressure tracking along two different radial directions in a cylindrical mold, the two directions corresponding to the fabric weft and warp directions. Results are then compared to the pressure profiles obtained from the numerical code.

The mold, presented schematically in Fig. 1, has a 300 mm in diameter and 60 mm high cylindrical cavity. A channel is machined on the circumference of the cavity to serve as vent. The upper plate is a cylindrical piston equipped with an o-ring to seal the mold when closing. The mold is placed in an hydraulic press, the lower plate being stationary. The injection point is located in the center of the upper mold. Three pressure transducers are placed along a radial direction on the lower plate at 40, 80 and 120 mm from the injection inlet. Three others are placed on the upper mold, along a direction perpendicular to the transducers in the lower plate, and also placed at 40, 80 and 120 mm from the resin inlet as shown in Fig. 1.

The 5.2 mm thick fiber preform is composed of four plies of an unbalanced woven glass fiber fabric (1 × 3 twill weave S31500, Chomarat, France), leading to a 44% fiber
volume fraction. In order to perform an in-plane central injection, a 10 mm diameter hole is drawn in the center of the preform, right below the injection gate. The flow front thus only spreads radially, there is no through thickness flow. The pressure transducers are connected to a Labview interface via an appropriate data acquisition card. The pressure transducers on the lower mold aligned with the warp direction are named P1warp, P2warp, P3warp from the mold center to the mold periphery while the pressure transducers on the upper mold, placed along the weft

direction of the fiber preform, are named P1weft, P2weft, P3weft. Injections are conducted with a non reactive fluid, dioctylphthalate (DOP), which viscosity value as a function of temperature is known to be slightly under 0.1 Pa s at 25 °C [24].

Pressure transducers response are shown in Fig. 2 for a 500 cm³/min injection flow rate. The delay obtained between the transducers placed along the two different directions for the same radius is due to the fabric anisotropy between weft and warp directions.

<figure><img src="image_2.png" /><figcaption>Fig. 1. Experimental instrumented mold.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 2. Pressure transducers responses.</figcaption></figure>
### 3. Numerical procedure for void content prediction

A numerical implementation of this procedure is performed in LIMS, a software developed at the University of Delaware and dedicated to the simulation of liquid composite molding injections. The numerical method to predict fiber tow saturation developed by Simacek and Advani was used as a basis for the present work. The method is briefly presented, exhaustive description can be found elsewhere [17]. The solution domain is meshed with a fixed finite element mesh and the porous fiber tows are considered as an impermeable medium to provide accurate solutions for Darcy's law. The sink effect is provided externally by adding extra volumes in the form of 1D elements at each node as, illustrated in Fig. 3. The studied part is implemented in the code as 2D shell elements. Those elements represent the macroscopic flow in the inter-tow free volume. 1D elements are then added at each mesh node so as to represent the intra-tow volume (Fig. 3b).

The free volume in 1D elements represents the porous volume within fiber tows. To achieve correct calculations, fiber volume fraction within the original mesh must be modified (impermeable tows) to ensure conservation of the global pore volume. Fiber tows are supposed to be rectangular with rounded corners and impregnation is considered only transverse from top and bottom sides. The previous work on prediction of void content for unidirectional flow [1] cannot be applied to bidirectional flow as the flow front velocity is not constant and as the angle between fibers and the flow front normal varies as a function of position. It was observed in the experimental work that air will only be trapped in weft fiber tows placed transversely to the flow front [24]. As a result, the predicted impregnation time to reach an infiltration radius $r_i$ also depends on the element $i$ considered, or more exactly on the resin velocity at that location defined as

$$v_1 = \frac{V_{\text{elem}}}{S_{\text{elem}} \Delta t_i} \qquad (2)$$

where $V_{\text{elem}}$ and $S_{\text{elem}}$ are the volume and cross-section area of the 2D element considered, $\Delta t_i$ the filling time of that 2D element and $v_1$ the volume averaged flow velocity. The trapping time $\Delta t_{p,i}$ can thus be derived as being

$$\Delta t_{p,i} = \frac{l_{\text{tow}}}{v_1} \qquad (3)$$

where $l_{\text{tow}}$ is the tow width. In the calculation, the real geometry of the mesh is not considered. Instead an equivalent tow radius given as

$$r_0 = \sqrt{l_{\text{tow}}h_{\text{tow}}} \qquad (4)$$

is considered, where $r_0$ is the equivalent tow radius, and $h_{\text{tow}}$ the tow thickness. A geometric presentation of the tow is shown in Fig. 4. In order to define the initial volume of voids created at each location when resin flows through the transverse fiber tows, a first simulation is performed without the saturation module, the only searched parameter being the filling time of the 2D elements. Then the initial radius of the generated air bubble $r_i$ needs to be defined.

The derivation was taken from [25] and reproduced here for better understanding. It is based on Darcy's law written for a radial injection

$$\dot{r}_i = \frac{-K_t}{\eta(1 - Vf_0)} \frac{\partial P}{\partial r_i} \qquad (5)$$

where $\mu$ is the resin viscosity, $Vf_0$ is the fiber tow fiber volume fraction and $K_t$ is the fiber tow transverse permeability. A mass balance on the fiber tow can be written as

$$\dot{r}_0(2\pi r_0)(1 - Vf_0) = \dot{r}_i(2\pi r_i)(1 - Vf_0) \qquad (6)$$

And simplified to

$$\dot{r}_i = \dot{r}_0 \frac{r_0}{r_i} \qquad (7)$$

Including Eq. (7) in (5) leads to the following expression

$$\frac{dP}{dr_i} = \frac{\eta}{-K_t} (1 - Vf_0) \dot{r}_0 \frac{r_0}{r_i} \qquad (8)$$

<figure><img src="image_4.png" /><figcaption>Fig. 4. (a) Tow geometry and (b) equivalent representation.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 3. Original (a) and modified (b) meshes for tow saturation calculations [17].</figcaption></figure>
The pressure can now be expressed with an integration between the equivalent radius of the tow and the equivalent radius of the position of the flow front

$$ \Delta P = \int_{r_0}^{r_i} \frac{A}{r_i} dr_i = A \ln \left( \frac{r_i}{r_0} \right) \qquad (9) $$

by using

$$ A = \frac{\eta}{-K_t} (1 - Vf_0) r_0 \dot{r}_0 \qquad (10) $$

The pressures involved are the capillary pressure $P_{cap}$ and the resin pressure $P$

$$ \Delta P = -P - P_{cap} \qquad (11) $$

Thus the air bubble radius is now expressed by

$$ \dot{r}_i = \frac{K_t}{\eta(1 - Vf_0)r_i} \frac{P + P_{cap}}{\ln\left(\frac{r_i}{r_0}\right)} \qquad (12) $$

Integration of Eq. (12) allows to determine the filling time to reach radius $r_i$ in the fiber tow

$$ \Delta t_i = \mu(1 - Vf_0)r_0^2 \left[ \frac{-2\left(\frac{r_i}{r_0}\right)^2 \ln\left(\frac{r_i}{r_0}\right) + \left(\frac{r_i}{r_0}\right)^2 - 1}{4K_t(P_{cap} + P)} \right] \qquad (13) $$

where $P_{cap}$ is the capillary pressure defined as

$$ P_{cap} = \frac{-2\gamma \cos(\theta)}{l_t} \qquad (14) $$

where $\gamma$ is the fiber surface tension, $\theta$ the contact angle between the fluid and the fiber and $l_t$ the distance between two fibers. The surface tension and contact angle values are obtained from the literature [20] for DOP (dioctylphthalate) used during this study ($\gamma$ 25.4 mN/m, $\theta$ 0).

The evolution of the fiber volume fraction for the 1D element $i$ considered is calculated from the following relations, assuming the ideal gas law applies

$$ V_{\text{air}} = \left(\frac{r_i}{r_0}\right)^2 (1 - Vf_0) \qquad (15) $$ $$ Vf_i = Vf_0 + V_{\text{trans}}V_{\text{air}}\left(\frac{P_0}{P_i}\right) $$

where $V_{\text{air}}$ is the volume of air in the 1D element, $P_0$ the initial pressure of the air bubble and $P_i$ its pressure at the time step considered, and $V_{\text{trans}}$ the ratio of transverse tows to the total fiber weight

$$ V_{\text{trans}} = \frac{W_{\text{weft}}}{W_{\text{warp}} + W_{\text{weft}}} \qquad (16) $$

where $W_{\text{weft}}$ and $W_{\text{warp}}$ are the areal weights of the weft and warp fiber tows, respectively, $V_{\text{trans}}$ represents for the studied fabric 58% of the tows.

Following this methodology, a map of the initial void content at each location can be drawn, as represented in Fig. 5.

For a radial injection, velocity decreases along the flow front direction, thus affecting the impregnation time derived in Eq. (13). The volume of the created air bubble will thus be higher at the mold inlet than close to the vent. However, as local pressure will increase, air bubbles will collapse according to the perfect gas law. This collapsing would be more important close to the inlet where local pressure is higher, thus inversing the saturation profile

<figure><img src="image_6.png" /><figcaption>Fig. 5. Initial volume of entrapped air for a 500 cm³/min injection flow rate.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Fig. 6. Voids content versus modified capillary number (Eq. (15)).</figcaption></figure>

along the radial direction. The profile thus agrees with Fig. 6 which gives a general representation of voids content versus modified capillary number, Ca*, defined as

$$Ca^* = \frac{\mu u_s}{\gamma \cos(\theta)} \qquad (17)$$

where μ is the fluid viscosity, u_s the average fluid velocity, γ the surface tension and θ the contact angle between fluid and fiber. The optimal capillary number at which void content is minimal was studied in previous work [1,23]. Microvoids content is higher for a higher injection velocity. During a radial injection, velocity decreases with the radius, a void content gradient thus appears along the radial direction. In a previous experimental study [24], saturation on the S13500 fabric was studied. This fabric is unbalanced, and experimental measurement showed that air was entrapped only when the flow front direction was aligned with the warp fiber tows, leading to the conclusion that only weft fiber tows contributed to air entrapment. In a radial experiment, air entrapment is also expected to occur preferably only in the directions where the flow is perpendicular to weft fiber tows. There thus should exist a

limit angle β for the flow direction for which air entrapment process is possible. It is thus necessary to account for the angle α formed between the weft tow axis and the normal to the flow front. The limit angle β is then defined such that the volume of trapped air is maximum if

$$\frac{\pi}{2} - \beta \le \alpha \le \frac{\pi}{2} + \beta \qquad (18)$$

In the other cases no air would be trapped. The angles definition is also presented in Fig. 7. Fig. 8 represents the map of the voids created when a angle β of 20° is chosen.

In addition when a critical pressure is reached, air bubbles are expelled out of the preform. Thus fiber volume fraction is set to the original fiber tow volume fraction and the fill factor is updated for mass conservation purposes. The value of the critical pressure was defined experimentally [24].

## 4. Results and discussion

Radial injection experiments where conducted at a constant flow rate of 500 cm³/min. The analysis is conducted by comparing the pressure transducers response with numerical pressure profiles. The pressure level obtained for all pressure transducers for any entrapment angle β are similar and reproduce faithfully the experimental pressure measured, except for the case β 45°. For instance, pressure response of the pressure transducer P2weft is reported along with the numerical pressures calculated for entrapment angles comprised between 10° and 45° in Fig. 9. The injection filling time t_inj reported on the figure represents the time at which resin flows out of the preform along the most permeable direction, so along the warp direction. As injection is not complete at t_inj, pressure still increases until the total impregnation of the preform. For the cases β 10°, 20° and 30°, the pressure profiles and the response time agree with the corresponding experimental profile of the pressure transducers. For the case β 45°,

<figure><img src="image_8.png" /><figcaption>Fig. 7. Angles definition.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Fig. 8. Initial volume of entrapped air for a 500 cm³/min injection flow rate taking into account the angle of entrapment $\beta$.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 9. Experimental and numerical pressure profiles for the P2weft pressure transducer calculated with different entrapment angles.</figcaption></figure>

the pressure level and the triggered time calculated are far from the pressure profiles obtained experimentally. It is not clear why the numerical pressure response for angle 45° greatly defers from the other entrapment angles evaluated.

Those comments are also valid on the pressure profiles for each pressure transducers placed along the weft direction. If we only consider angles 10-30°, it cannot be directly inferred from Fig. 9 that angle $\beta$ has an influence on the
pressure profile. However, one should consider the fiber volume content $V_{ftrans}$ that can contribute to air entrapment and that is evaluated as being

$$V_{insat} = V_{ftrans} \frac{\theta}{90} \qquad (19)$$

where $V_{insat}$ is the unsaturated volume. In a previous study [1], it was shown that the air entrapped volume in the preform considered is around 6.4%. An unsaturated volume of 6.4% is obtained for $\beta$ 10. As only a small part of the preform can generate microvoids, pressure profiles do not seem to be accurate enough to detect void creation or elimination. In order to validate this statement, injection simulations were performed without the saturation module. The resulting pressure profiles are reported in Fig. 10 along with the pressure profiles obtained experimentally and from simulations with the saturation module (with angle $\beta$ 10°).

Pressure profiles from the simulation with or without saturation module are quite similar. Thus pressure profiles

are not relevant to monitor saturation evolution during a radial injection. However, delays are observed between the impregnation times obtained experimentally and from the simulation, especially for the sensors P2 and P3 placed at 80 and 120 mm form the resin inlet. For illustration, experimental and numerical P3weft transducer responses are reported in Fig. 11. A different impregnation time is evident, while pressures reach the same level after a few seconds. There is a delay between the pressure transducers trigger times between each numerical curve. An impregnation time thus potentially presents a better parameter to account for saturation during a radial injection, providing the use of thin and highly sensitive sensors to capture the exact resin arrival time.

Saturation profiles obtained numerically are presented in Fig. 12 for different $\beta$ angle. Close to the inlet, preform is completely saturated, as pressure is more important at the inlet than at the periphery where atmospheric pressures is applied. In the area comprised between angles $\beta$ and $-\beta$,

<figure><img src="image_11.png" /><figcaption>Fig. 10. Experimental and numerical pressure transducers responses.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 11. Experimental and numerical pressure P3weft transducers responses.</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>Fig. 12. Numerical saturation for a 500 cm³/min injection flow rate according to the entrapment angle $β$.</figcaption></figure>

the saturation level is close to 85%, whereas in the rest of the domain a full saturation is observed. The saturation decreases when distance from inlet increases, which is an opposite behaviour compared to the initial voids profiles shown on Figs. 5 and 8. This trend is due to the pressure profiles, as pressure decreases with the radius, air bubbles are more compressed close to the inlet than at the mold periphery, so air volume is more important far from the injection inlet.

void content was created. Although good correlation between experimental and numerical pressure profiles was obtained, no direct relationship between pressure level and the void content could be identified. The pressure transducer triggered time could be an investigation path to help void prediction for radial injection schemes. Further investigation should also be conducted in the determination of the fiber tow angle with the flow front that governs the entrapment occurrence.

## 5. Conclusion

This study proposed a method to adapt the numerical prediction of void content from the unidirectional case to the bidirectional case by assuming that the angle formed between the flow front direction and the transverse tows of the preform is a determinant parameter to define the zones where voids would be generated. As for the unidirectional case, void content due to the dual scale porosity of the preform is lower close to the injection inlet than at the end of the mold. The void content is thus directly linked to the pressure level reached during the injection.

As pressure governs the void generation during preform filling, a numerical code that would link pressure profiles to

## References

[1] Gourichon B, Binetruy C, Krawczak P. A new numerical procedure to predict dynamic void content in liquid composite molding. Composites Part A 2006;37(11):1961 9.

[2] Chan AW, Morgan RJ. Tow impregnation during resin transfer molding of bi directional nonwoven fabrics. Polym Compos 1993;14(4):335 40.

[3] Binetruy C, Hilaire B, Pabiot J. Tow impregnation model and void formation mechanisms during RTM. J Compos Mater 1998;32(3): 223 45.

[4] Parnas RS, Salem AJ, Sadiq TAK, Hsin Peng Wang, Advani SG. The interaction between micro and macro scopic flow in RTM preforms. Compos Struct 1994;27(1 2):93 107.

[5] Markicevic B, Papathanasiou TD. The hydraulic permeability of dual porosity fibrous media. J Reinf Plast Compos 2001;20(10):871 80.
[6] Jinlian H, Yi L, Xueming S. Study on void formation in multi layer woven fabrics. Compos Part A: Appl Sci Manufact 2004;35(5): 595 6037.

[7] Spaid MAA, Phelan Jr FR. Modeling of void formation dynamics in fibrous porous media using the Lattice Boltzmann method. Composites Part A 1998;29:749 55.

[8] Parseval YD, Pillai KM, Advani SG. A simple model for the variation of permeability due to partial saturation in dual scale porous media. Transport Porous Med 1997;27:243 64.

[9] Zhou F, Kuentzer N, Simacek P, Advani SG, Walsh S. Analytic characterization of the permeability of dual scale fibrous porous media. Compos Sci Technol 2006;66(15):2795 803.

[10] Kuentzer N, Simacek P, Advani SG, Walsh S. Permeability characterization of dual scale fibrous porous media. Compos Part A, Appl Sci Manufact 2006;37(11):2057 68.

[11] Breard J, Saouab A, Bouquet G. Numerical simulation of void formation in liquid composite molding. Composites Part A 2003;34: 517 23.

[12] Labat L, Grisel H, Breard J, Bouquet G. Original use of the electrical conductivity for voids detection during injection of composite materials. CR Acad Sci II B Mec 2001;329(7):529 34.

[13] Slade J, Pillai KM, Advani SG. Investigation of unsaturated flow in woven, braided and stitched fiber mats during mold filling in resin transfer molding. Polym Compos 2001;22(4):491 505.

[14] Roy T, Pillai KM. Characterization of dual scale fiber mats for unsaturated flow in liquid composite molding. Polym Compos 2005;26(6):756 69.

[15] Lundstrom ST. Measurement of void collapse during resin transfer moulding. Composites Part A 1997;28:201 14.

[16] Lundstrom ST, Gebart BR, Lundemo CY. Void formation in RTM. J Reinf Plast Compos 1993;12:1339 49.

[17] Simacek P, Advani SG. A numerical model to predict fiber tow saturation during liquid composite molding. Compos Sci Technol 2003;63:1725 36.

[18] Patel N, Rohatgi V, Lee LJ. Microscale flow behavior and void formation mechanism during impregnation through a unidirectional stitched fiberglass mat. Polym Eng Sci 1995;35(10):837 51.

[19] Patel N, Lee LJ. Effect of fiber mat architecture on void formation and removal in liquid composite molding. Polym Compos 1995;16(5): 386 99.

[20] Patel N, Rohatgi V, Lee LJ. Macro and microvoid formation in liquid composite molding. In: 9th ASM/ESD advanced composites conference, Dearborn, MI, USA; 1993. p. 81 98.

[21] Rohatgi V, Patel N, Lee LJ. Experimental investigation of flow induced microvoids during impregnation of unidirectional stitched fiber mat. Polym Compos 1996;17(2):161 70.

[22] Kang K, Koelling K. Void transport in resin transfer molding. Polym Compos 2004;25(4):417 32.

[23] Ruiz E, Achim V, Soukane S, Trochu F, Bréard J. Optimization of injection flow rate to minimize micro/macro voids formation in resin transfer molded composites. Compos Sci Technol 2006;66(3 4): 475 86.

[24] Gourichon B, Binetruy C, Krawczak P. Experimental investigation of high fiber tow count fabric unsaturation during resin transfer molding. Compos Sci Technol 2006;66(7 8):976 98225.

[25] Foley M, Gillespie J. Modeling the effect of fiber diameter and fiber bundle count on tow impregnation during liquid molding processes. J Compos Mater 2005;39:1045 65.