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to account for the changes in the flow velocity over time. Lebel et al. ( LeBel et al., 2019 ) defined a critical capillary number that is required to mobilize a void. In a similar vein, Matsuzaki et al. ( Matsuzaki et al., 2015 ) developed an analytical expression to predict the void formation in anisotropic woven fabrics by decoupling the flow in different domains (meso-flow, transverse and axial micro-flow) and defining criteria for void formation depending on the relation between the required times to fill each domain.
Determination of Caopt or its modified counterpart (Ca*opt), as well as the other non-dimensional numbers discussed so far heavily relies on experimental studies with limitations that will be highlighted in the next section, as the current state of research is still far from linking the process conditions and geometrical descriptions of arbitrary matrix/fabric systems to a Caopt without requiring laborious experiments. Despite the efforts towards achieving flow simulation with ever increasing accuracy and fidelity, the complexity of the underlying physics and the need to account for those at several length scales hinders the developments in the field. The following sections will provide an overview of current developments in the experimental approaches for characterizing the extent of capillary effects in composite manufacturing and their link with residual porosity. Conventional approaches such as post-mortem analysis of composites will be followed by a survey of more advanced methods suitable for translucent reinforcements, mostly glass fibers, and recent developments in experimental approaches to study the capillary phenomena in other types of reinforcements, including but not limited to carbon fibers and natural fibers. Subsequent sections will then present the modeling efforts starting from microscale models to multiscale models that are inspired from the soil science literature to dual-scale models implemented using different numerical solvers and to semi-analytical approaches proposed to overcome the limitations of Ca-based residual void prediction.
3 Observation of Capillary Effects
3.1 Capillary Wicking
Capillary pressure can be characterized in capillary wicking experiments, allowing for direct quantification from a single experiment. Amico and Lekakou ( Amico and Lekakou, 2002 ) proposed a methodology where a fiber bundle, or a single ply of fibrous reinforcement ( Caglar et al., 2019 ), is partially immersed into a probe liquid, where the capillary pressure was directly derived from the rate of weight gain or height increase. Pucci et al. ( Pucci et al., 2015b ) proposed a tensiometric method, based on Washburn’s method ( Washburn, 1921 ), to characterize capillary wicking of water and n-hexane in stacks of carbon fibrous preforms. By varying the orientation of the fibrous preforms they were able to determine the advancing contact angles in three, i.e., weft, warp and through-thickness, directions, from which equivalent capillary pressures were derived. With coefficients of variation in the order of 30% this methodology is expected to be less accurate than that proposed by Amico and Lekakou ( Amico and Lekakou, 2002 ) but the possibility to characterize fabric stacks and potentially vary fiber volume fractions makes it a very suitable method to apply in the context of LCM processing. It should be noted that capillary pressures measured in capillary wicking tests are not directly representative of those acting in LCM processes as the typical fluid velocities (hence Ca) encountered in these processes are not reached, in contrast to, e.g., direct flow experiments under a given applied pressure or flow rate ( Salvatori et al., 2018 ). Nonetheless, capillary wicking experiments can be a valuable tool to obtain a first indication of capillary pressure in fibrous reinforcements, and to test changes in fiber surface conditions, volume fraction or pore morphology.
3.2 Post-Mortem Analysis
Post-mortem analysis on produced composite parts was the first and a facile method to observe and quantify the role of capillary effects. Post-mortem methods almost uniquely quantify capillary effects via the void content present after final consolidation of the composite, while varying process parameters ( Lundström et al., 1993 ; Lundström and Gebart, 1994 ; Patel and Lee, 1995 ; Patel and Lee, 1996 ; Labat et al., 2001a ; Leclerc and Ruiz, 2008 ) such as the flow rate or injection pressure and thereby the impregnation velocity. It is important to note that for impregnation under constant applied pressure, the velocity of the flow front decreases with the impregnation length. The presence of an optimum Ca ( Patel and Lee, 1995 ; Patel and Lee, 1996 ; Labat et al., 2001a ; Leclerc and Ruiz, 2008 ), where minimum void content is present within the composite, was often reported, while similar consequential observations were made for the resulting tensile modulus and tensile strength ( Leclerc and Ruiz, 2008 ). While bringing the advantage of being an easy method with low equipment costs, post-mortem analysis of capillary effects could lead to large inaccuracies. These arise partially from the methods used for void content analysis such as, in order of increasing accuracy ( Little et al., 2012 ), Archimedes ( Kedari et al., 2011 ), microscopy ( Lundström et al., 1993 ; Lundström and Gebart, 1994 ; Kedari et al., 2011 ) and micro-CT ( Madra et al., 2014 ; Sisodia et al., 2016 ) methods, while part void content is also affected by phenomena occurring after passing of the flow front, e.g., void transport and dissolution into the resin. In spite of the strong assumption that part saturation in a chosen location does not change after passing of the flow front and during the cure/solidification process, these analyses have nonetheless been crucial to highlight the strong influence of capillary effects on part void content, as illustrated in Figure 2 .
3.3 In-situ Analysis
An a priori more accurate method to analyze capillary effects taking place at the flow front is to observe, in-situ, the flow front progression and morphology, either very locally at the scale of a few fiber tows, or through the macroscopic analysis of the progressive saturation of the porous medium with the flowing fluid. These analyses usually refer to a saturation term, S, which is defined as the ratio of the volume fraction of liquid over the available pore space and is equal to 1 when the porous medium is fully filled with the liquid phase.
3.3.1 Transparent Fiber Reinforced Polymers
In-situ measurements allow for direct observations of capillary effects taking place in polymer composite processing. Optical methods can record impregnating resins in fibrous preforms in a non-intrusive manner and at a high spatial and time resolution with simple equipment, making it an effective and low-cost method for flow characterization ( LeBel et al., 2019 ). Optical imaging is generally limited to translucent fabrics and relies on the matching of refractive indices to distinct phases ( Lawrence et al., 2009 ; Nordlund and Michaud, 2012 ; LeBel et al., 2019 ), i.e., refractive indices of epoxy/fiberglass can be very different from that of the air/fiberglass interface and the distinction between the two interfaces can be further enhanced by colorants compatible with the test fluid ( Caglar et al., 2018 ; Salvatori et al., 2018 ). Recording a linear flow with a conventional camera and subsequent image analysis has allowed Nordlund and Michaud ( Nordlund and Michaud, 2012 ) and Facciotto et al. ( Facciotto et al., 2021 ) to estimate the width of the unsaturated region, which was subsequently modelled with finite difference ( Nordlund and Michaud, 2012 ) and finite element models ( Facciotto et al., 2021 ). Continuous imaging of these regions showed the progressive saturation of the preform, which was quantified from the pixel intensity in the successive pictures. Standard camera imaging however only captures the flow at the surfaces of the mold (in general a glass top surface), which are known to be vulnerable to wall-effects, i.e., race-tracking between the preform and the mold halves, while effects such as nesting are also not well captured ( Chen and Chou, 2000 ; Yousaf et al., 2017 ).
Visible Light Transmission (VLT), illustrated in Figure 3A , has been proposed as an elegant method to overcome this limitation ( Lawrence et al., 2009 ). Placement of a diffuse light source below the transparent mold halves and of a camera above it makes the recorded light intensity an average over the preform thickness. Moreover, the signal is also significantly intensified. Lebel et al. ( LeBel et al., 2017 ; LeBel et al., 2019 ) employed VLT to characterize the relation between processing conditions, i.e., Ca*, and saturation of a glass fabric. The increased light intensity allowed them to accurately estimate the local void content after calibration with burn-off composites after consolidation. Distinction of voids allowed them to estimate the optimum Ca* as well as the onset of pressure-induced void mobility. Further contrast enhancement could be achieved by the addition of fluorophores into the probe liquid. This resulted in strong contrast enhancement, e.g., for visualization of intratow flow ( Lebel et al., 2013 ; LeBel et al., 2014 ), even enabling the use of optical methods in opaque carbon fibrous preforms ( Lystrup et al., 2021 ). The addition of dyes may however induce changes in resin properties, e.g., wettability, and thereby may affect the apparent Ca or Ca*, making the resulting observations not directly representative of pure resin systems.
FIGURE 3
FIGURE 3. Demonstrations of optical methods for flow characterization at different scales, with increasing resolution: (A) Visible Light Transmission on centimetre-scale (Source: ( LeBel et al., 2017 )), (B) UV-flow freezing on millimetre-scale (Source: ( Caglar et al., 2019 )), (C) Microscope imaging on micron-scale (Source: ( Yoshihara et al., 2020 )).
Increases in spatial resolution and observations on tow-scale could be achieved with the use of optical microscopy imaging. This increased resolution, however, comes at the cost of the overall field of view, making the method better suited for local detection of voids rather than for the assessment of saturation. Yoshihara et al. ( Yoshihara et al., 2020 ) investigated the role of capillary pressure, varied by the application of different fluorine coatings on the fiber surface, on the dual-scale flow behavior in an optical microscopy setup. This allowed them to observe infusion of a woven fabric on a micron-scale, shown in Figure 3C , which were coupled to numerical simulations. Zhao et al. ( Zhao et al., 2019 ) and Matsuzaki et al. ( Matsuzaki et al., 2014 ) followed a similar approach in their studies on void formation and were able to accurately record capillary fingering and void formation upon the impregnation of a woven preform at a range of velocities falling in the capillary-dominated regime. This allowed them to accurately capture the void formation and evolution with the use of in-situ optical microscopy. However, flow analysis by means of optical microscopy can typically be applied to single ply fibrous reinforcements if based on light diffusion and suffers from the aforementioned wall effects in reflectance mode, while the upper limit of allowed infusion rates is defined by the maximum imaging rate of the microscope. Caglar et al. ( Caglar et al., 2019 ) proposed an in-situ UV flow-freezing method ( Figure 3B ), where infiltrating flows are in-situ cured by UV-photopolymerization. This overcomes any constraints in time resolution allowing for visualization of a large range of flow regimes. This method however requires the use of specially designed resin systems and rather thin and transparent samples to avoid inhibiting the cure reaction that is highly dependent on the penetration of UV light.
3.3.2 Non-Transparent Fiber Reinforced Polymers
The opaque nature of many commercially available fibers in polymer composites, e.g., carbon or flax, limits the optical observations of capillary effects in processing to the outer layers, which are susceptible to wall effects as discussed in Section 3.3.1. A multitude of methods have been proposed to overcome this limitation, ranging from methods already widely established in other fields, e.g., Magnetic Resonance Imaging (MRI), to more exploratory techniques such as infrared thermography. With no universal agreement on the preferred technique to elucidate the degree of fluid saturation as a function of time and position, each specific method brings its own advantages and trade-offs between spatial resolution, recording speed and ease of implementation.
One of the proposed methods to track resin front progression and thereby indirectly record progressive saturation and void formation in LCM processing is the inclusion of sensors in or in-between stacked preforms ( Konstantopoulos et al., 2014 ). Methods using conductive sensors typically require a non-conductive fibrous preform to be placed in between two conductive parallel plates. Labat et al. ( Labat et al., 2001b ) and later Gueroult et al. ( Gueroult et al., 2014 ) infused a glass fiber preform with a conductive liquid and simultaneously recorded the voltage over the preform, which increased with increasing saturation. The first strong increase of the voltage was attributed to the passing of the unsaturated flow front followed by a period of void removal, while the final voltage was directly linked to the saturation and hence the void content in the part. The recorded void contents moreover followed the expected “V-shaped” curve as a function of Ca*. Carlone et al. ( Carlone and Palazzo, 2015 ; Carlone et al., 2018 ) employed a similar experimental methodology while recording the capacitance over the fabric preforms and correlated the observations to numerical models. This methodology also allowed for impregnation with less conductive resins. Similar saturation curves were obtained and verified in comparison with the void contents in post-mortem optical microscopy images. They moreover compared the accuracy of progressive saturation tracking by dielectric sensors with that recorded by pressure sensors, e.g., as proposed by Refs. ( Di Fratta et al., 2013 ; Chiu et al., 2018 ), which was found to be significantly higher. The requirement for a non-conductive fibrous preform limits the use of the methods developed by Refs ( Labat et al., 2001b ; Gueroult et al., 2014 ; Carlone and Palazzo, 2015 ; Carlone et al., 2018 ). with several conventional fabric types. Developments have been made to overcome this issue, e.g., by insulating the sensor with a dielectric material and optimization of the sensor characteristics ( Pouchias et al., 2019 ; Caglar et al., 2021a ). However, these types of sensors have not yet been employed to study unsaturated flow phenomena to-date. Alternatively, Villière et al. ( Villière et al., 2015 ) proposed a method based on the saturation-dependence of the thermal behavior of a resin-fiber system. Recording of heat fluxes induced by an electric heater was found to give an accurate representation of the local saturation, which were coupled with mathematical models to fit progressive saturation curves. Implementation of optical micro-flow sensors within tows on the other hand gives the possibility to record capillary pressures, as was demonstrated by He et al. ( He et al., 2019 ) in their study on resin flow in prepreg processing. However, introducing thermal gradients in the fluid induces changes in the viscosity and surface tension characteristics and requires elaborated material characterization next to the experimental analyses.
The discrete nature of sensors limits the observations that can be made in a single impregnation while the spatial resolution of methods making use of integrated sensors is relatively low. Imaging techniques typically possess higher spatial resolution over a larger section of the composite part. Ultrasound techniques are known for their high acquisition rates and have been used to track resin flow in fibrous preforms ( Schmachtenberg et al., 2005 ), in particular for through-thickness resin infusion ( Stöven et al., 2003 ; Thomas et al., 2008 ; Konstantopoulos et al., 2018 ). Thomas et al. ( Thomas et al., 2008 ) tracked through-thickness resin flow via acoustic C-scan measurements giving a planar view of the sample. While this method gives an indication of through-thickness saturation of the preform, the limited spatial resolution does not allow for distinction of capillary effects such as localized saturation and void formation. Unsaturated permeability on the other hand was successfully characterized with use of ultrasound, given a microstructure-dependent minimum fiber content is present within the preform ( Konstantopoulos et al., 2018 ).
Magnetic Resonance Imaging (MRI) ( Callaghan, 1993 ) has been investigated as well to observe flow in porous media. While suffering from drawbacks such as large tooling costs and spatial resolutions that are limited to around 0.1 mm due to signal relaxation effects ( Endruweit et al., 2011 ), MRI brings the advantage of an excellent material contrast between constituents of composites, i.e., fibers, polymer and voids, which could be further enhanced by the addition of contrasting agents or by specified measurement sequences ( Neacsu et al., 2007 ). MRI has therefore been used for the characterization of flow in fibrous preforms ( Mantle et al., 2001 ; Bijeljic et al., 2004 ; Bencsik et al., 2008 ), with several studies specifically focused on visualizing dual-scale flow behavior. Leisen and Beckham ( Leisen and Beckham, 2008 ) proposed a method of nuclear MRI and subsequent image analysis to quantify inter-yarn voids and their morphologies in saturated woven nylon fabrics, while Neacsu et al. ( Neacsu et al., 2007 ) applied MRI to characterize capillary effects in glass fiber bundles. In the latter case they found fast MRI imaging able to track progressive transversal impregnation within bundles with different volume fractions and were able to use this data to back calculate the driving capillary pressures. Endruweit et al. ( Endruweit et al., 2011 ) carried out an extensive investigation regarding the use of MRI to in-situ image the impregnation of dual-scale textiles. Reconstructed 3D images had resolutions of 0.5 mm, visualizing the meso-structure of fibrous preforms. An intermittent injection strategy was used to overcome time resolution limitations, which allowed for imaging of various flow regimes. Resulting images clearly visualized the progressing flow front and the formation of inter-yarn voids, while progressive saturation was tracked by a gradual increase of relative signal intensities.
Intrinsic differences in X-ray absorption coefficients of composite constituents gave rise to a multitude of X-ray-based techniques that were applied to study in-situ the role of capillary effects in LCM processing. Bréard et al. ( Bréard et al., 1999 ) continuously tracked through-thickness impregnation of a random mat stack using X-ray radiography. While image resolution was insufficient to capture the fibrous preform, fast imaging allowed for accurate tracking of the infiltrating fluids. Teixidó et al. ( Teixidó et al., 2021 ) used an X-ray phase contrast method in-operando to assess saturation of several types of fibrous preforms. Based on the material-sensitive phase modulation due to interference formed after passing X-rays through a grating, the material contrast, which can be a limiting factor for composites, is significantly enhanced ( Gresil et al., 2017 ). Employing this method allowed them to image progressive saturation of 15 cm × 5 cm non-transparent fabrics over a range of capillary numbers and they were able to extract the thickness-averaged saturation curves from these images, with a time step below 10 s.
The use of X-ray micro computed tomography (μCT) has allowed for the observation of dual-scale flow at an unprecedented resolution. Based on the reconstruction of 3D images from a set of radial X-ray radiographs, X-ray μCT provides the ability to reconstruct through-thickness images of opaque materials ( Withers et al., 2021 ). Features down to sub-μm can be reached, e.g., allowing for accurate imaging of carbon composites and of the void morphology, while image resolutions typically come at a cost of the volume that can be analyzed, and the measurement speed. 4D μCT imaging (3D in space and time), e.g., to study the dual-scale flow behavior, is moreover typically complicated by possible blurring effects occurring, reducing image resolution due to movement of the flow front ( Castro et al., 2021 ). To avoid this, the acquisition time should be short enough to limit the movement to less than 1 voxel per scan ( Castro et al., 2021 ). While some studies have thus aimed at indirect observations of dual-scale flow behavior, e.g., by assessing thickness changes ( Hemmer et al., 2018 ) or image-based computational fluid dynamics simulations ( Ali et al., 2019 ), several investigations aimed at in-situ imaging dual-scale flow behavior through a fibrous preform. Vilà et al. ( Vilà et al., 2015 ) were the first to use μCT to study the intra-tow infiltration of a glass fiber bundle in a μCT synchrotron beamline. Infusion was carried out under a capillary-dominated regime and was halted to image the flow front. Images were reconstructed from 900 radiographs taken over a period of 120 min with a voxel size of 2.5 μm3. At a slightly reduced resolution, Larson et al. ( Larson and Zok, 2018 ; Larson et al., 2019 ) were able to drastically reduce the imaging time, i.e., to 1.5 min, which allowed them to in-situ record impregnation of an enclosed fiber bundle with capillary numbers up to 10−3. They furthermore employed advanced segmentation methods to distinguish local saturated and dry sections. Vilà et al. ( Vilà et al., 2015 ) and Larson et al. ( Larson and Zok, 2018 ; Larson et al., 2019 ) were both able to observe progressive saturation of the fiber bundle and were able to relate this to local capillary pressures and permeabilities, while the more homogeneous fiber distributions of Larson et al. ( Larson and Zok, 2018 ; Larson et al., 2019 ) resulted in more homogeneous distributions and magnitudes. They were moreover able to gain insight in the apparent dynamic contact angles and to relate this to fiber displacement. Static contact angles after capillary wicking of a fiber bundle was studied in more detail by Castro et al. ( Castro et al., 2020 ), who employed synchrotron-μCT to produce high resolution images. Image analysis then allowed for an assessment of axial and transverse contact angles.
The resolution requirement to obtain an accurate representation of (carbon) composites with a conventional μCT setup limits the sample size significantly. Castro et al. ( Castro et al., 2021 ) overcame this limitation by making use of so-called synchrotron radiation computed laminography, where significant gains in field of view can be achieved by imaging planar samples at an angle ( Helfen et al., 2011 ; Bull et al., 2013 ; Fisher et al., 2019 ). In combination with a fast acquisition rate, i.e., 1.8 min per tomogram, they were the first to in-situ image dual-scale flow behavior in woven textiles with micron-scale resolution. Equilibrated flow regimes ( Figure 4A ) were imaged and, although slightly affected by blurring due to movement of the flow front, the images clearly showed the microstructural evolution upon impregnation and the absence of void formation. Slower infusion rates in capillary-dominated regimes ( Figure 4B ) minimized the blurring effect, giving a highly detailed insight on progressive saturation and void formation upon impregnation. Moreover, they were able to segment and analyze both inter- and intra-yarn void distributions as well as gaining novel insights in the void formation mechanisms during LCM.
FIGURE 4
FIGURE 4. Progressive saturation recorded by synchrotron radiation computed laminography of (A) Equilibrated and (B) Capillary dominated flow regimes (Source: ( Castro et al., 2021 )).
3.4 The Case of Natural Fiber Reinforced Polymers
Composites made of natural fibers, in general plant-based, are gaining interest for the development of more sustainable and eco-friendly composite materials. Natural fiber reinforced composites still present a large amount of porosity and processing defects mainly due an incomplete understanding of the role of the initial humidity level in the fibers, surface characteristics, depending on the fiber treatment such as alkali treatments, and their complex morphology (illustrated in Figure 5 ). Compared to synthetic fibers, plant based fibers are also known to suffer from extensive resin absorption and swelling due to their microstructure, which highly alter flow characteristics ( Francucci et al., 2010 ; Pucci et al., 2017b ; Garat et al., 2020 ; Salokhe et al., 2021 ). Moreover, they present irregular and complex morphological and surface properties. Fibers are built-up from elementary cells with a given length and an irregular cross-section, and are composed of a hierarchical sequence of wall layers of different composition and thicknesses around an internal closed cavity called the lumen ( Pantaloni et al., 2021 ). Depending on the extraction conditions, fibers can be present in the fabric as elementary fibers with diameters around 20–40 µm or technical fibers (several elementary fibers bonded together with the middle lamella which acts as matrix) with larger variable sizes in the order of some hundred micrometers ( Melelli et al., 2020 ). The fiber surface roughness together with the composition of lignin, cellulose and hemi-cellulose of the outer layer define the wetting properties of the natural fiber. Given the complexity of the porous network and surface properties of natural reinforcements, the understanding of infiltration and in particular of capillary effects has remained as a very complex issue to-date.
FIGURE 5
FIGURE 5. Structure of natural fibers: Schematic representations of (A) technical (fiber bundle from the stem) and (B) elementary fiber, (C) optical microscopy image of technical and elementary fibers in a composite and (D) optical microscopy image of an elementary fiber surface.
Dual-scale flow behavior and void formation mechanisms in LCM processes have also been observed in the case of natural fiber preforms ( Pantaloni et al., 2020 ), and have received increasing attention over the past decade. Francucci et al. ( Francucci et al., 2010 ) found that natural fibers exhibit capillary pressures that are two or three times higher compared to synthetic fibers, elucidating the relevance of micro-flows and capillary effects occurring during impregnation. Some authors attributed this to the hollow structure of the fibers ( Francucci et al., 2010 ; Yin et al., 2018 ) however recent studies have shown limited evidence that the resin can impregnate the lumen since it is a closed cavity ( Pantaloni et al., 2020 ). Due to the polar nature of the fibers, the model fluid chosen to carry impregnation measurements highly influences the study of capillary effects. For example, Francucci et al. ( Francucci et al., 2010 ) carried out unidirectional impregnation experiments of woven jute fabrics with a water/glycerin solution and a vinylester resin. They measured the capillary pressure and obtained -25 and 36 kPa with the water-based solution and the resin respectively.
As already said, natural fibers are sensitive to liquid absorption. In consequence, during infiltration, fibers remove liquid from the main stream of infiltrating resin, acting as a sink component, decreasing the velocity of the flow as the fiber cross-section tends to enlarge due to liquid absorption and reduction in permeability during impregnation ( Francucci et al., 2010 ; Testoni et al., 2018 ). Testoni et al. ( Testoni et al., 2018 ) showed in capillary wicking tests that the swelling of the fibers leads to a reduction of the inter-fiber pores and thus an increase of the capillary pressure. With the aim of predicting and modeling the relation between capillarity and swelling in natural fibers, researchers used a similar approach based on physical wicking experiments coupled to modified Washburn’s equations ( Pucci et al., 2015a , 2016 ; Testoni et al., 2018 ; Vo et al., 2020 ). In wicking tests, synthetic fibers show a linear trend following Washburn’s equation whereas a non-linear trend is usually observed for natural fibers due to swelling. Pucci et al. ( Pucci et al., 2016 ) proposed a modified Washburn’s equation, taking into account the change in the porosity due to swelling over time. They assumed a capillary radius decreasing linearly with time, from the initial to the final swollen values, when wicking the fabrics in water. More recently, Vo et al. ( Vo et al., 2020 ) improved their numerical model by defining a dual scale porosity (dual scale capillary radius) of the flax fibers since wicking takes place in between individual yarns and in between elementary fibers. Swelling induced changes in the pore distribution and the effects on the capillary action more complex at high fiber volume fraction (Vf). The proposed method successfully predicted swelling of a flax fabric in water for Vf ranging from 30 to 60%. As recently reviewed by Pantaloni ( Pantaloni et al., 2020 ), flow modelling taking into account both swelling and fluid absorption by the natural fibers could be carried out by modifying the continuity equation accordingly, allowing for changes in both saturation (through a sink term) and porosity over time.
3.5 Role of Sizing and Additional Phases in the Textile Preform
3.5.1 Role of the Fiber Surface Treatment
Commercial fibrous preforms are coated with sizings that form an interphase region between fibers and polymer ( Thomason, 2021 ). Sizings are generally functionalized for compatibility with specific monomer types. Alteration of the surface chemistry of the fiber affects its wettability and thereby the capillary pressures exerted on infiltrating resins, in particular during intra-yarn flow ( Palmese and Karbhari, 1995 ; Thomason, 2021 ). The wettability of commercial sizings is reported to vary strongly ( Bernet et al., 2000 ) due to differences in the sizing composition, e.g., resin-fiber interactions of glass fibers determining contact angles are sensitive to the silane types ( Wei et al., 1993 ; Araujo et al., 1995 ) and content present in the sizing ( Nishioka, 1990 ; Karbhari and Palmese, 1997 ). Hence, the sizing composition could potentially be employed to control local capillary pressures and thereby dual-scale flow in LCM processing, but the confidential nature of commercial sizing compositions has impeded further investigations into the role of sizing compositions on the (intra-yarn) flow behavior. Sharma et al. ( Sharma et al., 2009 ) observed that permeabilities of fibrous preforms, measured with silicon oil and Karo syrup as model fluid phases, are lower in the presence of a compatible sizing. In the absence of capillary effects, saturated permeability decreases due to the stronger resin-fiber interactions experienced by an infiltrating resin in the presence of a dedicated sizing. The decrease in capillary driven unsaturated flow was in agreement with the intra-yarn flow analysis as reported by Wang et al. ( Wang et al., 2006 ) or Palmese and Karbhari ( Palmese and Karbhari, 1995 ; Karbhari and Palmese, 1997 ) and was attributed to resin-fiber interactions to differences specific surface free energy ( Steenkamer et al., 1995 ; Karbhari and Palmese, 1997 ). Capillary pressures moreover are reported to be lower for dedicated sizings due to the consequent increase of the contact angle. It should be noted however that dynamic, advancing, contact angles and thereby capillary pressures are highly dependent on the imposed flow rates in LCM ( Karbhari and Palmese, 1997 ), which could potentially explain the decrease in capillary pressure in the presence of a dedicated sizing by increased induced wicking rates.
Surface treatments on sized fabrics have furthermore shown promise to control resin-fiber interactions in LCM processing. Physical treatments comprise electric discharge/plasma treatments, which are extensively employed in polymer composite production ( Mittal et al., 2018 ). Application of electric discharge treatments increases polarity of the fiber surface due to the suggested formation of additional carboxyl and hydroxyl groups ( Morent et al., 2008 ; Sinha and Panigrahi, 2009 ; Mittal et al., 2018 ). Caglar et al. ( Caglar et al., 2019 ) assessed the influence of these oxidative treatments on the impregnation of glass fiber textiles. They found that the increased polarity decreased the capillary pressure drop, which subsequently accelerated capillary wicking. Analysis of UV-frozen flow fronts showed that the optimum Ca shifted after applying the treatment while the unsaturated region in capillary-dominated flow counterintuitively became smaller. This latter was attributed to a more favorable transverse flow when treated, spreading out the flow front. Application of this surface treatment strongly accelerated impregnation in capillary-dominated regimes, i.e., up to 50%. Further control of surface properties could be achieved by the application of numerous chemical treatments ( Mittal et al., 2018 ). As an example, Yoshihara et al. ( Yoshihara et al., 2020 ) controlled the capillary pressure by the application of fluorine coatings on glass fiber textiles, which enhanced the capillary effects acting during resin infiltration.
3.5.2 Role of Additional Phases in the Textile Preform
In the search to expand the areas of use of polymer composites, strategies to introduce additional functions have been proposed. Functionalization by the presence of second phase particles in the polymer matrix could improve the overall mechanical, thermal and electrical performance of the resulting composite. Examples of second phases include capsules for self-healing behavior ( Kessler et al., 2003 ; Cohades et al., 2018 ), hollow microspheres to reduce the composite density ( Porfiri and Gupta, 2009 ; Zhang et al., 2016 ) and powders to tailor capillary effects in porous structures ( Kostornov et al., 2015 ). The introduction of these particles can however introduce complications in LCM processing. Filtration effects are commonly observed upon the infiltration of nanoparticles ( Reia Da Costa et al., 2012 ; Yum et al., 2016 ; Zhang et al., 2017 ), which can even occur at fiber volume fractions of ∼40% ( Louis et al., 2014 ). A study by Louis et al. ( Louis et al., 2019 ) showed that the filtration behavior of nanoparticles mainly depends on the particle size and the fiber volume fractions, while the nature, i.e., type of particle is also reported to have a large influence. The role of second phases on the capillary effects taking place in LCM processing is little understood. In their work on the processing of self-healing capsules, Manfredi and Michaud ( Manfredi and Michaud, 2014 ) observed bilinear infusion rates, where, after an initial phase, the unsaturated permeability of the preforms strongly increased compared to that when no capsules were present. This was attributed to increased capillary effects that drive the flow in the presence of capsules, but no correlation between the particle concentration and the in-plane permeability was found. Caglar et al. ( Caglar et al., 2017 ) tried to gain an improved understanding of these effects by a combination of in-plane permeability experiments and computational simulations. They confirmed that permeabilities increased in the presence of spherical glass; this was moreover found to depend on the bead diameter and the concentration in the composite. In a parallel study ( Caglar et al., 2016 ), they reported on the influence of particle size and volume fraction on the capillary effects. They concluded that relatively small particles (40–70 μm and 100–200 μm) at low volume fractions enhanced the capillary effects, whereas an increase in the volume fraction resulted in a more homogenous pore distribution which yielded more balanced flows. On the other hand, large particles (400–800 μm) caused extensive deformation of the fabric layers and formation of new large flow channels resulted in less pronounced capillary flow enhancement.
Hierarchical composites have shown promising enhancements in mechanical, thermal and electrical performance ( Thostenson et al., 2002 ; Yamamoto et al., 2009 ; Qian et al., 2010b ; Chou et al., 2010 ; Spitalsky et al., 2010 ) when nanometer-spaced CNTs are grafted onto the fiber surfaces. With capillary pressure being inversely proportional to the channel diameter, strong capillary action ( Futaba et al., 2006 ; Liu et al., 2006 ; Garcia et al., 2007 ) is induced in the presence of these nanoporous CNT forests. Garcia et al. ( Garcia et al., 2008 ) observed complete impregnation of their 80 nm-spaced CNT forests grafted on an alumina textile and suggested capillary effects to have contributed to this. Recent investigations by Staal et al. ( Staal et al., 2021 ) on the permeability of the same fabric supported this suggestion. Induced capillary action by the presence of grafted CNTs can further be observed by fast droplet spreading over the surface of a single fiber ( Qian et al., 2010a ). Alternatively, Lee et al. ( Lee et al., 2020 ) exploited the strong capillary actions induced by nanoporous networks of aligned CNTs for void-removal in Out-of-Autoclave (OoA) prepreg processing. Introduction of a nanoporous network between plies was estimated to increase the pressure gradient at the resin/void interface, i.e., the driving force for void removal, by 57% resulting in a void free composite, while a layup without these networks had a large void content. Moreover, resulting mechanical properties of the OoA-produced composites were like those achieved after conventional autoclave processing.
3.5.3 Capillary Effects in Thermoplastic LCM Processing
Influence of capillary effects in reactive thermoplastics and melt thermoplastics is strongly linked to their viscosity: for the reactive thermoplastics-based monomer ( Rijswijk et al., 2009 ; Han et al., 2020 ; Obande et al., 2021 ), it is typically in the same range as or even lower than the viscosity of thermosetting polymers used in LCM processes while melt thermoplastics have a few orders of magnitude higher viscosities ( Rijswijk et al., 2009 ; Salvatori et al., 2019 ; Han et al., 2020 ; Obande et al., 2021 ). In reactive systems, the capillary phenomena and their effects are similar to those found in thermosetting systems, but with enhanced capillary action resulting from the low viscosity of the fluid phase. For instance, Zingraff et al. ( Zingraff et al., 2005 ) experimentally studied the resin transfer molding of a woven fabric with the precursor of an anionically polymerized polyamide 12 and also found an optimum capillary number range (in the order of 10−3) where the void content was minimal. Similarly, Murray et al. ( Murray et al., 2020 ) studied the resin transfer molding of unidirectional stitched glass fabrics with the precursor of in-situ polymerized polyamide six and demonstrated the dominance of viscous flow within the bundles as well as the void formation within bundles due to lack of balance between capillary and viscous forces. Melt thermoplastic impregnation is gaining importance in recent years, however capillary effects so far have not been analyzed ( Studer et al., 2019 ; Gomez et al., 2021 ) as their impregnation is dominated by viscous forces due to the high-pressure differential and/or high viscosity of thermoplastic resins. Research is however ongoing to better capture the role of molecular weight and temperature in the wetting characteristics of polymers ( Duchemin et al., 2021 ).
3.5.4 Capillary Effects in Continuous Composite Manufacturing
Next to LCM processes where the flow lengths can reach up to meters, capillary effects manifest themselves also in continuous composite manufacturing. For instance, resin bath impregnation pultrusion ( Strauß et al., 2019 ; Vedernikov et al., 2020 ) is a common technique for manufacturing fiber reinforced profiles of varying cross-sectional complexity. Irfan et al. ( Irfan et al., 2017 , 2021 ) modified the resin bath where the rovings are impregnated before entering the mold where they are shaped into the final cross-sectional profile. They demonstrated that in their modified pultrusion process, capillary impregnation was dominant owing to pre-spreading the fibers before entering the resin bath and the extended fluid reservoir promoting the capillary actions under low pressures. Another continuous composite route is the manufacturing of fiber reinforced (typically unidirectional) thermoplastic tapes that are then used in secondary processes such as automated fiber placement, press forming or in autoclave processes. Melt impregnation is generally used for thermoplastic tape manufacturing, as well as powder impregnation. In all cases, as well as in commingled yarns where reinforcement fibers and polymer fibers are intimately mixed, impregnation takes place after the polymer has melt, and capillary effects may again play a role towards local impregnation of the fiber tows. This was for example exploited by Ho et al. ( Ho et al., 2011 ) for improving the quality of their wet powder impregnation approach, and by Bernet et al. ( Bernet et al., 1999 , 2001 ) for PA12/Carbon commingled yarns.
4 Numerical Modelling
Capillary effects play, despite the low magnitude of capillary pressures as compared to applied pressures, a significant role in LCM processing and, while mainly acting on a yarn-scale, largely influence the final part quality on a macroscopic scale. Capillary effects must thus be considered for the development of accurate numerical models that are used to describe and predict flow behavior in LCM. Several approaches have been proposed towards the development of flow simulations over the past decades, describing dual-scale flow behavior and the role of capillary effects at different scales. Most approaches base their estimation of the effects on direct or indirect experimental observation of flow front position, and saturation over time during an infiltration experiment, under no (apart from gravity) or applied external body forces.
4.1 Microscopic Scale Models
At the microscopic scale and under static conditions, the capillary pressure ΔPγ is described as the pressure jump across the air-fluid interfaces arising from the solid surface and interfacial tensions defined by the Young–Laplace equation as previously described in Section 2. In the case of fibrous reinforcements, Ahn et al. ( Ahn et al., 1991 ) and Pillai and Advani ( Pillai and Advani, 1996 ) proposed an analytical expression of the capillary pressure, which was often used in later studies ( Amico and Lekakou, 2000 , Amico and Lekakou, 2001 , Amico and Lekakou, 2002 ; Matsuzaki et al., 2015 ; Vilà et al., 2015 ; Willenbacher et al., 2019 ; Facciotto et al., 2021 ). They considered a tow, formed of several fibers with different spacing in size and thus with different capillary diameters impregnated with a unidirectional flow, and defined the capillary pressure as:
Δ