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Abstract

In this study, the dispersion of reclaimed carbon fibres following cost-effective surface treatment is explored with a hydrodynamic fibre moving model, and a practical fibre dispersion effect is investigated through various physical dispersion methods. To utilise reclaimed carbon fibres for a desired composite product, our proposed low-cost surface treatment is shown to be beneficial to the physical and chemical properties of the reclaimed carbon fibres and to yield polar-hydrophilic characteristics. Single fibre tensile testing is performed to explore the effect of surface treatment on the reclaimed carbon fibres (a higher tensile strength was observed). A computational hydrodynamic fibre moving model based on a moving particle semi-implicit method is newly designed to perform hydrodynamic simulation to determine aqueous dispersion of discontinuous reclaimed carbon fibres. This simulation helps understanding fibre flocculation phenomena from the perspective of fibre stiffness, which should not be disregarded for the fibre dispersion. Fibre surface analyses including morphology and functional groups are carried out to investigate the effect of surface treatment. The hydrodynamic simulation and proposed fibre dispersion methods with a cost-effective surface treatment approach can be widely applicable to any type of reclaimed carbon fibres to produce recycled fibre reinforced polymer composite materials.

Keywords

reclaimed carbon fibres surface analysis fibre dispersion moving particle semi-implicit method

Introduction

Fibre reinforced polymer (FRP) composites are made from at least two constituent materials that are combined into a multi-phase material offering high strength and stiffness-to-weight ratio, and which are therefore used in various structural applications.^1,2 FRP composites often consist of continuous or discontinuous carbon and glass fibres providing strength and stiffness to the composites, and synthetic organic or semi-organic matrices are mostly processed as thermoset or thermoplastic polymers to allow the composites to be set into the desired form.

Fibres, used as reinforcement, with thermoplastic composites have the potential to be more easily recycled and reprocessed than those of thermoset composites. Thermoplastic matrices are characterised as being re-melted and re-moulded with no degradation of the polymer chains, whereas thermoset matrices have a cross-linked structure that leads to irreversible and insoluble characteristics.³ As such, thermoplastic matrices have been reprocessed by separating fibres with a variety of processes by controlling heat and pressure due to the intrinsic thermoplastic characteristics such as high melting temperature, high consolidation pressure and high viscosity. In contrast, thermoset matrices are widely used for composite engineering applications due to higher interfacial adhesion to fibres than thermoplastic matrices. This is because interphase region of the thermoset composite forms strong chemical bonds between the fibre and the matrix, whereas in thermoplastic composites, the thermoplastic matrix shrinks around the fibre and weak van der Waals bonds are formed at the fibre surface.^4,5 When the fibres are reclaimed, the thermoset matrix is almost inevitably sacrificed, which is less attractive from the perspective of achieving a more sustainable product and promoting circularity.

The increase in use of FRP composites has led to a concomitant increase in waste production, and currently tonnes of end-of-life composites are disposed in landfill sites or incinerated. This is a critical issue for environmental and economic impact. Thus, the disposal process of composite wastes is more demanding than reproducing composites.^6–9 According to the Composites Leadership Forum UK, in April 2021, the UK government set out its target to reduce carbon levels to 78% of those of 1990 to achieve ‘Net Zero’ by 2050.¹⁰ To fulfil this aim, it is imperative that re-use or recycling technologies are now implemented to reduce the environmental impact associated with the FRP composites industry. Therefore, for the circular economy and zero carbon emission globally, recycling technologies for composites are now increasingly demanding as part of the energy-saving strategy.^11,12

When considering how FRP composites are to be recycled, the first step is to reclaim fibrous reinforcements by separating them from the polymer matrices without causing damage to the fibres. Pyrolysis, fluidised bed, and combustion or incineration are currently used on varying industrial scales as reclamation methods to collect fibrous materials.^3,13 In particular, the pyrolysis method is widely implemented in the composites industry for fibre reclamation by applying high temperature under a controlled atmosphere. This is often referred to as a thermal recycling technology involving resin decomposition and volatilisation to reduce the molecular weight of resin fragments using high thermal temperature (ca. 400–600°C) to break the char formed on the fibre surface and yield reclaimed fibres.^3,14 However, during processing with the pyrolysis method, the reclaimed fibres tend to be highly entangled, making it necessary to separate and disperse the fibres at an early stage of the composite remanufacturing process prior to fibre alignment.

The High Performance Discontinuous Fibre (HiPerDiF) technology was invented in the University of Bristol and as a potential composite remanufacturing process to produce highly aligned discontinuous fibre prepreg tapes through fibre dispersion as shown in Figure 1. This technology involves a fibre-suspended water jet through a fibre alignment head and subsequent production of a highly aligned fibre preform and an ultimately prepreg,^15,16 which has now been spun out as Lineat Composites (https://lineat.co.uk). The process is applicable to different types of fibres including natural and synthetic fibres as feedstock, but regardless of the fibres used, it is of critical importance that a stable fibre suspension is obtained. However, it is still challenging to get the stable fibre suspension because of various intrinsic physical and chemical properties of fibres.

Figure 1.

A schematic of the HiPerDiF (High Performance Discontinuous Fibre) technology.

This study investigates the suspension of discontinuous reclaimed carbon fibres as a component of the advanced HiPerDiF technology. Achieving homogeneous fibre suspension is critical and challenging. However, we proposed a cost-effective method for obtaining a stable fibre suspension using fibre surface treatment in an aqueous medium environment. The primary limitation of this study is that it exclusively employs an aqueous medium for the fibre suspension. Nonetheless, the fibre suspension is effective in an aqueous medium environment, and the fibre alignment process has been developed as another component of the HiPerDiF technology. This technology can be widely applied to any type of fibres as long as surface-treated fibres are used, and it can impact recycling fibre reinforced composite structures through the use of discontinuous fibre prepreg tapes.

In this study, a cost-effective fibre surface treatment is designed under the aqueous medium environment, and the critical parameters to achieve a homogeneous and stable fibre dispersion are investigated. A hydrodynamic fibre moving simulation model is numerically newly designed using a moving particle semi-implicit method to investigate the fibre suspension. Furthermore, single fibre tensile testing is performed to explore the effect of the surface treatment of the reclaimed carbon fibres, and which is compared to virgin carbon fibres. Fibre surface analyses including morphology and element composition are carried out for reclaimed carbon fibres before and after surface treatment. The proposed low-cost surface treatment lies in tailoring reclaimed fibres with no detrimental effect on the fibre surface properties, and which is much more favourable compared to other more complicated and expensive chemical treatments disclosed in other literature (the detailed information is described in the sections of Materials and Surface treatment). Experimental results of fibre dispersion are discussed with computational simulations, and physical dispersion methods such as ultrasonication and high-shear mixing are additionally summarised with their respective mechanisms and characteristics.

Materials and methods

Materials

Discontinuous carbon fibre samples, reclaimed from end-of-life FRP composite materials using a commercial scaled pyrolysis process, were provided by ELG Carbon Fibre Ltd. (now renamed as Gen 2 Carbon Ltd., 2021). In this study, as lab-scale experiments, the surface treatment of the discontinuous reclaimed carbon fibres (DRCFs, that are 6 mm and longer in length as received; the longer DRCFs were treated with the optimised surface treatment and used for single fibre testing, which is referred to the section of Single fibre tensile performance) was performed via chemical treatment at different pH levels using various aqueous solutions of acetone, methyl acetate, vinegar and sodium bicarbonate. Acetone and methyl acetate solutions were obtained from Sigma-Aldrich, UK, while ethanoic acid (vinegar) and sodium bicarbonate powder (here, in the form of baking soda) were common household products. Aqueous solutions were prepared with vinegar (12% v/v), acetone (15% v/v), methyl acetate (15% v/v) and sodium bicarbonate (2% w/v). Tap water (pH 7.03 at 18.4°C) was used as solvent for each chemical concentration and as working fluid to investigate DRCFs dispersion before and after surface treatment. Tenax^® short ‘water soluble’ carbon fibres (WSCFs) were obtained from Teijin Ltd. as the counterpart of DRCFs to compare fibre dispersion (N.B., the WSCFs are not literally soluble, but the term refers to a proprietary water-soluble sizing that is applied).

Surface treatment

The pyrolysed DRCFs used as received, and referred here as ‘virgin DRCFs’, were processed with surface treatment. The virgin DRCFs are inherently highly fluffy and entangled, so it is difficult to disperse them in water. In contrast, the commercial WSCFs with water-soluble sizing disperse well in water as their hydrophilic surface agents attract water molecules and facilitate hydrogen bonding, therefore leading to better fibre surface wetting. The main aim is to investigate fibre dispersion for the virgin DRCFs before and after surface treatment compared to WSCFs to yield relatively high fibre concentration and homogeneous suspension without fibre flocculation.

In this study, the surface treatment for the virgin DRCFs was carried out to increase surface polarity and the number of active sites on the fibres to yield surface wettability. This is due to the fact that the virgin DRCFs are pyrolysed and some impurities on the fibre surface are removed, thereby exhibiting a hydrophobic and relatively clean fibre surface.

The prepared chemical solutions are associated with alkalisation and acetylation modifications to remove undesired organic compounds and improve the wetting and adhesion properties of the virgin DRCFs by use of commodity chemicals, that is, acetic acid and sodium bicarbonate. Consequently, the dispersion in a fluid medium with the surface-treated DRCFs can be utilised via a simple and cost-effective way, which is competitive with other more complex and expensive chemical treatments. Surface-active agents in those solutions can contribute to the chemical functionalisation of the virgin DRCFs by creating functional groups on the fibres through the reaction of the hydrophilic and hydrophobic moieties. Consequently, hydrophilic fibres attract water molecules due to hydrogen bonds, and the fibre surface wetting promotes fibre dispersion.

Table 1 summarises the prepared solutions for the surface treatment of the virgin DRCFs. The virgin DRCFs were simply immersed for 24 h and subsequently collected and dried at room temperature. Then, the dried fibres were immersed completely in a transparent glass beaker filled with tap water (500 mL). Ultrasonication was applied for 1 min and the fibre dispersion was observed and noted. The fibre dispersion was considerably improved for the solutions containing vinegar and sodium bicarbonate even with hand stirring after ultrasonication. However, in the vinegar solution, when stirring ceased, settled fibres adhered to one another and fibre flocs were observed. In contrast, in sodium bicarbonate solution, the fibres formed a stable dispersion even after hand stirring. Consequently, sodium bicarbonate solution is more preferable for the fibre surface treatment for the fibre dispersion with the virgin DRCFs. With these experimental findings, it can be concluded that the mild alkaline solution from sodium bicarbonate is beneficial for the surface treatment of the reclaimed carbon fibres and improves fibre dispersion. It is because the aqueous sodium bicarbonate solution can promote the formation of hydroxyl functional groups on the fibre surface. Hence, polar covalent molecules of the water can associate with the surface-treated fibres more readily since the fibres have polar hydroxyl functional groups on their surface. As a result, fibres-to-water interaction is relatively adhesive and the surface-treated DRCFs move freely in water, whereas they interact with each other in a repulsive manner due to their similar polar characteristics.

Table 1.

Chemical materials for the surface treatment of virgin DRCFs (fibre length 6 mm as received, crowding factor 10; crowding factor refers to the section of Fibre dispersion through physical methods).

Material	Molecule	pH
Vinegar (Acetic acid; systematically named ethanoic acid)	CH₃COOH (1.05 g/cm³)	pH ∼ 2.5
Sodium bicarbonate (Baking soda; a salt composed of a sodium cation and a bicarbonate anion)	NaHCO₃ (2.2 g/cm³)	pH ∼ 8.4
Acetone (2- propanone or dimethyl ketone)	C₃H₆O (0.78 g/cm³)	pH ∼ 7
Methyl acetate (Acetic acid methyl ester or methyl ethanoate)	C₃H₆O₂ (0.93 g/cm³)	pH ∼ 7

The further optimised surface treatment of the virgin DRCFs was observed after immersion in sodium bicarbonate solution (0.15 M) for 24 h. The chemical reaction of the virgin DRCFs in the sodium bicarbonate solution is shown in Figure 2.

Figure 2.

Chemical reaction of sodium bicarbonate to virgin DRCFs in water.

Sodium bicarbonate commonly consists of carbonic acid and hydroxide ion, and its aqueous solution performs as mildly alkaline. This surface treatment is designed to be a simple and cost-effective way to yield functional groups on the virgin DRCFs for the affinity to bond hydrogen molecules in water.

Characterisation

The surface morphology of the prepared fibres was determined by scanning electron microscopy (SEM; TM3030 Plus Tabletop, HITACHI, Berkshire, UK). The operating voltage of the machine was 15 kV, and the image resolution was adjusted corresponding to its magnification. Energy dispersive X-ray (EDX) spectroscopy was employed for investigating the change of elemental composition before and after surface treatment.

Fourier transform infrared spectroscopy (FTIR) was carried out with a PerkinElmer Spectrum 100 model. This is for the analysis of functional groups on the fibre surface using infrared spectroscopy (IR). In attenuated total reflectance mode, an IR spectrum resolution and its frequency ranges were adjusted to 1 cm⁻¹ and 4000–600 cm⁻¹, respectively.

Single fibre tensile testing was carried out using a Dia-Stron LEX 820 Extensometer machine (Dia-Stron Limited, Andover, UK) with a 20 N load cell. The surface-treated DRCF samples were prepared and set on the machine with a gauge length of 30 mm, in accordance with ASTM C 1557 standard. An ultraviolet curing adhesive, Dynamax 3139 adhesive, was used to consolidate the prepared single DRCFs at the end tabs. The single fibre diameter of the DRCF samples was measured at three different locations along the axial direction using an optical microscope (Zeiss Axio Imager M2). The mean diameter of the single fibre was used to calculate the axial tensile stress which results from the applied force divided by the cross-sectional area of the single fibre. During the test, the stress-strain graph was recorded with a crosshead speed of 0.02 mm/sec along the fibre direction until the fibre breakage was reached.

With the surface-treated DRCFs, a probe-type sonicator and a high-shear blending mixer as a physical dispersion method were used and compared each other for further fibre dispersion, respectively.

Computational fibre movement in a fluid

In fluid dynamics, Eulerian or Lagrangian methods are widely used in computational modelling of the particle transport and its distribution in an enclosed space. Eulerian methods are mostly used for fixed elements (volumes or points), whereas Lagrangian methods are to use elements (most usually points) that move with the flow velocity. In this study, a moving particle semi-implicit (MPS) method is used to investigate the effect of fibre dispersion, which is based on Lagrangian mesh-free particle tracking in an incompressible fluid phase. Fibre movement in an incompressible viscous fluid is described using Navier–Stokes and mass continuity equations as follows^17,18:

\frac{D u}{D t} = - \frac{1}{ρ} \nabla P + ν \nabla^{2} u + f

(1)

\frac{D ρ}{D t} + ρ \nabla \cdot u = 0, \frac{D ρ}{D t} = 0

(2)

v = \frac{μ}{ρ}

(3)

where

u

is the velocity vector;

ρ

is the mass density of the fluid;

P

is the pressure of the fluid;

ν

is the kinematic viscosity coefficient;

μ

is the dynamic viscosity coefficient;

f

is the external force with respect to the volume of the fluid.

The MPS method for a particle $i^{t h}$ can be expressed with a simple time derivative form of Navier–Stokes equation (Equation (1)) in which each fibre behaves as a particle suspension.

\frac{{d u}_{i} (t)}{d t} = - \frac{1}{ρ_{i}} \nabla P_{i} (t) + \frac{1}{{R e}_{i}} \nabla^{2} u_{i} (t) + f_{i}

(4)

{R e}_{i} = \frac{L_{0}^{2} \dot{γ}}{v_{i}}

(5)

where

L_{0}

is the initial interparticle distance corresponding to the fluid particle size;

\dot{γ}

is the strain rate of shear deformation;

R e

is Reynolds number.

The weight function of fibre distribution in the MPS method can present the particle-to-particle interaction of fibres with the surrounding incompressible fluid particles.^17–19

w (L, L_{e}) = {\begin{array}{c} L_{e} / L - 1 \\ 0 \end{array} \begin{array}{l} (0 \leq L / L_{e} < 1) \\ (L / L_{e} \geq 1) \end{array}

(6)

where

w (L, L_{e})

is the weight function;

L

is the actual distance between fibre particles;

L_{e}

is the effective distance of the fibre-to-fibre interaction. The effective distance between fibres is attributed to the interactive fibre strength. Here,

L_{e}

is assumed to be 2. Maintaining an appropriate distance between fibres is important to dispersion due to the interactive fibre strength. In Figure 3, the weight function of fibre distribution is inversely proportional to the distance of inter-fibre particles.

Figure 3.

Weight function of the fibre distribution in the MPS method.

A dimensionless parameter, namely, fibre particle number density, $n_{i}$ , is the summation of the weight function, $w (L, L_{e})$ , within the total particles, $N$ . The mass density of particles ( $ρ_{i})$ is described with the mass of a single particle ( $m$ ) and the effective volume ( $V_{e}$ ) including the effective distance of the fibre particle-to-particle interactions. These are considered in a 2-dimensional space.

n_{i} = \frac{ρ_{i} V_{e}}{m} = \sum_{j \neq i}^{N} w (| L_{j} - L_{i} |)

(7)

Results and discussion

SEM-EDX study

The simple and cost-effective surface treatment detailed in the section of Surface treatment was applied to the virgin DRCFs using a mild alkaline solution, that is, sodium bicarbonate solution at 0.15 M concentration. The surface morphology and element analysis are shown in Figures 4 and 5, which represent images of the fibre surface before and after surface treatment. The WSCFs, which were used as a counterpart to the DRCFs, are coated with a water-soluble binding agent. Hence, the treated WSCFs, that is, rinsed with water and dried, show an increase of surface roughness and a reduction in fibre diameter of 0.35%, following removal of the surface coating layer binding agent. In Figure 4, the virgin DRCFs show smooth and clean surfaces due to the pyrolysis process, whereas the surface-treated DRCFs display an increase in surface roughness, meaning that surface elements have changed as a result of the surface treatment. The surface element analysis was carried out using EDX.

Figure 4.

Surface morphology of WSCFs and DRCFs; (a) and (c) are virgin; (b) and (d) are treated with water and a mild alkaline solution, respectively. In particular, (b) is simply rinsed with water and dried.

Figure 5.

EDX spectra of DRCFs with different immersion time for the surface treatment; (a) indicates virgin DRCFs, and (b)–(f) are 3, 6, 24, 30 and 48 h immersion time at the 0.15 M of sodium bicarbonate solution, respectively.

In Figure 5, the changes in element composition of the DRCF surface are identified as a function of immersion time, where the sodium bicarbonate solution was optimised at 0.15 M concentration. A weight percentage change of C, O and Na elements before and after surface treatment with the increase of immersion time is evident. According to the chemical reaction as shown in Figure 2, the presence of hydroxyl groups on the fibre increases with the immersion time. In Figure 5, the main elements that showed a weight percentage change were C and O. As the immersion time increased, the weight percentage of C decreased, while that of O increased. Although the weight percentage of the element Na was not significantly observed during the immersion time, it increased after 3 h immersion time for the surface treatment. The weight percentage of Na element after 3 h immersion time is the critical factor because the O–Na⁺ formation on the carbon fibre surface is varied, and the C element gradually decreases. As such, the surface morphology of DRCFs shows more roughness due to the decrease in the C element. Also, the lower percentage of C element results in a DRCF diameter decrease of about 0.28% when the immersion time was 24 h. The decreased fibre diameter can influence the fibre dispersion due to the higher aspect ratio with the same fibre length. Consequently, the surface treatment alters the reclaimed carbon fibre morphology and surface roughness. The use of mildly basic sodium bicarbonate is sufficient for the surface treatment of reclaimed fibres to increase the number of active sites (-H-C=O, -C-OH-, -O-C-, -C=O, -O-C=O) on the fibre surface to react with water molecules for the suspension, and resulting in no fibre flocculation. The further discussion is followed by sections.

FTIR spectral analysis

The presence of functional groups on the DRCFs after surface treatment were analysed using FTIR spectroscopy in the 4000–600 cm⁻¹ range. In Figure 6, FTIR spectra were collected and compared with the different proportional transmittance and peak ranges of the prepared fibres by acquiring 16 co-added FTIR spectral scans. It is interesting to note that the functional groups are at 1465 cm⁻¹ and 860 cm⁻¹ (C–H bending) for the surface-treated DRCFs and at 1680 cm⁻¹ (C = O stretching) for the virgin WSCFs due to the presence of a water-soluble binding agent. A very broad band characteristic of O–H stretch from polymeric hydroxyl groups was found in the 3550–3200 cm⁻¹ range, where this is common to both surface-treated DRCFs and virgin WSCFs. Methylene groups (-CH₂) were also commonly detected as a resolved combination of asymmetric and symmetric C–H stretches in the vicinity of 2925 cm⁻¹ wavelength.²⁰ Characteristic vibrations were observed at 1420 cm⁻ and 1268 cm⁻¹ for the virgin WSCFS, which were attributed to O–H bending and C–O stretching, respectively. For the surface-treated DRCFs, O–H bending and vibration spectra were also broadly observed in the 1480–1400 cm⁻¹ range,²⁰ corroborating the presence of the hydroxylic group. In short, the virgin WSCFs show predominantly bands due to conjugated C = O stretching on the fibre surface, whereas the surface-treated DRCFs show both C–H stretching and bending modes and O–H bending and vibration modes on the fibre surface.

Figure 6.

FTIR spectra for the prepared samples; virgin WSCFs are used for the counterpart of DRCFs to compare each other.

Figure 7(a) shows the FTIR transmittance spectra of both treated and virgin WSCFs in comparison with the virgin DRCFs. The FTIR transmittance spectra of the virgin DRCFs and the treated WSCFs are similar, as the water-soluble binding agent on the virgin WSCFs is dissolved during immersion in water; hence, there are no unique surface reactive sites remaining on the treated WSCFs, and therefore they become similar to virgin DRCFs. Figure 7(b) shows the effect on different molar concentrations of sodium bicarbonate and its surface functional groups. The increasing concentration of sodium bicarbonate applied to virgin DRCFs yields the same spectrum noting the same functional groups.

Figure 7.

FTIR spectra (a) to compare WSCFs before and after treatment and (b) to compare the effect of molar concentration on DRCFs.

In Figure 6, the presence of hydroxyl groups on the treated DRCFs are evidenced by the presence of broad bands observed between 1480–1400 cm⁻¹ as bending and vibration spectra, meaning that this is beneficial for fibre dispersion due to the presence of polar groups on the fibre surface yielding polar-hydrophilic characteristics. The presence of hydroxyl groups on the fibre leads to a hydrophilic behaviour improving dispersibility of the fibres through the formation of hydrogen bonds with water molecules. Therefore, polar-hydrophilic fibres can be obtained through a surface treatment based on a mild alkali solution from sodium bicarbonate.

Single fibre tensile performance

Single fibre tensile testing was conducted to investigate the effect of fibre surface treatment on the mechanical properties. Typical stress-strain graphs for DRCFs before and after optimised surface treatment are shown in Figure 8. The tensile stress is calculated from the mean diameter of each fibre (fibre cross-sectional area) and the applied loading force. The stress-strain graph shows an elastic-brittle behaviour. The test results and change ratios are summarised in Table 2. The chemical treatment does not change adversely the intrinsic elastic properties of the fibre. The surface-treated fibre shows a comparatively higher ultimate tensile strength. The axial modulus is observed at a little higher to the surface-treated fibre. The interesting finding is that the surface-treated fibre shows a modest increase in the axial modulus of 0.38%, while the change ratio of the ultimate tensile strength is incremental of 15.86%. This is caused by a reduction in the mean fibre diameter and in a chemical change of the fibre surface resulting in a weakening of the surface stress concentration and an increased resistance to the tensile force. Those ratios falling below 1% after surface treatment (and summarised in Table 2) are not significant. However, the data help to identify the optimised surface treatment proposed in our work by confirming which offer the most effective treatment to achieve strength against external load. Thus, it is evident that this optimised surface treatment does not adversely affect virgin type of reclaimed carbon fibres by creating active functional groups on the fibre surface due to a slight change in intrinsic physiochemical properties.

Figure 8.

Stress-strain plots of (a) virgin DRCFs and (b) surface-treated DRCFs using single fibre tensile testing.

Table 2.

Single fibre tensile testing results with virgin and surface-treated DRCFs.

Fibre properties		(A) Virgin reclaimed CFs (i.e., virgin DRCFs)	(B) Surface-treated reclaimed CFs (i.e., surface-treated DRCFs)	Ratio {(B-A)/A}
Diameter (μm)		7.18	7.16	–0.28%
Length (mm), gauge length = 30 mm		50	50	—
Density (g/cm³)		1.821 ± 0.003	1.824 ± 0.002	0.16%
Axial Young’s modulus (GPa)	No.1	1.77E + 02	1.95E + 02	—
	No.2	1.86E + 02	1.69E + 02	—
	No.3	1.89E + 02	1.92E + 02	—
	No.4	1.89E + 02	1.88E + 02	—
	Average	1.85E + 02 (±5.79)	1.86E + 02 (±1.19E + 1)	0.38%
Ultimate tensile strength (MPa)	No.1	2.06E + 03	2.53E + 03	—
	No.2	1.84E + 03	2.25E + 03	—
	No.3	2.00E + 03	2.18E + 03	—
	No.4	1.97E + 03	2.16E + 03	—
	Average	1.97E + 03 (±9.20E + 01)	2.28E + 03 (±1.73E + 02)	15.86%

The density of DRCFs was measured using the pycnometer method with distilled water as the immersion liquid, following ASTM D2320-98(2003). The density was calculated using the following relation²¹:

ρ_{D R C F s} = \frac{(w_{3} - w_{1})}{[(w_{2} - w_{1}) - (w_{4} - w_{3})]} ρ_{w}

(8)

where

ρ_{w}

is the density of distilled water (0.9970 g/cm³ at 25°C);

w_{1}

is the mass of the empty pycnometer;

w_{2}

is the mass of the pycnometer filled with distilled water at 25°C;

w_{3}

is the mass of the pycnometer filled with DRCFs;

w_{4}

is the mass of the pycnometer filled with DRCFs and distilled water at 25°C.

In Table 2, the fibre density after surface treatment showed a small increment. The reason is that the mild alkali treatment of DRCFs etched the surface of the fibre leading to increased surface roughness and reduced diameter after treatment. In addition, this alkali solution led to the dissolution of amorphous fibre components, altering the chemical composition and causing a denser packing structure. As such, a layer of the mild alkali was deposited, resulting in an increase in both density and tensile strength of the single DRCF after surface treatment.

As a result of the surface treatment, reclaimed carbon fibres are less prone to undergo fibre flocculation in a fluid medium and transfer more load to the polymer matrix when remanufactured to composite product than using the virgin type of reclaimed fibres.

Computational fibre model and dispersion

Eulerian and Lagrangian methods are commonly used numerical methods in fluid dynamics. Fluid flow simulations based on the Eulerian approach generally employ a mesh-based technique, that is, the discretisation of space into regular grids or meshes for simulation. This mesh-based Eulerian method has certain limitations when modelling complicated fluid phenomena involving large motions. Mesh-free methods in comparison offer great flexibility in terms of boundary motion, including for cases where there is a rigid body motion. Common approaches for the mesh-free method are Smoothed Particle Hydrodynamics (SPH^22–24) and Moving Particle Semi-implicit simulation (MPS^17,18). The SPH method is mainly applied to the weakly compressible form in fluid dynamics, whereas the MPS method is well adapted for incompressible fluid flows involving an explicit calculation of the external force and an implicit calculation of the pressure.^25–28

In this study, the MPS method based on Lagrangian approach is considered using the semi-implicit algorithm of a simplified marker and cell method which is widely used in incompressible fluid flow. Here, in practice, water (incompressible fluid flow) is used as a suitable phase for fibre dispersion since the water pressure changes involved are too small to make an appreciable change to the density. Pressure gradients between inter-fibre particles act as a repulsive force, which prevents close approach of the particles and facilitates dispersion. As part of a multi-phase flow involving solid and liquid phases, physical quantities pertain to each of the phases at position and velocity. For fibre dispersion in fluid flow, the fibre model is expressed as a set of particles of the bead-chain formation.^29,30 The fibre movement in the fluid is characterised as exhibiting extension, bending and torsion, whereas the fluid model is assumed as extension and bending; fibre and fluid phases are derived from Stokes flow.³⁰

Fibre orientation is determined by several parameters such as fibre aspect ratio (length to diameter), fibre density (fibre concentration) and shear fluid flow. The fibre orientation can be influenced by fluid-mediated interactions between fibre-to-fluid and fibre-to-fibre contacts. Shear fluid flow is assumed in which fluid-mediated interactions with fibres occur continuously when the fibre concentration is set. The fibre orientation in relation to the fibre concentration influences the fibre dispersion along the fluid flow. At lower fibre concentrations, that is, when the extent of fibre orientational distribution is large, fibre flocculation rarely arises since the lower fibre concentration causes fewer fibre-fibre interactive contacts, so that fibre flocculation rarely arises.

In this study, the fibre model based on the MPS method is developed by stretching and bending forces in 2-dimensional space. A stretching force is to maintain the distance between the fibre particles, and a bending force is to set an angle between the neighbouring fibres. The stretching force on a fibre is expressed as

F_{i j}^{s} = k_{s} (| r_{j} - r_{i} | - L_{o}) \frac{r_{j} - r_{i}}{| r_{j} - r_{i} |}

(9)

where

F_{i j}^{s}

is the stretching force to make a straight fibre to the neighbouring fibre particle;

k_{s}

is the stretching spring constant;

L_{o}

is the initial distance between particles. If the neighbouring particles are far from the initial distance of the particle (i.e.,

| r_{j} - r_{i} | > L_{o}

), a restoring force retrieves back to its equilibrium position. If

| r_{j} - r_{i} | < L_{o}

, the restoring force acts inversely.

The bending force applied to a particle is shown in Figure 9.

U (θ_{j}) = k_{b} (1 + \cos θ_{j})

(10)

\cos θ_{j} = \frac{(r_{i} - r_{j}) \cdot (r_{k} - r_{j})}{| r_{i} - r_{j} | | r_{k} - r_{j} |}

(11)

where

k_{b}

is the bending spring constant; bending potential

{U (θ_{j}) |}_{θ = π}

indicates the stable state of fibre movement. The bending force can be derived by the potential energy at the j^th fibre particle.

F_{i j}^{b} = - \frac{\partial U (θ_{j})}{\partial r_{i}} = - \frac{\partial U (θ_{j})}{\partial θ_{j}} \frac{\partial θ_{j}}{\partial r_{i}}

(12)

\frac{\partial U (θ_{j})}{\partial θ_{j}} = - k_{b} \sin θ_{j}

(13)

\frac{\partial θ_{j}}{\partial r_{i}} = \frac{1}{| r_{i} - r_{j} | | r_{k} - r_{j} | \sin θ_{j}} {- (r_{k} - r_{j}) + \frac{(r_{i} - r_{j})}{| r_{i} - r_{j} |} | r_{k} - r_{j} | \cos θ_{j}}

(14)

Figure 9.

A pair of fibre particles used to build a fibre model.

The computational fibre model is executed using PETSc (Portable, Extensible Toolkit for Scientific Computation) libraries for partial differential equations and sparse matrix computations.³¹ Thus, the incomplete Cholesky conjugate gradient (ICCG) method and the message passing interface (MPI) for pressure calculation are used in PETSc library. For boundary conditions, two layers of ghost (or so-called dummy) particles are used to avoid density deficiency near the boundary, and the velocity of the solid inner wall particles are set to zero so that fluid particles can flow without interference of the wall.

The fibre dispersion analysis with different fibre concentrations is shown in Figure 10. As time flows, fibre movement becomes more vigorous. Fibre orientation is changed along the shearing fluid flow in which the higher fibre density comes to yield a lower degree of orientational fibres. This is attributed to the higher fibre volume occupied in a fluid space, so the fluid resistance to fibre orientation relatively increases. This can be also applied to the longer fibres due to the larger fibre volume fraction occupied. Besides, the increase in fibre-to-fibre contacts cause fibre aggregation as shown in Figure 10. When the fibre bending ratio to stretching is high, the whirling of fibres occurs more as shown in Figure 10(c) and (f). At the higher fibre concentration, when the fibre-to-fluid contacts are achieved more, fibre accumulation is clearly observed.

Figure 10.

Fibre dispersion varied by fibre concentration and stiffness ratio.

In Figure 11, the fibre bending angle is traced with respect to time for each case of Figure 10. The fibre bending effect is characterised according to the fibre concentration. Also, the fibre bending effect can respond to the fibre stiffness in that the higher fibre bending indicates the lower fibre stiffness. At the higher fibre stiffness index ( $k_{i j}^{b} / k_{i j}^{s}$ ) at each column in Figure 10 (Figure 10(c) and (f)), it yields a remarkable whirling effect on the fibres. It is due to the increase of fluid particles to rotate the fibres more. However, at the lower fibre concentration (Figure 10(B)), a whirling effect is not that much due to the shearing fluid flow to stretch fibres and the less frequencies of fibre-to-fluid interactions. Therefore, fibres that are longer and stiffer can yield larger and stronger flocs at the same mass density of fibres in suspension. In this simulation, the fibre stiffness index ( $k_{i j}^{b} / k_{i j}^{s}$ ) can be $1 < k_{i j}^{b} / k_{i j}^{s} \leq 10$ for the fibre dispersion due to not that much of bending stiffness of the fibre by considering a real experimental situation, which corresponds to the stiffness change ratio from the single fibre tensile testing. This simulation was conducted by incorporating fibre stiffness characteristics without considering the polarity of the fibres. Therefore, from the increased stiffness observed during single fibre tensile testing, one may assume the more fibre flocculation. However, experimental determinations of the fibre dispersion yielded favourable dispersion due to the polar-hydrophilic surface characteristics of the fibres preventing fibre flocs, which means overcoming the interaction of fibre stiffness characteristics. The hydrodynamic simulation is limited to the fibre stiffness index, which is a factor to consider in fibre suspension. This is because the polar-hydrophilic carbon fibres obtained after surface treatment are more prevalent in the fibre suspension than the interaction of fibre stiffness characteristics in simulation. Therefore, our proposed optimised surface treatment method contributes to desirable fibre dispersion. The simulation considers only the physical stiffness of the fibres without their chemical characteristics. The experimental results mean that the influence of fibre dispersion depends largely on the chemical composition changes on the fibre surface. This simulation helps understanding fibre flocs from the perspective of fibre stiffness, which is also not disregarded for fibre dispersion. The following section addresses the effect of physical methods practically to make homogeneous fibre dispersion.

Figure 11.

Fibre bending effect corresponding to Figure 10; (a)–(c) indicating to Figure 10(A) and (d)–(f) indicating to Figure 10(B).

Fibre dispersion through physical methods

Fibre flocculation, that is, the formation of fibre entanglement by inter-fibre collisions, is a critical issue in the achievement of a stable fibre dispersion. The phenomenon of the inter-fibre collision is mainly attributed to the long fibres, fibre concentration (or fibre volume fraction) and the fibre thickness. The effect of fibre flocculation can be inversely interpreted by how uniformly the fibres are dispersed in water. The crowding factor is widely used for the fibre dispersion and as indication of fibre flocculation to predict a degree of the fibre flocs.³² The crowding factor $n_{f}$ is defined as

n_{f} = \frac{2}{3} C_{v} {(\frac{l}{d})}^{2}

(15)

where

C_{v}

l

and

d

are fibre volume fraction, length and diameter, respectively. An increase in crowding factor results in fibre entanglement and flocculation. The longer and stiffer fibres tend to produce more inter-fibre collisions, which is detrimental to the fibre dispersion.

Fibre surface treatment contributes to a reduction in the number of fibre-fibre contacts and an increase in the number of interactions between the functional active sites on the fibres and water molecules. To investigate fibre dispersion before and after surface treatment, physical methods were used, that is, ultrasonication and high-shear mixing to break the initial fibre clumps and create high-shear fluid flow to overcome the fibre flocculation. Ultrasonication has been widely used and reported in many applications for the dispersion of strong agglomerates such as nanoparticles, because it can provide high energy to break interparticle bonds of the agglomerates.^33–35 However, it has adverse effects on the surface damage of dispersive media when high power and long-lasting ultrasonication time are applied. Thus, a mixing system including a vessel size and a probe position in ultrasonication is important when attempting to achieve a homogeneous dispersion.³³ On the other hand, high-shear mixing can be used to quickly suspend more fibres due to the highly intensive shear force available to overcome fibre flocs due to the turbulent flow. However, the design of the vessel, baffles, and the number and shape of the mixing blades are critical to achieve the desired level of dispersion.^36,37

The practical fibre dispersion was experimentally observed as shown in Figure 12; the vertical axis indicates the fibre dispersion in an arbitrary unit. Fibre dispersion per unit volume with respect to crowding factor implies how much fibre suspension was achieved per unit volume by observing a 3-dimensional volume vessel. It is obvious that the fibre dispersion is clearly influenced by the crowding factor. Polar-hydrophilic fibres obtained from surface treatment have large functional active sites to interact water molecules, thereby the less fibre flocculation is shown. Figure 13 shows the effect of fibre dispersion depending on the physical dispersion methods. When setting a 6 mm fibre length for the prepared fibres, the surface-treated DRCFs have the highest crowding factor, followed by ultrasonication and WSCFs. As for WSCFs, there was no such outstanding dispersion effect even using ultrasonication and high-shear mixing methods. This is because non-polar hydrophobic fibres are suspended after coated binding agents on the fibres are dissolved in water, and prone to fibre flocs. This is the limitation to the non-polar hydrophobic fibres in terms of fibre dispersion, which is unlike to the surface-treated DRCFs. The surface-treated DRCFs are acting as polar-hydrophilic fibres, so water molecules of the working fluid are more active to react with them.

Figure 12.

Fibre dispersion per unit volume with respect to crowding factor.

Figure 13.

Fibre dispersion per unit volume with respect to crowding factor.

Comparison of physical dispersion methods

Table 3 summarises the mechanism and characteristics of ultrasonication and high-shear mixing methods, respectively. Fibre flocs were observed around the turbulent eddies due to the van der Waals effect on the interactions between polar-hydrophilic fibres and water molecules. It is apparent that the increasing surface roughness of the fibres produces an increase in the residual turbulence and results in fibre aggregation along the flow. Regarding ultrasonication, as the ultrasonic energy is generated from the probe tip and goes directly downward, fibres are pushed down in all directions. If the vessel is too wide, then the ultrasonic energy cannot reach all the areas properly, and consequently, some of the fibres remain as clumps. Whereas a conical vessel shape yields a short dispersion time and increases the homogeneity of mixing. Therefore, a conical-shaped narrow vessel is preferred to a wide vessel. High-shear mixing utilises the hydrodynamic turbulence and shear fluid force in that additional design of baffles is recommended, which is differentiated to ultrasonication.

Table 3.

The summary of physical methods for fibre dispersion.

	Ultrasonication	High-shear mixing
Mechanism	• Cavitation and wave propagation.	• Hydrodynamic turbulence and shear fluid force.
Characteristics	• Influence on fibre damage. - Fibre damage can be occurred by the high intensity of ultrasonic sound field around the sonication tip. - Depending on ultrasonic intensity and time during ultrasonication. • Homogeneous mixing. • High localised energy to the disruption of cavitation bubbles in liquids. • Clearing surface impurities.	• Influence on fibre damage to break into pieces. - Fibre damage can be occurred around the sharp impeller when applied longer time. • High shear flow to disperse quickly. • Homogeneous mixing. • Baffled design to control vortex flow. • Controllable power to save dispersing energy.
Desired design for fibre dispersion

Compared to ultrasonication, high-shear mixing is much preferred to achieve the high level of fibre dispersion with a relatively lower power and less time. The effect of baffles was investigated with the use of DRCFs. In Figure 14(a), without baffles, fibre initial clumps and flocs remained to the virgin DRCFs. However, the surface-treated DRCFs produce a stable dispersion. In Figure 14(b), fibre dispersion is shown with respect to time for the simple baffled design of the vessel. The homogeneous fibre dispersion was observed to the surface-treated DRCFs as the baffles obstruct turbulent eddies and contribute to a more homogenous suspension flow.

Figure 14.

Baffle effect for achieving a stable fibre dispersion.

Consequently, the desired surface roughness and the functional groups on the fibres are important to control fibre suspension in a fluid medium with no flocculation. Most of the research literature relating to fibre flocculation cites the increasing fibre stiffness as one of the parameters to cause fibre flocs; however, polar-hydrophilic fibres even with the increased stiffness do not present adverse effects on the fibre dispersion in this study, which is interesting in our findings. Thus, the increased fibre stiffness induced by the surface treatment can contribute to the interfacial bonding with polymer resins to yield the improving mechanical properties of FRP composites.

Conclusion

The desired surface roughness and the surface functional groups on the reclaimed fibres are critical parameters to effect on the fibre suspension in a fluid medium to avoid fibre flocculation. In this study, the surface treatment of virgin discontinuous reclaimed carbon fibres yields C–H stretching and bending modes and O–H bending and vibration modes, and the increase of hydroxyl functional groups on the fibres acts as polar-hydrophilic performance, which is favourable for the interactions with water molecules. After surface treatment of the reclaimed carbon fibres, fibre dispersion increases higher than the proprietary water-soluble carbon fibres used for comparison (N.B., the water-soluble carbon fibres are not literally soluble, but the term refers to a proprietary water-soluble sizing that is applied). The mild alkali surface treatment on the reclaimed carbon fibres yields improving mechanical properties (15.86% increase in the ultimate tensile strength and 0.38% increase in the axial Young’s modulus).

Hydrodynamic simulation with a fibre model was carried out using a moving particle semi-implicit method. Fibre stiffness index ( $k_{i j}^{b} / k_{i j}^{s}$ ) was considered to determine the performance of fibre dispersion. At the fibre movement simulation, fibre orientation is determined by fibre aspect ratio, fibre concentration and shear fluid flow; the more whirling and entanglement of fibres were observed at the higher fibre concentration. In addition, the longer and stiffer fibres yielded the larger and stronger flocs at the same fibre concentration in suspension. However, in contrast to the simulation, polar-hydrophilic carbon fibres show less fibre flocs experimentally when suspended in flow despite their increased stiffness. This is because the simulation takes into account fibre physical stiffness, but does not consider polar fibre chemical characteristics that influence the manner in which the surface-treated fibres interact with water molecules at the chemical level.

With the increase in crowding factor used to characterise fibre dispersion effect in water suspension, the fibre surface treatment contributes to the decrease in bridging fibre-fibre contacts and the relative increase in affinity to the water molecules, and thereby the level of fibre dispersion reaches high. Physical dispersion methods including ultrasonication and high-shear mixing were compared, and consequently, the high-shear mixing method was shown for the better fibre dispersion due to the hydrodynamic turbulence and shear fluid force. A baffled vessel yielded the formation of a stable fibre dispersion for the surface-treated reclaimed fibres; this is due to the reason that the baffles obstruct hydrodynamic turbulent eddies and contribute the more homogenous suspension flow.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Engineering and Physical Sciences Research Council (EPSRC) through grant EP/P027393/1 (High Performance Discontinuous Fibre Composites - a sustainable route to the next generation of composites) and the EPSRC Centre for Doctoral Training in Advanced Composites for Innovation and Science (EP/L016028/1) (DB) University of Bristol.

ORCID iDs

Kyungil Kong

Marco L Longana

References

Y-Y

Liang

S-D

Feng

, et al. Recyclable LRS FRP composites for engineering structures: Current status and future opportunities. Compos B Eng 2021; 212: 108689. DOI: 10.1016/j.compositesb.2021.108689.

van den Einde

Zhao

Seible

. Use of FRP composites in civil structural applications. Constr Build Mater 2003; 17: 389–403. DOI: 10.1016/S0950-0618(03)00040-0.

Pakdel

Kashi

Varley

, et al. Recent progress in recycling carbon fibre reinforced composites and dry carbon fibre wastes. Resour Conserv Recycl 2021; 166: 105340. DOI: 10.1016/j.resconrec.2020.105340.

Safarabadi

Shokrieh

. Understanding residual stresses in polymer matrix composites. In: Residual stresses in composite materials. Elsevier, 2014, pp. 197–232. DOI: 10.1533/9780857098597.2.197.

Ozsoy

Choi

Joseph

, et al. Reinforced thermoplastic composites with interfacial microarchitectural anchoring: computational study. Int J Solids Struct 2017; 112: 54–64. DOI: 10.1016/j.ijsolstr.2017.02.021.

Meng

Olivetti

Zhao

, et al. Comparing life cycle energy and global warming potential of carbon fiber composite recycling technologies and waste management options. ACS Sustain Chem Eng 2018; 6: 9854–9865, DOI: 10.1021/acssuschemeng.8b01026.

Khalil

. Comparative environmental and human health evaluations of thermolysis and solvolysis recycling technologies of carbon fiber reinforced polymer waste. Waste Management 2018; 76: 767–778. DOI: 10.1016/j.wasman.2018.03.026.

Rybicka

Tiwari

Leeke

. Technology readiness level assessment of composites recycling technologies. J Clean Prod 2016; 112: 1001–1012. DOI: 10.1016/j.jclepro.2015.08.104.

Bai

McKechnie

. Environmental and financial performance of mechanical recycling of carbon fibre reinforced polymers and comparison with conventional disposal routes. J Clean Prod 2016; 127: 451–460. DOI: 10.1016/j.jclepro.2016.03.139.

10.

Composites

. Meeting the greatest Challenge: how the UK composites sector will deliver Net zero, composites Leadership Forum Report, 2021, https://www.nccuk.com/news/composite-leadership-forum-releases-net-zero-report-for-the-uk/ (accessed 01 February 2023).

11.

Meng

McKechnie

Turner

, et al. Energy and environmental assessment and reuse of fluidised bed recycled carbon fibres. Compos Part A Appl Sci Manuf 2017; 100: 206–214. DOI: 10.1016/j.compositesa.2017.05.008.

12.

Witik

Teuscher

Michaud

, et al. Carbon fibre reinforced composite waste: an environmental assessment of recycling, energy recovery and landfilling. Compos Part A Appl Sci Manuf 2013; 49: 89–99, DOI: 10.1016/j.compositesa.2013.02.009.

13.

Karuppannan Gopalraj

Kärki

. A review on the recycling of waste carbon fibre/glass fibre-reinforced composites: fibre recovery, properties and life-cycle analysis. SN Appl Sci 2020; 2: 433. DOI: 10.1007/s42452-020-2195-4.

14.

Feih

Boiocchi

Mathys

, et al. Mechanical properties of thermally-treated and recycled glass fibres. Compos B Eng 2011; 42: 350–358. DOI: 10.1016/j.compositesb.2010.12.020.

15.

Potter

Wisnom

. A novel manufacturing method for aligned discontinuous fibre composites (high performance-discontinuous fibre method). Compos Part A Appl Sci Manuf 2014; 65: 175–185. DOI: 10.1016/j.compositesa.2014.06.005.

16.

Longana

Ong

, et al. Multiple closed loop recycling of carbon fibre composites with the HiPerDiF (high performance discontinuous fibre) method. Compos Struct 2016; 153: 271–277. DOI: 10.1016/j.compstruct.2016.06.018.

17.

Yashiro

Sasaki

Sakaida

. Particle simulation for predicting fiber motion in injection molding of short-fiber-reinforced composites. Compos Part A Appl Sci Manuf 2012; 43: 1754–1764. DOI: 10.1016/j.compositesa.2012.05.002.

18.

Koshizuka

Oka

. Moving-particle semi-implicit method for fragmentation of incompressible fluid. Nucl Sci Eng 1996; 123: 421–434, DOI: 10.13182/NSE96-A24205.

19.

Shakibaeinia

Jin

Y-C

. A weakly compressible MPS method for modeling of open-boundary free-surface flow. Int J Numer Methods Fluids 2010; 63: 1208–1232. DOI: 10.1002/fld.2132.

20.

Maia

Tjong

Sain

. Material characterization of recycled and virgin carbon fibers for transportation composites light weighting. Mater Today Sustain 2019; 5: 100011. DOI: 10.1016/J.MTSUST.2019.100011.

21.

Maache

Bezazi

Amroune

, et al. Characterization of a novel natural cellulosic fiber from Juncus effusus L. Carbohydr Polym 2017; 171: 163–172. DOI: 10.1016/J.CARBPOL.2017.04.096.

22.

Gingold

Monaghan

. Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon Not R Astron Soc 1977; 181: 375–389. DOI: 10.1093/mnras/181.3.375.

23.

Monaghan

. An introduction to SPH. Comput Phys Commun 1988; 48: 89–96. DOI: 10.1016/0010-4655(88)90026-4.

24.

Cummins

Rudman

. An SPH projection method. J Comput Phys 1999; 152: 584–607. DOI: 10.1006/jcph.1999.6246.

25.

Morris

Fox

Zhu

. Modeling Low Reynolds Number Incompressible Flows Using SPH. J Comput Phys 1997; 136: 214–226. DOI: 10.1006/jcph.1997.5776.

26.

Rojas Fredini

Limache

. Evaluation of weakly compressible SPH variants using derived analytical solutions of Taylor–Couette flows. Comput Math Appl 2013; 66: 304–317. DOI: 10.1016/j.camwa.2013.05.008.

27.

Kondo

. A physically consistent particle method for incompressible fluid flow calculation. Comput Times Part Mech 2021; 8: 69–86. DOI: 10.1007/s40571-020-00313-w.

28.

Liu

Morita

Zhang

. An advanced moving particle semi-implicit method for accurate and stable simulation of incompressible flows. Comput Methods Appl Mech Eng 2018; 339: 467–487. DOI: 10.1016/j.cma.2018.05.005.

29.

Sasayama

Inagaki

. Simplified bead-chain model for direct fiber simulation in viscous flow. J Nonnewton Fluid Mech 2017; 250: 52–58. DOI: 10.1016/j.jnnfm.2017.11.001.

30.

Yamamoto

Matsuoka

. A method for dynamic simulation of rigid and flexible fibers in a flow field. J Chem Phys 1993; 98: 644–650. DOI: 10.1063/1.464607.

31.

Balay

Abhyankar

Adams

, et al. PETSc Web page 2022, https://petsc.org/ (accessed 01 February 2023).

32.

Kerekes

Schell

. Characterization of fibre flocculation regimes by a crowding factor. J Pulp Pap Sci 1992; 18. J32–J38, https://www.researchgate.net/publication/279605370_Characterization_of_Fibre_Floccula_tion_Regimes_by_a_Crowding_Factor (accessed 01 February 2023).

33.

Girard

Vidal

Bertrand

, et al. Evidence-based guidelines for the ultrasonic dispersion of cellulose nanocrystals. Ultrason Sonochem 2021; 71: 105378. DOI: 10.1016/j.ultsonch.2020.105378.

34.

Girard

Bertrand

Tavares

, et al. Rheological insights on the evolution of sonicated cellulose nanocrystal dispersions. Ultrason Sonochem 2021; 78: 105747. DOI: 10.1016/j.ultsonch.2021.105747.

35.

Metzger

Drexel

Meier

, et al. Effect of ultrasonication on the size distribution and stability of cellulose nanocrystals in suspension: an asymmetrical flow field-flow fractionation study. Cellulose 2021; 28: 10221–10238. DOI: 10.1007/s10570-021-04172-3.

36.

Major-Godlewska

Karcz

. An effect of the tubular baffles configuration in an agitated vessel with a high-speed impeller on the power consumption. Chem Pap 2018; 72: 2933–2943. DOI: 10.1007/s11696-018-0533-4.

37.

Foukrach

Ameur

. Investigation of the flow patterns and power requirements in agitated systems: effects of the design of baffles and vessel base. Int J Chem React Eng 2020; 18: 20200046. DOI: 10.1515/ijcre-2020-0046.

Experimental and hydrodynamic methods to determine aqueous dispersion of discontinuous reclaimed carbon fibres

Abstract

Keywords

Introduction

Materials and methods

Materials

Surface treatment

Characterisation

Computational fibre movement in a fluid

Results and discussion

SEM-EDX study

FTIR spectral analysis

Single fibre tensile performance

Computational fibre model and dispersion

Fibre dispersion through physical methods

Comparison of physical dispersion methods

Conclusion

Footnotes

Declaration of conflicting interests

Funding

ORCID iDs

References