A Theoretical and Experimental Study of Oil Wicking Mechanism of Kapok Fibrous Powder Assembly

ABSTRACT Kapok fiber has a large lumen with a natural waxy surface which endows it with distinct hydrophobic-oleophilic properties. Oil-impregnated kapok fibrous powder (KFP) has great potential as a lubricant carrier material. To study the oil wicking mechanism of KFP assemblies with different pore structures (interfibrous pores and the lumens), a dual-scale model was established based on Washburn capillary theory. The theoretical model was verified by capillary rise test of KFP assemblies in various packing densities ranging from 0.08 g/cm3 to 0.14 g/cm3. It was found that the experimental results have good consistency with theoretical values at low packing densities. The deviation between the experimental result and the theoretical value increases with the increase of packing density. This can be largely attributed to compression of the lumens at increased packing density, leading to the reduction of oil sorption capacity within the lumens. The outcomes of this research are believed to provide important references for the usage of fibrous powder materials as lubricant carrier.


Introduction
Kapok fiber is a lignocellulosic fiber derived from the seedpod of Ceiba pentandra (Hori et al. 2000;Zheng, Wang, and Wang 2021).It has a large lumen and a natural waxy surface.Due to its unique features, including large hollowness, light in weight, low in density, good buoyancy, and hydrophobic characteristics (Hu et al. 2017;Mani, Rayappan, and Bisoyi 2012), kapok fiber has opened up possibilities for plenty of application fields.The applications range from stuffing materials (Zhang et al. 2013), sound absorption materials (Kassim, Putra, and Ramlan 2023;Liu et al. 2022), thermal insulation materials (Jabbar et al. 2022, Thenmozhi andThilagavathi 2023) and reinforced fiber materials (Bhambure, Rao, and Senthilkumar 2023;Chen et al. 2022) to oil-absorbing materials (Abdullah, Rahmah, and Man 2010) and functional template materials (Cao et al. 2018;Xu et al. 2018).Among them, due to the excellent hydrophobic-oleophilic performance, various research studies on the use of kapok fiber as sorbent oil spill clean-up and oil-water separation were reported (Dong, Cao, and Xu 2017;Lim and Huang 2007;Thilagavathi, Praba Karan, and Thenmozhi 2020).
The sorption between oil and kapok fiber is primarily based on physical adsorption, which makes it reversible in nature.Meanwhile, the fiber assembly contains abundant capillary channels, which give it great potential for oil release (Xu et al. 2020).Therefore, kapok fiber has the necessary properties to serve as a lubricant carrier material.Lubricant usually needs to be pushed to the designated sites (commonly bearings) by mechanical pressing (Gordon, Gainer, and Russell 1978;Abel 1967).The powdered material facilitates transmission and can be filled into any shape, whereas long fiber is prone to tangling and clogging.The working mechanism of oil-impregnated fibrous powder in lubrication is as follows.When machine is in operation with bearing rotation, the oil-impregnated fibrous powder material in contact with the bearing surface will release the oil through capillary action.This release occurs due to contact friction and local temperature rise resulting from the heat generated by rotational friction.When the machine is not in operation, the fibrous powder material can store oil and prevent oil leakage.According to its working mechanism, studying the oil sorption characteristics and mechanism of fibrous powder assemblies is essential for understanding the roles of fibrous powder as a lubricant carrier material.Our group has conducted research on the oil sorption properties of natural cellulose powder and the oil sorption/release properties of oil-containing KFP under different temperature conditions (Xu et al. 2020(Xu et al. , 2022)).However, there is still a lack of research on the oil sorption mechanism of fibrous powders.
In this study, the oil wicking mechanism of KFP assembly was studied.Based on the pore characteristics of KFP assembly, a dual-scale model was established to analyze the oil sorption mechanism.To validate the theoretical model, the oil sorption coefficient values obtained from capillary rise tests were compared with theoretical values.The outcomes of this research are believed to provide important reference for the usage of fibrous powder materials as lubricant carrier.

Construction of oil sorption theoretical model
To study the role of pores between fibrous powders and the lumen structure of kapok fiber itself in the process of oil sorption, a two-scale model was constructed, as shown in Figure 1.The model is based on the classical capillary theory, where the fibers are represented as numerous equivalent cylindrical capillary components, and the driving force for liquid transport is from the capillary pressure (Washburn 1921).
There are three basic hypotheses: (1) It is assumed that all KFP has the same length and diameter and is arranged in a parallel manner to each other.(2) It is assumed that the lumens of the fibrous powder assemble a bundle of parallel capillaries, with the diameter of the capillaries being the same as that of lumen.(3) It is assumed that the interfibrous pores are also a bundle of parallel capillaries, with their diameters represented by equivalent hydrostatic diameters.Furthermore, the wetting region of the capillary assembly is equivalent to the wetting region of the interfibrous pores, and that the porosity of the capillary assembly is the same as that of the interfibrous pores.
From hypothesis (2) it can be inferred that: where d h represents the capillary diameter of lumen, and d i represents the inner diameter of kapok fiber.
In order to calculate the equivalent capillary diameter between KFP, the following equation can be used based on the packing density "ρ" of the fibrous powder assembly, the volume of the entire fibrous powder (including the lumens) Q f and the volume of the kapok fiber wall Q W at the given packing density of the fibrous powder assembly can be expressed by the following equation: where ρ f and ρ w represent the kapok fiber density and the density of fiber wall, respectively.The porosity ε of the fibrous powder assembly, the porosity ε e between the interfibrous powder and the porosity ε i of kapok fiber itself can be expressed by the following equation: Using n to represent the number of interfibrous capillaries, d he represent the corresponding hydrostatic diameter, the following relation can be derived according to hypothesis (3): where S v represents the specific surface area of the fibrous powder material, which can also be expressed by the following relation: where d e represents the outer diameter of kapok fiber, and the hydrostatic diameter can be obtained by combining formulas ( 7), ( 8) and ( 9): According to Washburn equation, for a capillary with a diameter of d c , the relationship between the wicking length Land the wicking time tis as follows: where σ represents the surface tension of the liquid, θrepresents the contact angle between solid and liquid, and μ represents the viscosity of the liquid.Besides, the wicking height can also be expressed by the wicking mass: where, M represents the wicking mass, A represents the cross-sectional area of the filling medium, ε 0 represents the porosity of the filling medium, and ρ l represents the density of the liquid.Therefore, by combining equations ( 10), ( 11) and ( 12), we can obtain the mass of liquid entering the fiber lumens during the capillary rise test M i and the mass of liquid entering the interfibrous pores M e , respectively: The ratio between the mass square of liquid and the corresponding time is defined as sorption coefficient (Nishi et al. 2002).Therefore, the sorption coefficient of the fiber lumens D i and the sorption coefficient of the interfibrous pores D e are: For kapok fiber: where d e and d i are the outer diameter and inner diameter of kapok fiber, respectively, ρ f is the density of kapok fiber, ρ w is the density of kapok fiber wall, N dt is the linear density of kapok fiber, A f and A 0 represent the cross-sectional area of the lumen and kapok fiber, respectively.The basic structural parameters of kapok fiber are shown in Table 1.

Materials
Kapok fiber used in the study was from Pate County, Java Tengah, Indonesia.Fibrous powder was obtained by mechanical cutting using fiber cutting machine (SBJ800E, Qinghang, China).
The morphological structure of fiber powder was examined using scanning electron microscope (SEM-TM3000, Hitachi, Japan).As shown in Figure 2, the length range of KFP varied from dozens of microns to 2 mm.Kapok fiber exhibited a hollow structure and smooth surface.
Test oils are two commonly used lubricants, mineral oil and Polyalphaolefin (PAO) synthetic oil.Mineral oil, also known as liquid paraffin, which is primarily composed of alkanes, is extracted from crude oil.PAO is made by polymerization of ethylene to produce alpha olefin, which is then further polymerized and hydrogenated.Oil density was tested using a dynamic Tensiometer (DCAT11, Dataphysics, Germany).The viscosity of oil was tested using an intelligent viscosity measuring instrument (DV2TLV, Brookfield, USA).The instrument is a digital display viscometer, which is driven by a motor to rotate the rotor at constant speed.When the rotor rotates in the liquid, the liquid will generate a torque due to its viscosity, which acts on the rotation of the rotor.The viscous torque acting on the rotor is detected by the sensor, and the viscosity of the liquid is obtained through computer processing.Appropriate rotor and rotation speed should be set according to the viscosity of the test liquid.For the test oils, rotor No. SC4-18 (18) was used, and the rotation speed was set at 200 rpm.The tests were conducted at 20 ± 2°C.The oil properties, including density and viscosity, are listed in Table 2.

Capillary rise test
Capillary rise test was conducted to measure the wicking behavior of KFP.The instrument was dynamic tensiometer (DCAT11, Dataphysics, Germany), and a schematic of the instrument can be found in Figure 3.A cylindrical tube was used as sample tube 3. The inner diameter of the sample tube is 12 mm, and the filling length is 20 mm.Hence, the volume of the sample tube that can be filled is constant (2.26 cm 3 ).Various packing densities of the KFP were achieved by uniformly filling different mass of fiber materials into the tube, and then compressing the piston of the tube to a filled length.The sample preparation process involves filling the sample into the sample tube as evenly as possible to ensure the accuracy of the test results and the repeatability of the test.
During the test, the oil in liquid reservoir 5 was elevated at a speed of 0.1 mm/s until it contacted the KFP material.The change in mass over time was accurately detected by the electronic balance 1 and recorded on a computer.To ensure the repeatability and reproducibility of the results, three samples were prepared for each test; therefore, the average values along with standard deviations were obtained.The tests were conducted at 20 ± 2°C.

Oil sorption behavior analysis
Figure 4 shows the relationship between the square of sorption mass and time at various packing densities.As can be seen from Figure 4, the sorption process can be divided into two stages.At the beginning of sorption, oil entered the sample at a fast speed, and the sorption mass increased with time.After the sorption equilibrium was reached, the amount of oil entering the porous material no longer changed with time.After 1000 s and 500 s, the sorption of mineral oil and PAO synthetic oil reach sorption equilibrium, respectively.The lower the packing density of the material, the faster the sorption occurs, and the quicker the sorption equilibrium was reached.It is mainly attributed to the smaller the packing density, which creates a larger space inside the material, making it easier for the oil to penetrate into the porous material.For two different test oils, it took more time for the sorption of mineral oil to reach equilibrium under the same volume density condition.It is mainly due to the higher viscosity of oil (74.7 mPa • s) compared to that of PAO synthetic oil (29.55 mPa • s).
To further analyze the wicking behavior of KFP under different packing densities, the saturated oil sorption capacity (M 0 ) and sorption coefficient (D 0 ) were obtained according to the capillary rise test.M 0 was obtained by the mass of oil sorption at equilibrium.D 0 was obtained by performing linear fitting of the square of the sorption mass at the initial stage over time.The linear fits of initial sorption period are depicted in Figure 4, with all correlation coefficients R 2 >0.98. Figure 5 presents the relationship between saturated oil sorption and sorption coefficient with respect to packing density.As can be seen from Figure 5(a), with the increase of the packing density, M 0 decreased linearly.The reason was that with the increase of packing density, the pores between fibrous powders decreased, resulting in the space available for oil sorption decreased.For different types of oil, M 0 of mineral oil was slightly higher than that of PAO synthetic oil at the same packing density.It is mainly attributed to the oil density of mineral oil (0.85 g/cm 3 ) was slightly higher than that of PAO synthetic oil (0.82 g/ cm 3 ).When the oil sorption volume was fixed, denser oil had greater mass.As can be seen from Figure 5(b), D 0 decreased exponentially with the increase of the packing density, resulting from the increased flow resistance to oil.Under the same packing density, the D 0 of mineral oil was significantly higher than that of PAO synthetic oil.Viscosity of oil was a key factor affecting the sorption speed.The  higher the viscosity, the greater the viscosity resistance, the the fluidity, and the lower sorption coefficient.At 20°C, the viscosity of mineral oil (74.73 mPa • s) was much higher than that of PAO synthetic oil (29.55 mPa • s).Therefore, the sorption coefficient of mineral oil was lower than that of PAO synthetic oil.

Oil sorption mechanism analysis
According to the theoretical formula of the two-scale model and the relevant parameters of kapok fiber itself, the theoretical values of the sorption coefficient of the interfibrous pores (D e ) and the sorption coefficient of the fiber lumens (D i ) can be calculated.The sum of the two is the total sorption coefficient (D theory ).The model was verified by comparing the oil sorption coefficients obtained from the capillary rise test and their theoretical values, and the specific are shown in Tables 3 and 4.
Figure 6 shows the comparison of theoretical and experimental values of sorption coefficients.As can be seen from Figure 6, the experimental sorption coefficient values of the two test oils were in good agreement with the theoretical values of sorption coefficient derived from the two-scale model theory at the packing densities of 0.08 g/cm 3 and 0.10 g/cm 3 , with a deviation of less than 6%.In other words, The unit of sorption coefficient in the table is 10 −3 g 2 /s.The unit of sorption coefficient in the table is 10 −3 g 2 /s.its sorption characteristics conformed to the predications of the two-scale oil sorption model theory.
When the packing densities increased to 0.12 g/cm 3 and 0.14 g/cm 3 , the deviation increased obviously to 15-20%.This indicates that its adaptability to the two-scale model declined sharply under these packing densities.It is largely attributed to part of the lumens of the fibrous powder squashed to different degrees for compact assembly, the volume of the fibrous itself became smaller.It resulted in an increase in the porosity of the interfibrous powders, and the porosity of the fibrous powder itself decreased.According to formula ( 15) and ( 16), the value of D e increases and the value of D i decreases.For oil sorption KFP assembly, the pores between powders played a dominant in oil sorption, while the contribution of the internal lumen of fibrous powder to oil adsorption was secondary.The increase of D e was much greater than the decrease of D i .Therefore, the overall sorption coefficient of KFP material was larger compared to the theoretical value.Researchers reported a dual-scale model to study the relationship between the dual-scale pore structure (primary pores and secondary pores) of kapok/microfibrillated cellulose aerogels (Zhang et al. 2021).It was found that the experimental values of the porous aerogels with varying ratios of kapok and microfibrillated cellulose showed good consistency with theoretical values.However, the effect of packing density on porous aerogels was not considered.
From the above discussion, it can be concluded that for loose KFP assembly (packing density less than 0.10 g/cm 3 ), the established dual-scale theory model could accurately describe the oil sorption behavior.Therefore, according to formula ( 13) and ( 14), the amount of oil entering the interfibrous pores and lumens can be quantitatively characterized, as shown in Table 5. Figure 7 shows the oil distribution in the lumens and interfibrous pores of kapok fibrous.This study provides valuable insights into the practical application of the findings.The results indicate that the oil sorption behavior of KFP assemblies is strongly influenced by factors such as oil density, viscosity, and packing density.The threshold packing density of 0.10 g/cm 3 was identified as a crucial parameter for the potential use of KFP as a lubricant carrier.Below this threshold, KFP assembly exhibits excellent oil sorption ability and can serve as an effective potential carrier material.However, as the packing density exceeds this value, the effectiveness of KFP as a lubricant diminishes significantly.These findings have important implications for the design and selection of lubricant carrier materials, highlighting the need to consider the packing density and other factors that impact the oil sorption behavior.By understanding these factors, engineers and researchers can optimize the performance of lubricant carriers for various applications, leading to enhanced efficiency and effectiveness in lubrication systems.
While this study has provided valuable insights into the oil sorption behavior of KFP assemblies, there are certain limitations that should be acknowledged.First, the investigation focused on a specific range of particle sizes for the KFP assemblies.The impact of broader particle size ranges on the oil sorption mechanism remains an area requiring further exploration.Additionally, the influence of temperature on the properties of oil and the interaction between oil and fibrous porous materials was not considered in this study.Future research should aim to investigate the oil sorption mechanism of KFP assemblies with broader particle size ranges and explore the effect of temperature on the oil sorption behavior.These investigations will provide a more comprehensive understanding of the oil sorption process and contribute to the development of optimized lubricant carrier materials.

Conclusion
In summary, a dual-scale model was developed based on the Washburn capillary theory to investigate the oil wicking mechanism of KFP assembly.Capillary rise tests were employed to verify the applicability of the model, and the results demonstrated that the experimental sorption coefficient values were in good agreement with the theoretical values at low packing densities (0.08 ~ 0.10 g/cm 3 ).This finding confirms the high applicability of the model in describing the oil wicking behavior of KFP assembly.However, as the packing density increases, there is an observed increase in the deviation between the experimental results and the theoretical values.This can be largely attributed to the compression of the lumens with increased packing density, which reduces the oil sorption capacity into lumens, and the inferior applicability of dual-scale model.It is worth noting that a packing density of 0.10 g/cm 3 was identified as the threshold value for KFP, beyond which its potential as a lubricant carrier is not recommended.The proposed oil sorption model is significant in studying the relationship of pore structure and oil sorption of KFP and other porous materials, which could provide valuable insights for their practical applications.

Highlights
• Oil-impregnated kapok fibrous powder (KFP) as a potential lubricant carrier material was proposed.
• According to the characteristics of KFP assembly, a dual-scale model was established based on Washburn capillary theory.• The packing density of 0.01 g/cm 3 was proposed as threshold value for KFP assembly used as a potential lubricant carrier.

Figure 4 .
Figure 4. Relationship between the square of oil sorption mass and time (a) mineral oil, and (b) PAO synthetic oil.Solid line represents the linear fitting at the initial stage.

Figure 5 .
Figure 5. relationship between (a) saturated oil sorption, and (b) sorption coefficient of KFP to test oils with packing density.

Figure 6 .
Figure 6.Theoretical and experimental values of sorption coefficient (a) mineral oil, and (b) PAO synthetic oil.

Figure 7 .
Figure 7. Oil sorption in lumens and interfibrous pores of KFP, M i represents oil sorption in lumens, and M e represents oil sorption in interfibrous pores.

Table 1 .
Structural parameters of kapok fiber.

Table 2 .
Basic properties of test oils at 20°C.

Table 3 .
Experimental and theoretical values of sorption coefficient (mineral oil).

Table 4 .
Experimental and theoretical values of sorption coefficient (PAO synthetic oil).

Table 5 .
Theoretical values of oil sorption by interfibrous pores of KFP and kapok lumens.