1. Introduction

Porosity is the ratio of the total amount of void space in a material to the bulk volume occupied by the material. Fabric porosity is an important parameter in assessment of clothing comfort and physical properties of technical textiles. This paper reports the influence of constructional parameters of a woven fabric, such as yarn linear density, type of weave, and relative fabric density on the macropore area and its distribution. Predictive models of macropore area and macropore area distribution have been developed for engineering one-layer woven fabrics.

The production of modern woven fabrics demands developing strategies considering new structures. It is clear that a new fabric structure should have the desired quality at minimum production costs, and the highest possible weaving efficiency. Achieving such a demand is a complex task based on our knowledge of the connections between woven fabric structure parameters and the predetermined fabric properties that fit the desired quality. The evolution of ‘maximum construction theories’, as well as the fast development of computer science, allows us a faster and more precise planning of new products. In the field of ‘maximum construction theories’ some relationships are well known, which can, in the form of computer programs, serve as a part of an expert system for the development of new fabrics.

However, in the field of connections between the woven fabric structure and the individual fabric properties, such as for example porosity, a need arise further to determine some of such relationships; firstly should be developed a ‘maximum construction theory’ about square fabrics using simple geometry. Gee introduced the well known ‘ends plus intersection theory’, which he upgraded, and named the ‘curvature theory’ [1]. Until then a ‘maximum theory’ had been the subject of several research. Some researchers, such as Peirce, Love, Kemp, Hamilton, Weiner, Peirce & Womersley [2], Love, Kemp, Hamilton, and Weiner [3, 4, 5, 6] have used a more theoretical approach, whereas some other as Armitage, Law, Brierley, Seyam & El-Shiekh (1993), Gee (1953), and Brierley [7] used more experimental means. M. Kienbaum [8] has successfully joined theoretical and experimental investigations, and presented his own theory which can be applied to all weaves and different yarn structures.

Woven fabric, as a porous material, enables the transmission of energy in the form of light and heat, as well as of substances, such as liquids, gases and particles, and therefore is interesting for different applications, e.g. for garment and technical applications. Several experimental methods including optical methods, methods on the basis of liquid penetration, absorption, filtration, and airflow have been developed to determine the woven fabric’s porosity. All these methods can be used only on real fabrics. The geometrical method developed by Jakšić.[9] differs from the above-mentioned, as it is based on an ideal geometrical model of individual textiles, which are considered as porous materials, and on input data such as fiber length, fiber diameter, yarn linear density, and thread density. Such a method obviously does not need expensive laboratory equipment or sample weaving. However, the results of the geometrical method do not compare well with the real values determined by other experimental methods [10].

A new geometrical method to predict the macroporosity of woven fabrics developed by us, which is based on the tube-like system of the porous material and on two geometrical parameters of the woven structure, namely the thread density and the yarn linear density, is more precisely described as the effect of the linear density of threads, the weave factor, and the relative fabric density on the woven fabric’s macroporosity. New experimental models are proposed to predict the porosity in terms of the pore cross-section area, and the equivalent maximum and minimum pore diameters, pore density and open porosity. The models are based on the geometrical parameters of the woven structure, the thread linear density, the weave factor, and the relative fabric density. The main difference between the theoretical model, and the experimental models proposed in this study to predict the macroporosity of woven fabrics, is that the latter models also include the weave factor and the relative fabric density, as well as the geometrical parameters, which have a direct effect on all parameters of the woven fabric’s porosity. Besides that, the proposed experimental models are not based on an ideal model of porous structure, but on experiments, which better describe the real porous structure of woven fabrics.

A lot of models for description of porosity in woven fabrics can be made, among others such which describes the porosity between yarns (the inter-yarn porosity), and the porosity between fibers inside the yarn (the intra-yarn porosity). From the point of view of air permeability evaluation, this assumption is questionable for a tightly woven fabric with staple fiber yarn. Accepting the introduced assumption, a classical 2-D pore model seems to be sufficient. In a theory of a 2-D model, the porosity Ps is defined as a complement to the woven fabric cover factor CF. An area of pores is calculated as a perpendicular projection of the woven fabric. Real values can be measured as:

Ps = 1- CF = 1- (do Do +du Du - do du Do Du) (1)

where: do, du are the diameters of warp and weft yarn respectively, and Do, Du are the sets of warp and weft yarns respectively.

A classical 2-D model of porosity seems as insufficient for a tightly woven fabric. Neighboring yarns are very close and the projected area of inter-yarn pores approaches to zero. As air flows through the woven fabric, it flows around the yarns and it does not flow only in the perpendicular direction [11, 12].

When a woven fabric is treated as a three dimensional formation, the void spaces (called pores) could be situated in the fibers, between fibers in the thread, and between warp and weft threads in the fabric [13]. The latter of these above-mentioned pores are also called macropores, and will be the subject of the following discussion.

Woven fabrics, while compared to knitted fabrics or nonwovens, have the most exactly determined inner geometrical model of a porous structure in the form of a tube-like system, where the macropores has a cylindrical shape with a permanent cross-section over all its length [9]. To compare woven fabrics by their macroporosity, the following parameters are commonly used: the area of the pore cross-section, the pores’ area distribution, the pore density, the equivalent pore diameter, the maximum and minimum pore diameters, the pore length, and the pore volume, as well as the content of the open area and the content of the pore volume in relation to the total quantities of the fabric.

Within the black frame in the weave repeat of a plain weave, the area of the thread’s intersection (TI); the area of the weave passage (WI) and the area of the macropores (MP) are designated. Because warp density is usually greater than weft density, an elliptical shape of the pore cross-section is accepted to represent the situation.

Permeability is a feature, which represents the ease with which a fluid moves through a porous medium. The permeability of the textile medium is directly related to the volume of the fibre fraction of the textile medium. The various governing relationships that are used in this study of permeability, and the relation between permeability and fiber volume fraction are described in detail in the following chapters. The most commonly used description of the flow of a Newtonian fluid through a porous medium is that proposed by Darcy [14].

Permeability of porous materials depends very strongly on their morphological structure. Due to the complexity of the fiber architecture and the lack of an adequate mathematical model, many researchers continue to determine permeability experimentally. The main aim of theoretical analysis of air permeability of textile materials is usually to find a relationship between the air permeability and the structure of textiles. A textile structure is in this case usually represented by its porosity. A number of theoretical and experimental methods exist for the determination of porosity. Every method includes some simplifying assumptions which causes inaccuracy. Generally, the porosity indicates how much air contains a textile material with a given warp-ends density distribution. Further details about the configuration of pores in textiles, such as the pore size, shape, and arrangement are very important for the description of physical properties of multi-layer woven fabrics [13], and the air flow through textile materials. The subject of this research is:

1. To study the porosity models of multi-layer woven fabrics considering the flow interaction between porosity and thread distribution; this research modifies an existing three-dimensional model to include in it the simulation capabilities, and to verify this model with the fabrication of structural composites.
2. To characterise the eight-harness fabric (for use in processing) by the porosity, the thread distribution in the multi-layer woven fabric, the thickness, and the permeability.
3. To use the model for analysis of the manufacturing process, where this model should enable the user to design the best process for manufacturing composites of high quality.

2. Experimental study

3. Experimental methods

The experimental study was carried out as a new approach to predict the parameters of the woven fabric’s macroporosity by using a factor analysis based on the mathematical model developed by us.

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4. Results and discussion

The Modified 2-dimensional model of porosity, includes partly a 3-D structure of pores in the multi-layers. Various types of pores do not show the same relationship between the designed and the real effective area opened for the flow. The influence of the pores was described by a basic denting system of unit cells. According to [11], each type of woven fabric can be described by the following pore types. We created the pores into the double-layer of a woven fabric by the denting systems as are shown in Figures 1, 5 and 6 and Tables 2÷5

Correlation between porosity and air permeability of a fabric is very complicated because changes of the textile structure (by influence of the denting system), can be possible classified as a horizontal increase in porosity, by removing the free yarn section. Yarn are interlaced very closely in a plain weave; in twill or satin weaves a relative removing of yarns causes an increase in its porosity, predominantly in vertical direction. Air-flow through the fabric causes a move of not interlaced parts of yarn-floats which in textiles depends on the length of these floats. So the horizontal increase in porosity can result in a considerable increase in air-, moisture, and vapour permeability.

Figure 1. Denting regular system as 2/gate in reed for upper layer fabric (plain weave for lower layers) Table 2. Woven fabric construction

Parameter	Upper fabric	Lower fabric
Linear density of warp, tex	20.4	39.4
Linear density of weft, tex	39.4	39.4
Warp density, threads/cm	32	16
Weft density, threads/cm	18	16
Reed dents, threads per dents	2	2
Open Porosity, %	24.2	45.3
Weave structure	plain1/1	plain1/1

Figure 2. Cross-section (plain weave 1/1 for tow layers) Table 3. Woven fabric structure

Parameter	Upper fabric	Lower fabric
Linear density of warp, tex	20.4	39.4
Linear density of weft, tex	39.4	39.4
Warp density, threads/cm	32	16
Weft density, threads/cm	18	18
Reed dents, threads per dents	3	2
Open Porosity, %	15.9	45.3
Weave structure	basket 3/3	plain1/1

Table 4. Woven fabric structure

Parameter	Upper fabric	Lower fabric
Linear density of warp, tex	20.4	39.4
Linear density of weft, tex	39.4	39.4
Warp density, threads/cm	32 threads/cm	16
Weft density, threads/cm	18 threads/cm	18
Reed dents, threads per dents	3	2
Open Porosity, %	15.9	45.3
Weave structure	Twill 3/3	plain1/1

Figure 3. Cross-section (Twill weave 3/3 for upper and plain weave 1/1 for lower fabric)

Table 5. Woven fabric construction

Parameter	Upper fabric	Lower fabric
Linear density of warp, tex	20.4	39.4
Linear density of weft, tex	39.4	39.4
Warp density, threads/cm	32 threads/cm	16
Weft density, threads/cm	18 threads/cm	18
Reed dents, threads per dents	3	2
Open Porosity, %	18.6	45.3
Weave structure	Satin 6 weft	plain1/1

Figure 4. Fabric cross-section (Satin weave 6 weft for upper fabric and plain weave1/1 for lower fabric)

Figure 6. Reed denting system as 3:3:0 /3gate in reed for upper fabric

Table 6. Air permeability of fabrics with various densities

Fabric	Fabric code	Type of Weave		Weight per square meter, g	Cloth thickness, mm	warp Crimp C,%		Weft Crimp C,%		Air permeability, Ft3/ cm2
		upper	lower			Upper	lower	Upper	Lower
I	s tandard	Plain1/1	Plain1/1	276.6	0.82804	23.4	13.6	5.2	4.8	38
	B 1	Plain1/1	Plain1/1	268.8	0.82042	18.6	12	5.8	8.2	42 40 50
	B 2			288.7	0.82804	19.8	12.8	4.7	6.0
	B 3			297.6	0.82804	27	15.4	4.6	5.2
	C 1	Plain1/1	Plain1/1	292.05	0.87122	29.8	22.81	4.2	2.8	43 43.5 45
	C 2			292.6	0.8636	21.2	13.4	6.0	7.0
	C 3			299.4	0.82042	20.0	13.6	4.6	4.4
	D 1	Plain1/1	Plain1/1	317	0.90424	15.4	17	5.2	5.4	69 63 75
	D 2			321	0.8636	21.8	20.6	7.4	8.4
	D 3			316	0.889	26.6	20.6	10.4	8.6
II	standard	twill 3/3	Plain1/1	252.4	0.92202	10.4	11.8	5.2	6.2	35
	B 1	twill 3/3	Plain1/1	275	0.87884	8.4	13.6	4.8	4.3	39 40 49
	B 2			281.6	0.904	9.2	13	3.4	3.7
	B 3			292	0.92202	11.8	15.6	4.4	4.0
	C 1	twill 3/3	Plain1/1	294.65	0.889	13.6	15.2	7.2	5.8	47 54 54
	C 2			289.89	0.9144	14.4	16	11.8	7.2
	C 3			305	0.9398	23.8	18	5.8	5.4
	D 1	twill 3/3	Plain1/1	305	0.9271	23	16	6.8	8.4	46 58 55
	D 2			297	0.94488	25	16	6.5	5.6
	D 3			294	1.00	19	12.5	8.9	8.8
III	standard	Satin 6 weft	Plain1/1	289	0.980	11.6	12.8	3	3.2	35
	B 1	Satin 6 weft	Plain1/1	281.3	0.8788	8.4	13.6	4.8	4.3	49 57 58
	B 2			280.78	0.955	9.2	13	3.4	3.7
	B 3			293.5	0.9728	11.8	15.6	4.4	4.0
	C 1	Satin 6 weft	Plain1/1	295.66	0.9271	12.6	18.2	3.4	4.2	51 72 76
	C 2			300.75	0.9398	10.2	13	4.2	2.4
	C 3			306.5	0.9398	7.6	8	6.2	3.8
	D 1	Satin 6weft	Plain1/1	327	0.998	13	22	4.2	5.8	49 76 99
	D 2			324	1.02362	12	19.8	5.4	4.8
	D 3			317	1.1684	11	22	5	5.6

The fabrics were made from cotton yarns produced at twist factor 4 with (S) direction for warp and with twist factor 4.4 with (Z) direction for weft.