Dyeable Polypropylene Fiber

The ability to dye polypropylene fibers using conventional disperse dyes makes the fibers more attractive for apparel end-uses.

TW Special Report

Polypropylene fibers possess a number of attractive properties when compared to other fibers (See Table 1). Despite desirable properties, polypropylene fibers traditionally have suffered from a major drawback that has limited their adoption in textile apparel applications: In contrast to other fibers, conventional polypropylene fibers cannot be dyed. Instead, the color has to be imparted at the fiber extrusion step through mass coloration or solution dyeing. The process involves adding a relatively thermally stable pigment color during the melt spinning of the fiber. The pigments used are not usually miscible with polypropylene. Thus, the pigments are present as discrete particles in the fiber, and the color imparted becomes permanent in the fiber. While this has the benefit of very good colorfastness, there are two significant disadvantages. The first is that introducing new colors involves a relatively complex color-matching step. The second is the absence of greige goods to be dyed. This means that relatively large lots of fiber are made for every new color, and the time required to go from a new color concept to the final fabric or garment can be long.

There has been a long-standing interest in commercializing a dyeable polypropylene fiber. Ideally, it should have a dyeing profile similar to or compatible with large-volume fibers such as polyester, nylon or cotton, so that it is compatible with the dyeing and related processes that are already well-established. Furthermore, it should not change the essential benefits of polypropylene fibers presented in Table 1, especially its low density and its low surface energy. There have been several attempts to make dyeable polypropylene fibers, but they have not been successful because the resulting product did not meet these criteria.
FiberVisions has developed a revolutionary new polypropylene fiber, CoolVisions™ dyeable polypropylene fiber, that meets the needs of facile dyeing and polypropylene fiber characteristics by incorporating an additive within the polypropylene fiber. The fiber can be dyed using conventional disperse dyes in a manner similar to that used for polyester fibers. The fibers feature a wide array of inherent benefits and properties including:

  • light weight and comfort;
  • cottony softness;
  • easy care, easy wear;
  • moisture management;durability;
  • breathability;
  • thermal insulation; and
  • stain resistance.


Lightweight And Comfortable

Polypropylene fibers are among the lightest in weight of all commercial fibers. The increased number of polypropylene fibers per kilogram of fabric offers added value compared to many other fibers, resulting in improved coverage for the same weight range or equal coverage in lighter-weight fabrics for comfortable garments. In addition, CoolVisions fibers are inherently softer than traditional polypropylene fibers, resulting in greater comfort, according to FiberVisions. This combination of attributes makes garments made from these new fibers inherently easy care, easy wear.

Moisture Management

According to FiberVisions, CoolVisions polypropylene fibers outperform all other dyeable fibers in low-moisture-absorption tests. In addition, garments made from polypropylene tend to have a high moisture-vapor-transmission rate. This is important in comfort, especially when one wants the skin to stay cool and dry. The mechanical properties of polypropylene fibers are not affected when the fabric is wet an inherent advantage compared to fibers like rayon, which can lose strength substantially.
As with traditional polypropylene, CoolVisions offers excellent chemical resistance and aqueous stain resistance. Bleach and other household cleaning chemicals do not affect the fibers, which also are not attacked by microbial organisms such as mold, mildew and bacteria.

Dyeable polypropylene fibers are suitable for apparel end-uses including sports applications.

Dyeing Characteristics

CoolVisions dyeable polypropylene fibers can be dyed using commonly available polyester high-energy disperse dyes and in standard high-pressure dyeing processes used for polyester fibers, but with lower dyeing temperatures possible. The color range and color-matching process are similar to those for polyester fibers.
The ability to dye fabrics results in many benefits over the use of fabrics made with traditional solution-dyed fibers, including value chain and styling benefits. Some of the value-chain benefits include the ability to store greige goods, match colors quickly, produce smaller lot volumes and serve niche or fashion-related color lines, respond rapidly to market demand, and offer a wider range of colors without greatly increasing inventory costs. There are added financial benefits from reduced working capital needs and shortened production times. Styling benefits include reduction in barré found in solution-dyed garments and the ability to print with dye inks rather than pigment inks. Dye-printed fabrics exhibit a softer hand and better colorfastness than pigment-printed fabrics. CoolVisions fibers also have been engineered to have an inherently soft hand and cotton touch not found in traditional polypropylene fibers.
As noted previously, CoolVisions fibers contain an additive that acts as a dye receptor. The additive is present in the fibers as small domains into which the disperse dyes dissolve during the dyeing process. At dyeing temperatures greater than the boiling point of water, the disperse dyes diffuse readily through the polypropylene fiber into the encapsulated domains of the additive. Under actual garment use conditions — which include much lower temperatures — the diffusion of the disperse dyes back out of the fiber is greatly diminished, resulting in good colorfastness. As with polyester fibers, high-energy disperse dyes should be used to obtain optimum colorfastness.
The approach of encapsulating the additive within the polypropylene fiber has many benefits. The surface of the fiber is essentially unchanged, resulting in excellent aqueous stain resistance and low water absorption. The polypropylene fiber also serves to protect the dyes from chemicals such as chlorine, resulting in excellent bleach fastness.
Since the ability to dye the polypropylene fiber is imparted by the incorporation of an additive, the level of the additive affects the depth of shade. This has a couple of benefits, according to FiberVisions: The additive level can be controlled quite well, resulting in reduced shade sensitivity to processing conditions. In addition, the level can be intentionally changed to produce fibers that dye to different depths, thereby offering an additional styling tool.
FiberVisions officially launched CoolVisions dyeable polypropylene fibers at the recent Outdoor Retailer Show in Salt Lake City. A number of partner companies are currently working with these fibers to develop new fabrics and apparel styles. Activities are underway to develop air-jet spun and filament-type products to broaden the range of styling tools.

September/October 2006




A number of methods are available for characterization of the structural, physical, and chemical properties of fibers. The major methods available are outlined in this chapter, including a brief description of each method and the nature of characterization that the method provides.

Optical and Electron Microscopy

Optical microscopy (OM) has been used for many years as a reliable method to determine the gross morphology of a fiber in longitudinal, as well as cross-sectional views. Mounting the fiber on a slide wetted with a liquid of appropriate refractive properties has been used to minimize light scattering effects. The presence of gross morphological characteristics such as fiber shape and size and the nature of the surface can be readily detected. Magnifications as high as 1,500X are possible, although less depth of field exists at higher magnifications. Scanning electron microscopy (SEM) can be used to view the morphology of fibers with good depth of field and resolution at magnifications up to 10,000X. In scanning electron microscopy, the fiber must first be coated with a thin film of a conducting metal such as silver or gold. The mounted specimen then is scanned with an electron beam, and back-scattered particles emitted from the fiber surface are detected and analyzed to form an image of the fiber. Transmission electron microscopy (TEM) is more specialized and more difficult to perform than SEM. It measures the net density of electrons passing through the thin cross sections of metal-coated fibers and provides a method to look at their micro-morphologies.

Elemental and End-Group Analysis

The qualitative and quantitative analysis of the chemical elements  and groups in a fiber may aid in identification and characterization of a fiber. Care must be taken in analysis of such data, since the presence of dyes or finishes on the fibers may affect the nature and content of elements and end groups found in a given fiber. Gravimetric and instrumental chemical  methods are available for analysis of specific elements or groups of elements in fibers. Specific chemical analyses of functional groups and end groups in 26 Tufted Carpet
organic polymers that make up fibers may be carried out. For example, analyses of amino acids in protein fibers, amino groups in polyamides and proteins, and acid groups in polyamides and polyesters aid in structure determination, molecular characterization, and identification of fibers.

Infrared Spectroscopy

Infrared spectroscopy is a valuable tool in determination of functional  groups within a fiber. Functional groups in a polymer absorb infrared energy at wavelengths characteristic of the particular group and lead to changes in the vibrational modes within the functional group. As a result of the infrared absorption characteristics of the fiber, specific functional groups can be identified. Infrared spectroscopy of fibers can be carried out on the finely divided fiber segments pressed in a salt pellet, or through the use of reflectance techniques. Functional groups in dyes and finishes also can be detected by this technique.

Ultraviolet-Visible Spectroscopy

The ultraviolet-visible spectra of fibers, dyes, and finishes can provide clues concerning the structure of these materials, as well as show the nature of electronic transitions that occur within the material as light is absorbed at various wavelengths by unsaturated groups giving an electronically- excited molecule. The absorbed energy is either harmlessly dissipated as heat, fluorescence, or phosphorescence, or causes chemical reactions to occur that modify the chemical structure of the fiber. Ultraviolet-visible spectra can be measured for a material either in solution or by reflectance. Reflectance spectra are particularly useful in color measurement and assessment of color differences in dyed and bleached fibers.

Nuclear Magnetic Resonance Spectroscopy

Nuclear magnetic resonance (NMR) spectroscopy measures the relative magnitude and direction (moment) of spin orientation of the nucleus of the individual atoms within a polymer from a fiber in solution in a highintensity magnetic field. The degree of shift of spins within the magnetic field and the signal splitting characteristics of individual atoms such as hydrogen or carbon within the molecule are dependent on the location and nature of  Fiber Identification and Characterization the groups surrounding each atom. In this way, the “average” structure of long polymeric chains can be determined. Line width from NMR spectra also can provide information concerning the relationship of crystalline and amorphous areas within the polymer.

X-Ray Diffraction

X-rays, diffracted from or reflected off crystalline or semicrystalline polymeric materials, give patterns related to the crystalline and amorphous areas within a fiber. The size and shape of individual crystalline and amorphous sites within the fiber are reflected in the geometry and sharpness of the x-ray diffraction pattern and provide an insight into the internal structure of the polymeric chains.

 Thermal Analysis

Physical and chemical changes in fibers may be investigated by measuring changes in selected properties as small samples of fiber are
heated at a steady rate over a given temperature range in an inert atmosphere such as nitrogen. There are four thermal characterization methods.

1. Differential thermal analysis (DTA)
2. Differential scanning calorimetry (DSC)
3. Thermal gravimetric analysis (TGA)
4. Thermal mechanical analysis (TMA)

In DTA, small changes in temperature (ΔT) in the fiber sample compared to a reference are detected and recorded as the sample is heated. The changes in temperature (ΔT) are directly related to physical and chemical events occurring within the fiber as it is heated. These events include changes in crystallinity and crystal structure, loss of water, solvents and volatile materials, and melting and decomposition of the fiber. Differential scanning calorimetry is similar to DTA, but measures changes in heat content (ΔH) rather than temperature (ΔT) as the fiber is heated; it provides quantitative data on the thermodynamic processes involved. In an inert gas such as nitrogen, most processes are endothermic (heat absorbing). If DTA or DSC is carried out in air with oxygen, data may be obtained related to the combustion characteristics of the fiber, and fiber decomposition becomes exothermic (heat generating). Thermal  radiometric analysis measures changes in mass (ΔΜ) of a sample as the temperature is raised at a uniform rate. It provides information concerning loss of volatile materials, the rate and mode of decomposition of the fiber, and the effect of finishes on fiber
decomposition. Thermal mechanical analysis measures changes in a specific mechanical property as the temperature of the fiber is raised at a uniform rate. A number of specialized mechanical devices have been developed to measure mechanical changes in fibers, including hardness and flow under stress.

Molecular Weight Determination

Molecular weight determination methods provide information concerning the average size and distribution of individual polymer molecules making up a fiber. Molecular weights enable one to calculate the length of the average repeating unit within the polymer chain, better known as the DP. The distribution of polymer chain lengths within the fiber provides information concerning selected polymer properties.
The major molecular weight determination methods include number average molecular weights (M¯ n), determined by end-group analysis, osmometry, cryoscopy, and ebullioscopy; weight average molecular weights (M¯ w), determined by light scattering and ultracentrifugation; and viscosity molecular weights (M¯ v), determined by the flow rate of polymer solutions. Since each method measures the average molecular weight of the polymer differently, the molecular weight values obtained will differ depending on the overall number and distribution of polymer chains of varying lengths present in the fiber. The differences in value between M¯ n and M¯ w provide measures of the breadth of distribution of polymers within the fiber. By definition the distribution of molecular weights for a given polymer will always be M¯ w > M¯ v > M¯ n.

Mechanical and Tensile Property Measurements

Mechanical and tensile measurements for fibers include tenacity or tensile strength, elongation at break, recovery from limited elongation, stiffness (relative force required to bend the fiber), and recovery from bending. The tensile properties of individual fibers or yarns are usually measured on a tensile testing machine such as an Instron®, which subjects  fibers or yarns of a given length to a constant rate of force or loading. The force necessary to break the fiber or yarn, or tenacity, is commonly given in grams per denier (g/d) or grams per tex (g/tex), or as kilometer breaking length in the SI system. The elongation to break of a fiber is a measure of the ultimate degree of extension that a fiber can withstand before breaking. The degree of recovery of a fiber from a given elongation is a measure of the resiliency of the fiber to small deformation forces. The stiffness or bendability of a fiber is related to the overall chemical structure of the macromolecules making up the fiber, the forces between adjacent polymer chains, and the degree of crystallinity of the fiber. Mechanical and tensile property measurements can provide valuable insights into the structure of a fiber and its projected performance in end use.

Specific Gravity

The specific gravity of a fiber is a measure of its density in relation to the density of the same volume of water, and provides a method to relate the mass per unit volume of a given fiber to that of other fibers. The specific gravity relates in some degree to the nature of molecular packing, crystallinity, and molecular alignment in the fiber. Specific gravity of a fiber will give an idea of the relative weight of fabrics of identical fabric structure, but of differing fiber content. End-use properties such as hand (feel or touch), drapability, and appearance are affected by fiber density.

Environmental Properties

Environmental properties include those physical properties which relate to the environment in which a fiber is found. Moisture regain, solvent solubility, heat conductivity, the physical effect of heat, and electrical properties depend on the environmental conditions surrounding the fiber. The uptake of moisture by a dry fiber at equilibrium will depend on the temperature and relative humidity of the environment. Solvent solubilities of fibers will depend on the solubility parameters of the solvent in relation to fiber structure and crystallinity. Heat conductivity, the physical effect of heating such as melting, softening, and other thermal transitions, and the electrical properties of a fiber depend on the inherent structure of the fiber and the manner in which heat or electrical energy is acted upon by the macromolecules within the fiber. Environmental properties are measured by subjecting the fiber to the appropriate environmental conditions and measuring the property desired under such conditions.

Chemical Properties

The chemical properties of fibers include the effects of chemical agents like acids, bases, oxidizing agents, reducing agents, and biological agents such as molds and mildews on the fiber, and light- and heat-induced chemical changes within the fiber. Acids and bases cause hydrolytic attack of molecular chains within a fiber, whereas oxidizing and reducing agents cause chemical attack of functional groups through oxidation (removal of electrons) or reduction (addition of electrons). Such chemical attack can change the fiber’s structure and possibly cleave the molecular chains within the fiber. Biological agents such as moths on wool or mildew on cellulose use the fiber as a nutrient for biological growth and, subsequently, cause damage to the fiber structure. Sunlight contains ultraviolet, visible, and infrared light energy. This energy can be absorbed at discrete wavelength ranges by fibers depending on their molecular structure. Ultraviolet and visible light absorbed by a fiber will cause excitation of electrons within the structure, raising them to higher energy states. Shorter ultraviolet wavelengths are the most highly energetic and give the most highly excited states. Visible light usually has little effect on the fiber, although its absorption and reflectance of unabsorbed light will determine the color and reflectance characteristics of the fiber. Infrared energy absorbed will increase the vibration of molecules within the fiber andwill cause heating. The excited species within the fiber can return to their original (ground) state, through dissipation of the energy as molecular vibrations or heat, without significantly affecting the fiber. Ultraviolet and some visible light absorbed by the fiber, however, can lead to molecular scission within the fiber and cause adverse free radical reactions, which will lead to fiber deterioration.

Heating a fiber to progressively higher temperatures in air will lead to physical as well as chemical changes within the fiber. At sufficiently high temperatures, molecular scission, oxidation, and other complex chemical reactions associated with decomposition of the fiber will occur causing possible discoloration and a severe drop in physical and end-use properties for the fiber.

Carbon Fiber (Bamboo Charcoal)

Wove by Carbon fiber yarn, Used as Fireproof cloth, like as against for welding fire in Shipbuilding Line, the cloth are long lasting, and very safe to human skin, can replace other fireproof cloth, include glass fiber cloth, ceramic fiber cloth and asbestos fiber cloth. Bamboo charcoal yarn is produced by bamboo charcoal fiber. The bamboo charcoal fiber is one of the common fibers, each fiber is with honeycomb paths and these paths run through from inside to outside. This design can put the function of bamboo charcoal into full play. This fiber is an innovation of textile material.image


Anion Generator: Bamboo Charcoal Fiber can release 2600 anions per cm3. As we know, anions are very helpful for our health, for example, activating our cells of body, purifying our blood, free from tiredness, calming vegetative nervous system, improving allergic constitution, etc. 82% negative ions can be absorbed by our skin, so it is a good option to increase anions for health improvement by using Bamboo Charcoal fiber textiles.

  • High ability of absorption and deodorization Moisture Management
  • Bacteria and mildew resistant.
  • Absorb moisture, quick dry,
  • breathe freelyGood
  • Anti-pilling and Anti-fuzzing

Fiber Migration in yarn structure

Yarn structure plays a key role in determining the yarn physical properties and the performance characteristics of yarns and fabrics. The best way to study the internal structure of the yarns is to examine the arrangement of single fibers in the yarn body, and analyze their migration in crosswise and lengthwise fashions. This requires visual observation of the path of a single fiber in the yarn. Since a fiber is relatively a small element some specific techniques have to be utilized for its observation. In order to perform this task, two different experimental techniques have been developed by previous researchers.

a. Tracer fiber technique: This technique involves immersing a yarn, which contains a very small percentage of dyed fibers, in a liquid whose refractive index is the same as that of the original undyed fibers. This causes the undyed fibers to almost disappear from view and enables the observation of the path of a black dyed tracer fiber under a microscope. Dyed fibers are added to the raw stock before spinning to act as tracers. This technique was introduced by Morton and Yen .

b. Cross sectional method: In this method first the fibers in the yarn are locked in their original position by means of a suitable embedding medium, then the yarn is cut into thin sections, and these sections are studied under microscope. As in the tracer fiber technique, the yarn consists of mostly undyed fibers and a small proportion of dyed fibers such that there is no more than one dyed fiber in any yarn cross-section.

Fiber Migration

Fiber migration can be defined as the variation in fiber position within the yarn. Migration and twist are two necessary components to generate strength and cohesion in spun yarns. Twist increases the frictional forces between fibers and prevents fibers from slipping over one another by creating radial forces directed toward the yarn interior while fiber migration ensures that some parts of the all fibers were locked in the structure.

It was first recognized by Pierce that there is a need for the interchange of the fiber position inside a yarn since if a yarn consisted of a core fiber surrounded by coaxial cylindrical layers of other fibers, each forming a perfect helix of constant radius, discrete layers of the yarn could easily separate. Morton and Yen discovered that the fibers migrate among imaginary cylindrical zones in the yarn and named this phenomenon “fiber migration.”

Mechanisms Causing Fiber Migration

Morton [42] proposed that one of the mechanisms which cause fiber migration is the tension differences between fibers at different radial positions in a twisted yarn. During the twist insertion, fibers are subjected to different tensions depending on their radial positions. Fibers at the core will be under minimum tension due to shorter fiber path while fibers on the surface will be exposed to the maximum tension. According to the principle of the minimum energy of deformation, fibers lying near the yarn surface will try to migrate into inner zones where the energy is lower. This will lead to a cyclic interchange of fiber position. Later Hearle and Bose  gave another mechanism which causes migration. They suggested that when the ribbon-like fiber bundle is turned into the


Apart from the theoretical work cited above, several experimental investigations have been carried out during 1960’s to find out the possible factors affecting fiber migration. Results showed that the fiber migration can be influenced mainly by three groups of factors:

q fiber related factors such as fiber type, fiber length, fiber fineness, fiber initial modulus, fiber bending modulus and torsional rigidity;

q yarn related factors, such as yarn count and yarn twist ; and

q processing factors such as twisting tension, drafting system and number of doubling.

Methods for Assessing Fiber Migration

To study fiber migration Morton and Yen introduced the tracer fiber method. As explained in the previous section, this method enables the observation of the path of a single tracer fiber under a microscope. In order to draw the paths of the tracer fibers in the horizontal plane, Morton and Yen made measurements at successive peaks and troughs of the tracer images. Each peak and trough was in turn brought to register with the hairline of a micrometer eyepiece and scale readings were taken at a, b, and c as seen in Figure 22. The yarn diameter in scale units was given by c-a, while the offset of the


peak or trough, the fiber helix radii, was given by

The distance between

adjacent peaks and troughs was denoted by d. The overall extent of the tracer fiber was obtained from the images, as well. Morton and Yen concluded that in one complete cycle of migration, the fiber rarely crosses through all zones of the structure, from the surface of the yarn to the core and back again, which was considered as ideal migration.


Later Morton [42] used the tracer fiber method to characterize the migration quantitatively by means of a coefficient so called “the coefficient of migration.” He proposed that the intensity of migration i.e., completeness of the migration, or otherwise, of any migratory traverse could be evaluated by the change in helix radius between successive inflections of the helix envelope expressed as the fraction of yarn radius. For example intensity of migration in Figure 23 from A to B was stated as


where rA and rB are helix radius at A and B, respectively and R is yarn radius.

In order to express the intensity of migration for a whole fiber, Morton used the coefficient of migration, which is the ratio of actual migration amplitude to the ideal case. The coefficient of migration was given by




Merchant [ 1 ] modified the helix envelope by expressing the radial position in terms of (r / R) in order avoid any effects due to the irregularities in yarn diameter. The plot of (r / R) along the yarn axis gives a cylindrical envelope of varying radi
us around which the fiber follows a helical path. This plot is called a helix envelope profile. Expression of the radial position in terms of (r / R) involves the division of yarn cross sections into zones of equal radial spacing, which means fibers present longer lengths in the outer zones. Hearle et al. [18] suggested that it is more convenient to divide the yarn cross sections into zones of equal area so that the fibers are equally distributed between all zones. This was achieved by expressing the radial position in terms of (r / R)2, and the plot of (r / R)2against the length along the yarn is called a corrected helix envelope profile which presents a linear envelope for the ideal migration if the fiber packing density is uniform (Figure 24). The corrected helix envelope profile is much easier to manage analytically.


In 1964 Riding [52] worked on filament yarns, and expanded the tracer fiber technique by observing the fiber from two directions at right angles by placing a plane mirror near the yarn in the liquid with the plane of the mirror at 45° to the direction of observation. The radial position of the tracer fiber along the yarn was calculated by the following equation:


where x and y are the distances of the fiber from the yarn axis by the x and y co­ordinates; and dx and dy are the corresponding diameter measurements.

Riding also argued that it is unlikely that any single parameter, such as the coefficient of migration will completely characterize the migration behavior due to its statistical nature. He analyzed the migration patterns using the correlogram, or Auto-correlation Function and suggested that this analysis gives an overall statistical picture of the migration. Riding calculated the auto-correlation coefficient, rs from a series of

values of r / R for a separation of s intervals and obtained the correlogram for each experiment by plotting rs against s. Later a detailed theoretical study by Hearle and Goswami showed that the correlogram method should be used with caution because it tends to pick up only the regular migration.

Hearle and his co-researchers worked on a comprehensive theoretical and experimental analysis of fiber migration in the mid 1960’s. In Part I of the series Hearle, Gupta and Merchant came up with four parameters using an analogy with the method of describing an electric current to characterize the migration behaviors of fibers.

These parameters are:

i. the mean fiber position, which is the overall tendency of a fiber to be near the yarn surface or the yarn center.


ii. r.m.s deviation, which is the degree of the deviation from the mean fiber position


iii. mean migration intensity, which is the rate of change in radial position of a fiber.


iv. equivalent migration frequency, which is the value of migration frequency when an ideal migration cycle is formed from the calculated values of I and D.


r is the current radial position of the fiber with respect to the yarn axis;

R is the yarn radius;

n is the number of the observations; and

Zn is the length of the yarn under consideration

By expressing the migration behavior in terms of these parameters, Hearle et al. replaced an actual migration behavior with a partial ideal migration which is linear with z (length along the fiber axis) but has the same mean fiber position, same r.m.s deviation, and the same mean migration intensity.

Later Hearle and Gupta [20] studied the fiber migration experimentally by using the tracer fiber technique. By taking into consideration the problem of asymmetry in the yarn cross section they came up with the following equation:



r1 and r2 are the helix radii

R1 and R2 are the yarn radii at position z1 and z2 along the yarn.

In 1972 Hearle et al. carried some experimental work on the migration in open-end spun yarns, and they observed that migration pattern in open-end yarns was considerably different from that of ring spun yarns. They suggested that this difference was the reason for the dissimilarity between mechanical and structural parameters of these two yarns.

Among numerous investigations of migration, there have been some attempts to develop a numerical algorithm to simulate yarn behavior. Possibly the most promising

and powerful approach was to apply a finite element analysis method to the mechanics of yarns.

One of the most recently published researches on the mathematical modeling of fiber migration in staple yarns was carried out by Grishanov, et al. They developed a new method to model the fiber migration using a Markov process, and claimed that all the main features of yarn structure could be modeled with this new method. In this approach the process of fiber migration was considered as a Poisson’s flow of events, and the fiber migration characteristics were expressed in terms of a transition matrix.

Another recent study was done by Primentas and Iype. They utilized the level of the focusing depth of a projection microscope as a measure of the fiber position along the z-axis with respect to the body of the yarn. Using a suitable reference depth they plotted the possible 3-dimensional configuration of the tracer fiber. In this study they assumed that yarn had a circular cross section and the difference between minimum and maximum values in depth represented the value of the vertical diameter, which was also equal to horizontal diameter. However, the yarn is irregular along its axis, and its cross section deviates from a circle. Besides, it is questionable that the difference between minimum and maximum values in depth would give the value of the vertical diameter. As these researchers stated this technique is in the “embryonic stage of development.”