National Textile Center

Project Team:

Leader: Matthew W. Dunn, Textile Materials Science

Email: mdunn@fibers.texsci.edu Phone: (215) 951-2683

Objective:

Arterial graft fabrics are required to have minimal thickness yet maintain specified levels of strength and blood permeability. The models of thickness and strength are fairly well understood. But, although there is significant work in the literature addressing the flow of fluid through fabric structures (see McGregor, Peirce, Backer, etc.) this work has focused on Newtonian fluid flow through regular structures. It is well known that blood behaves in a non-Newtonian manner and can even be considered as an Einsteinian particulate reinforced fluid.

The use of small yarns (1-7 tex) and small fibers (1-5 m m diameter) in the production of the fabrics requires improved modeling capabilities. Since blood cells are similar in dimension to the fibers, the presence of these cells directly influences the flow through the fabric.

Thus the overall objectives of this program are

• Model the flow of Newtonian fluid through fabrics
• Model non-Newtonian, heterogeneous particulate reinforced fluid
• Model the flow of non-Newtonian fluid through fabrics
• Develop fabric constructions to minimize thickness, maintain strength and permeability based on model parameters
• Evaluate the performance of the designed fabrics
• Compare experimental and theoretical predictions

Relevance to NTC Mission:

The major goals of the NTC that will be fulfilled are 1) the development of accurate fabric permeability modeling, and 2) the development of new weaving configurations with improved fabric properties. The evolution of the textile industry has been inexorably linked to the dynamic interaction of fabrics and fluids. Properties such as filtering, permeability, dyeability, and porosity are directly related to fluid flow through a porous structure. To model fabric porosity and the resulting permeability of non-Newtonian particulate reinforced fluids would be beneficial to multidisciplinary technical fields.

State of the Art:

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The filtration performance of fabrics has been examined for a number of years [ , , for example] and can be described mathematically in many ways. One approach is to describe the flow of air or fluid through a filtration media based on the properties of the air or fluid penetrant. Fluid flow through a porous membrane can be described by the relationship

(1)

where m is the viscosity of the fluid, t the thickness of the membrane, V the velocity of the fluid, and DP the pressure drop across the membrane. Equation (1) is one form of Darcy’s Law [], named for the French engineer who published an equivalent relation based on experiments with the water supplies for fountains in the city of Dijon []. Here B is considered as a constant for the relationship between V and DP and is called Darcy’s constant or (more

commonly) the permeability of the membrane. The value for B will depend on the type of porous media and the pore geometry.

To account for void content, the Kozeny-Carman equation was developed to provide a description of fluid flow based on the filtration media properties. One form of this equation [] is

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(2)

where K₀ is the Kozeny Constant, S₀ a shape factor, and F the media porosity. The shape factor is found from

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(3)

where the solid phase characteristics are based on the construction and content of the filtration media. It has been found that image analysis methods applied to equation (3) may yield reasonable results when predicting the Kozeny-Carman parameters by providing a realistic measurement of pore size and distribution [].

The Kozeny-Carman equation is designed for a packed porous bed with random, tortuous paths available for fluid flow. This assumption is representative of the pore assembly present in a nonwoven fabric with random fiber orientations throughout the fabric structure, but has also been shown to have the capability of being extended to woven and knitted textile structures. Pierce [] attempted to describe the resistance a textile material will exhibit based on material properties:

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(4)

where R is the resistance to flow, S the surface of void channels per unit mass (or the total specific surface of the media mass), and r the overall mass density of constituents within the media. Pierce noted that this is in fact a method of "extreme simplification," and suggested that the shape factor be determined empirically, with the other variables being calculated from derived relationships. This equation was the first published attempt at describing fluid flow through textile materials.

Ergun [], working with experimental results gathered from filtration media based on different shape parameters, developed the following relationship for filtration media with cylindrical solid constituents:

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(5)

where f is a shape factor, D the diameter of the cylinders, and g_c the gravitational constant.

MacGregor [] extended the Kozeny-Carman equation for a textile assembly in order to model the flow of dyes through textile yarn packages. If the solid phase is composed of circular fibers with diameter d, it can be easily found that for textile beds:

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(6)

The MacGregor equation provides a method to predict permeability based on fiber diameter and fabric porosity. Our current objectives include predicting fabric permeability and examining the predictions through experiment.

Approach:

The following proposed approach will be used to accurately model woven fabric properties. The approach used to reach the stated goals of this proposal are broken down into tasks and listed below:

I. Model fluids as Einsteinian particulate reinforced fluids. The viscous properties of blood are known and the elastic properties of blood cells are known. A model of the heterogeneous mixture can be developed following the models of Einstein. The predictions will be compared with experimental data, and model fluid systems will be identified which have similar mechanical responses to blood.

II. The flow of the heterogeneous fluid through porous media will be modeled starting with tradition flow through porous media models (e.g., Kozeny-Carman) and modifying them to account for the non-Newtonian fluid and the nonlinear "clogging" of the fabric due to blood cell presence.

III. Establish a controlled set of fabric tests (ASTM and AATCC) as well as other in-house designed tests to quantify the fabric performance. These will be used to describe weaving variables.

IV. Compare the quantified fabric properties collected from Task III, to investigate the model accuracy.

V. Iterate and improve the computer porosity model to correlate tested fabric properties.

VI. Model and predict different fabric properties and then compare these results to a matching manufactured fabric.

By accurately modeling a woven fabric, the researchers will be able to determine the relationship of fluid visco-elastic response, pore size and distribution, fabric thickness, yarn type, yarn size, and yarn packing factor, to fabric porosity.

This Year’s Goal:

(Refer to descriptions in Task I and II)

1. Model of Newtonian Fluids and fabric geometry
2. Manufacture a woven fabric using a low denier yarn with high end count, test the fabric using ASTM tests and then compare to the models porosity values.

Outreach to Industry:

Many companies (Albany International, Prodesco, Dupont, etc.) have voiced an interest in understanding the flow of non-Newtonian fluids through a fabric structure. This area of investigation has validity in numerous textile fields, including dyeing, filitration, and chemical protection. The work will be presented in a variety of means, specifically through technical conferences and journals.

New Resources Required:

None.