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The relationship between the unique internal structure of biomimic woven fabric and its moisture management property is investigated using fractal derivative method. The biomimic fabric exhibits a fractal hierarchic inner structure, and its fractal hierarchy can be further extended by fleece finishing treatment on both surfaces of the fabric. Fractal derivative analysis indicates that the fuzzy biomimic fabric with a higher hierarchic construction after fleece finishing performs better in moisture permeability, and the result was proved by experimental tests.

A woven fabric is generally produced by interlacing two sets of yarns, the warp and the weft which are at right angles to each other in the plane of cloth. The yarns constructing the fabric play an important part in transporting moisture from the microclimate between the skin and the garment to the outside atmosphere [

Tremendous methods have been promoted by researchers to improve the moisture permeation property of textile fabrics, such as choosing fibers with particular properties [

Many elegant solutions to engineering problems have been inspired by biological phenomena [

Our biomimic fabric includes three layers. Figure

Schematic diagram of the original biomimic thermal fabric structure.

In order to simplify the fabric structure and give a mathematic description, the interlacing pattern of warp yarns was regarded as a tree-shaped model, shown in Figure

Tree-shaped model of the biomimic fabric, (a) original biomimic fabric with three hierarchies and (b) fuzzy biomimic fabric with four hierarchies:

After fleece finishing, the original biomimic fabric became a fuzzy fabric. Both fabric surfaces are covered with a fluff layer, which can be regarded as corresponding to the leaves and tiny roofs in the tree-shaped model. In this case, the hierarchic structure of the tree-shaped model is extended from three hierarchies to four hierarchies, shown in Figure

Fractal dimension of the biomimic woven fabric can be calculated. Suppose that the original scale equals the diameter of the trunk of tree, that is, the width of four yarns

The above analysis shows that the fractal dimension values in the main branching level, the slim branching level, and the tiny leaves and roofs level of the fabric are around 1.6. It is obvious that the scale affects the fractal construction of the fabric, which will inevitably impact the heat and moisture transfer process through the thickness direction of the fabric.

The fractal derivative is a novel and effective analytical tool to deal with the heat and mass transfer problem in a discontinuous medium. Yang [

He [

Based on the fractal derivative theory, moisture permeation in the hierarchic fabric obeys fractal Fick’s law expressed as

According to the above definition, moisture flux through the original three-layer biomimic fabric without fleece finishing can be expressed as

Moisture flux through the three-layer fuzzy fabric after fleece finishing is

According to (

Two three-layer woolen biomimic fabrics were prepared for test: one was a fuzzy fabric with fluff height, 1.5 mm after fleece finishing, and the other was an original fabric without fleece finishing. Moisture resistant property of the two woolen fabrics was tested using a M925 Sweating Guarded Hotplate (SDL Atlas, USA). All the samples were conditioned for 48 h in the atmospheric conditions of temperature

In order to explain the intrinsic moisture transfer characteristic of the fabric samples, moisture conductivity was calculated using the following equation:

The calculated moisture conductivity of the two fabrics shown in Figure

Moisture conductivity of biomimic woolen woven fabric.

Moisture permeability of biomimic woven fabric with fractal characteristic was investigated using fractal derivative method. Fractal derivative analysis indicated that the fuzzy fabric after fleece finishing performs better in moisture management comparing with the original fabric without fleece finishing, and the result was proved by experimental test. The functional performance of biomimic fabric significantly depends on its hierarchic internal structure. Fractal derivative provides a novel method for optimalizing the structure of hierarchic textile materials.

The authors declare that there is no conflict of interests regarding the publication of this paper.

The work is supported by National Natural Science Foundation of China under Grants nos. 51203114 and 11372205, Special Program of China Postdoctoral Science Foundation Grant no. 2013T60559, China Postdoctoral Science Foundation under Grants no. 2012M521122, Postdoctoral Science Foundation Jiangsu Province Grant no. 1301151C, Natural Science Funds of Tianjin under Grant no. 12JCQNJC01500, Program for New Century Excellent Talents in University under Grants no. NCET-12-1063, College Students' Innovative Entrepreneurial Training Plan Program of Tianjin Polytechnic University (Zhi Liu), and PAPD (a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions).