A mathematical model of a tubular fiber is analyzed to predict its rigidity and some of its physical properties which are essential in textiles. The change in the properties of a tubular fiber with increase in the size of hollow core is considered and compared with the cylindrical fiber of the same outside diameter, the same denier, and the same rigidity as that of the tubular fiber. The equations are developed in dimensionless quantities to make them invariant to the units of fiber dimensions. The analysis revealed that having a hollow core of 4/1Oth the size of the outside diameter, in a solid fiber, could reduce the fiber weight by 16% without making any significant change in the rigidity of the fiber.
A t present, different deniers of synthetic fibers are produced for fiberfill. Six denier fibers are used as filling fibers in pillows, 15 denier fibers in furniture, and 40 denier for filtration purposes.2 These fibers are 2-2.5 in. in staple length and made of polyester materials. In some cases the central core is made hollow which is approximately 15% of the total cross-sectional area of the fiber. The use of such fibers gives a 10-12% saving of the material. The fibers are crimped by stuffer-box technique to give them more bulk. Some fibers have their surface modified to give low stiffness properties to the product.
Use of tubular fiber in place of cylindrical fiber would affect the physical and mechanical properties of a p r ~d u c t . ~-~ Tubular fiber has higher bulk, crimp, covering power, thermal insulation, and absorbing capacity in comparison to cylindrical fiber.3 Short tubular fibers will have more crimp because of the difference in stresses on the inner and outer walls of the fiber tube during extrusion. The use of tubular fibers in sleeping bags showed better thermal insulation as compared to the use of cylindrical fibers? This increase in insulation was due to the amount of dead-air trapped in the tubular fibers.