Study of dielectric behaviour of woven fabric based on two phase models Kausik Bal, V.K. Kothari * Department of Textile Technology, Indian Institute of Technology, 8 New Campus, Hauz Khas, New Delhi, Delhi 110016, India article info Article history: Received 29 November 2008 Received in revised form 13 March 2009 Accepted 7 May 2009 Available online 12 June 2009 Keywords: Capacitance Dielectric constant Fibre HDPE Mathematical model Monofilaments Peirce’s fabric geometry Textile Woven fabric abstract Dielectric constant of textile fibres plays very important role in electrostatic behavior of textile materials during its processing and use. The effective dielectric constant of textile materials is defined as the ratio of capacitance of a parallel plate capacitor with the textile material to that of the capacitor without the textile material. This paper presents three models considering textile woven fabric as a mixture of air and fibre to relate dielectric constant of fibre material and the effective dielectric constant of fabric. The mathematical models have taken into account measured fabric parameters. Plain woven fabrics of high density polyethylene monofilament yarns were used to do the actual measurement and results of three models based on these fabrics are compared. Ó 2009 Elsevier B.V. All rights reserved. 1. Introduction Theoretical studies on dielectric behaviour of textile substrates kept between two parallel capacitor plates have been done by many researchers in the past. Some of these studies considered the behaviour of a fibrous mass under an electric field without considering any particular textile structure. Morton and Hearle [1] has discussed various such models which were empirically proposed to calculate the dielectric constant of fibres from capac- itance of a fibrous mass of a given porosity. Boyd [2] developed an equation to calculate the change in capacitance of a parallel plate capacitor when a straight yarn is passed through the space between the plates. His equation had the yarn porosity, fibre density and dielectric constant of the fibre material as material parameters which could be effectively used to establish a mathematical rela- tionship between the change in capacitance Dc and the linear density of the yarn. Mack [3] has investigated the factors that determine the behaviour of a cylindrical dielectric such as a textile fibre or yarn when kept between a parallel plate capacitor. Recently, Alekseeva [4] has derived equation relating the capacitance and dielectric constant of textile fibre material in a solid or hollow cylindrical shape. However, theoretical work on the dielectric behaviour of fabrics seems to be a rare thing in literature. The present paper proposes three models to establish a relationship between the dielectric constant of the fibre material and the capacitance of a parallel plate capacitor with the woven fabric between the parallel plates. The ratio of the capacitance of a parallel plate capacitor with a uniform homogeneous dielectric material occupying the entire space between the plates to that of the same capacitor system with air or vacuum occupying the entire volume between the plates is known as the dielectric constant or relative dielectric permittivity of the dielectric material. In case of a heterogeneous material such as a textile fabric material which is a mixture of air and fibres, the same ratio can be called as effective dielectric constant of the air-fibre mixture. For the sake of simplicity, the fabric has been considered to be consisting of only fibrous polymers and air, i.e., the effect of moisture has not been considered. Hence the present work is only limited to models having only two phases: fibres and air. The basic approach has been to incorporate the measurable fabric parameters in the model in order to make the theory useful. Three mathematical models have been discussed and proposed in this relation in this paper starting from an equivalent sheet which resembles the existing approaches that relates the dielectric * Corresponding author. Tel.: þ91 11 2659 1407; fax: þ91 11 2658 1103. E-mail address: kotharivk@gmail.com (V.K. Kothari). Contents lists available at ScienceDirect Journal of Electrostatics journal homepage: www.elsevier.com/locate/elstat 0304-3886/$ – see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.elstat.2009.05.005 Journal of Electrostatics 67 (2009) 751–758