The Viscous and Inertial Flow of Air through Perforated Papers

Inherently porous cigarette paper consists of an interlocking network of cellulose fibres interspersed with chalk particles. Spaces in this matrix are of the order of 1 AAµm wide which is small compared to the paper thickness (usually 20 AAµm to 40 AAµm). However, when cigarette paper is perforated after the paper-making process, e.g. by an electrostatic or mechanical process, the perforation holes are relatively large, usually having mean diameters of the same order of magnitude as the paper thickness. The total flow of air through perforated cigarette paper thus consists of two components: viscous flow through the porous structure of the paper inherent from the paper-making process, and inertial flow through the perforation holes. Since the air flow / pressure relationships due to these two components of flow differ and since the two components are additive, the total flow through perforated paper may be expressed as: Q = Z A P + Z’ A Pn, where Q is the air flow (cm3 min-1), A is the area of paper (cm2) exposed to the flowing air, P is the pressure difference across the paper (kilopascal), Z is the base permeability of the paper due to viscous flow through the spaces inherent from the paper-making process (cm min-1 kPa-1 or Coresta unit), Z’ is the permeability of the paper due to inertial flow through the perforation holes (cm min-1 kPa-1/n) and n is a constant for a given set of perforation holes. This equation adequately describes gas flow through a variety of perforated cigarette and tipping papers. By using different gases, it is confirmed that Z depends on viscous forces and Z’ depends on inertial forces. By examining the flow of air through a large number of papers with perforation holes of different sizes, it is shown that Z’ is dependent on the total area of perforation holes, and that a jet-contraction effect occurs as the air travels through the paper. The parameter n is shown to have a value between 0.5 and 1.0, and this value is related to mean perforation-hole size. The permeability of cigarette paper is defined as the flow of air through the paper when the pressure across the paper is 1 kilopascal. Thus from the above equation the “total permeability” of perforated cigarette paper is equal to Z + Z'.