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Beitr. Tabakforsch. Int., 1989, 14-5, p. 253-60. ISSN.0173-783X

The viscous and inertial flow of air through perforated papers

BAKER R.R.
British American Tobacco, R&D Centre, Southampton, UK
The total flow of air through perforated cigarette paper 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 = ZAP + Z'AP exn 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'.