<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This study investigates by nonlinear constitutive equations the influence of tipping paper, cigarette paper, filter, and tobacco rod on the degree of filter ventilation and draw resistance. Starting from the laws of conservation, the path to the theory of fluid dynamics in porous media and Darcy's law is reviewed and, as an extension to Darcy's law, two different nonlinear pressure drop-flow relations are proposed. It is proven that these relations are valid constitutive equations and the partial differential equations for the stationary flow in an unlit cigarette covering anisotropic, inhomogeneous and nonlinear behaviour are derived. From these equations a system of ordinary differential equations for the one-dimensional flow in the cigarette is derived by averaging pressure and velocity over the cross section of the cigarette. By further integration, the concept of an electrical analog is reached and discussed in the light of nonlinear pressure drop-flow relations. By numerical calculations based on the system of ordinary differential equations, it is shown that the influence of nonlinearities cannot be neglected because variations in the degree of filter ventilation can reach up to 20% of its nominal value.</p></abstract>

This study investigates by nonlinear constitutive equations the influence of tipping paper, cigarette paper, filter, and tobacco rod on the degree of filter ventilation and draw resistance. Starting from the laws of conservation, the path to the theory of fluid dynamics in porous media and Darcy's law is reviewed and, as an extension to Darcy's law, two different nonlinear pressure drop-flow relations are proposed. It is proven that these relations are valid constitutive equations and the partial differential equations for the stationary flow in an unlit cigarette covering anisotropic, inhomogeneous and nonlinear behaviour are derived. From these equations a system of ordinary differential equations for the one-dimensional flow in the cigarette is derived by averaging pressure and velocity over the cross section of the cigarette. By further integration, the concept of an electrical analog is reached and discussed in the light of nonlinear pressure drop-flow relations. By numerical calculations based on the system of ordinary differential equations, it is shown that the influence of nonlinearities cannot be neglected because variations in the degree of filter ventilation can reach up to 20% of its nominal value.

The Use of Nonlinear Constitutive Equations to Evaluate Draw Resistance and Filter Ventilation

Tann Papier GmbH, Fabrikstrasse 20, 4050 Traun, Austria

Contributions to Tobacco & Nicotine Research

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

This study investigates by nonlinear constitutive equations the influence of tipping paper, cigarette paper, filter, and tobacco rod on the degree of filter...

The Use of Nonlinear Constitutive Equations to Evaluate Draw Resistance and Filter Ventilation

Published Online: Dec 30, 2014

Page range: 177 - 188

Received: Apr 10, 2000

Accepted: Sep 21, 2000

DOI: https://doi.org/10.2478/cttr-2013-0706

© 2014 Beiträge zur Tabakforschung International

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.