On Fluffing of Cards

Abstract

When a stack of identical thin cards is placed in a straight rectangular channel so that the planes of the cards are parallel to the channel axis and an air flow is started, it is observed that under suitable conditions the cards get separated from the walls and each other if they are free to do so. This is called fluffing of cards. A two-dimensional analysis based on an application of the principle of minimum dissipation to viscous flows through card gaps is presented to explain the dynamical behavior of the fluffed cards. It is found that the state of uniform distribution is not only the state of static equilibrium but also, the state of absolute minimum viscous energy dissipation. The analysis determines the forces tending to separate the cards and then the equations for small amplitude oscillations of the cards about the state of uniform distribution. These equations are solved for corresponding modes and frequencies.