Fluid physics of telescoping cardboard boxes

The economics, environmental impact, and mechanical properties of paper-based storage containers have been widely studied. However, knowledge of the physical processes relevant to the end-user experience is unavailable. This presentation outlines the main effects associated with the closing and opening of telescoping boxes, which are used, for instance, to store and transport board games, footwear, mobile phones, and tablet computers. The sliding motion of the lid is controlled by flow in a thin film of air in the gap separating the top and base of the box. Based on a broad comparison between theory and experiments on natural and synthetic boxes, we find that the process is primarily controlled by the detailed shape of the gap between the base and the lid. Three distinct experimental regimes are observed, and an optimal design for a rapidly closing box is identified.