Combing a double helix

Abstract: Combing hair involves brushing away the topological tangles in a collective curl. Using a combination of experiment and computation, we study this problem that naturally links topology, geometry and mechanics. Observations show that the dominant interactions in hair are those of a two-body nature, corresponding to a braided homochiral double helix. Using this minimal model, we study the detangling of an elastic double helix via a single stiff tine that moves along it, leaving two untangled filaments in its wake. Our results quantify how the forces of detangling are correlated with the magnitude and spatial extent of the link density, a topological quantity, that propagates ahead of the tine. This in turn provides a measure of the maximum characteristic length of a single combing stroke, and thus the trade-offs between comfort, efficiency and speed of combing in the many-body problem on a head of hair.