Herczyński, Cernuschi, and Mahadevan reply: Since our primary aim was to invite readers to consider very simply the physics of pouring paint, we modeled paint as a Newtonian liquid. That model, as Michael Nauenberg writes, assumes a linear relation between the stress and the strain rate. Paint, a suspension of pigments and polymers in a solvent, may indeed exhibit nonlinear rheological characteristics. Taking that into account would lead to slightly different relationships than those we propose, but many of the qualitative features—for example, the coiling patterns on the substrate—would remain the same. However, effects due to elastic stresses, surface-tension gradients during drying, and so forth are not included in our description. We should have clearly noted the caveats of our minimal approach but are glad to have the opportunity to do so now.
Nauenberg also claims that our qualitative sketch of a thinning paint stream is inconsistent with observations. In fact, the shape of a draw-down jet is controlled by the competition between viscous and gravitational forces via the dimensionless parameter µ2/ρ2gR3, where R is the radius of the jet at its origin, μ is the viscosity, ρ is the density, and g is the acceleration due to gravity. For highly viscous paints, the parameter is large, and thinning would be relatively gradual as a result.
Helen Harrison is correct to point to Jackson Pollock’s wide range of implements, such as brushes of different bristle types and basting syringes. The artist kept experimenting and exploited many other techniques, even occasionally imprinting the canvas with his hand. Different tools produced different flows depending on the way Pollock employed them, though one cannot reliably infer a given technique from a given mark. Although those issues deserve attention, our study focused on the artist’s most characteristic and distinctive effects: the linear tracks that appear in the poured abstractions he created between 1947 and 1950.
