Painting with drops, jets, and sheets
A. Herczynski, C. Cernuschi, and L. Mahadevan, Physics Today June 2011, 31-36.
Author: Sofia Magkiriadou, Fall 2011
Note: The document is protected so the figures could not be pasted. The article has been attached for convenience.
The authors examine the fluid mechanics behind the artistic style introduced by American painter Jackson Pollock. Pollock developed a novel painting technique based on dipping a trowel in viscous paint and then translating it over a canvas in three dimensions; translations in the plane parallel to the canvas defined the directions of his lines whereas translations in height resulted in variations in their thickness. A characteristic sample of this technique is shown in Figure 1. While the artist gained physical intuition about the dependence of the flow of his paints on their viscosity and his movements, the physics behind it have not been fully described. In this article, a description of the fundamental principles behind this technique is presented.
PAINTING WITH DROPS
As can be seen in Autumn Rhythm, Pollock used primarily long, continuous streams of paint to compose his figures and shapes. In order to form such lines, he employed a long and thin trowel which he dipped into a can of paint, lifted rapidly to carry a big blob of paint with it, and then maneuvred it over his canvas, which the paint reached through a continuous viscous jet. He sometimes employed discontinuous drops, which were often created as the blob of paint ran out and the jet broke into discrete gusts of flow. It is possible to create drops from an otherwise continuous jet by thrusting the trowel - a technique used by another artist, Robert Motherwell (Figure 2). However, from the circular shape and the range of diameter values of the spots found on Pollock's paintings we can infer that his drops were the result of jet breakdown due to a decrease in flow rate: according to the Rayleigh formula, which relates the mass of a drop (m) to the surface tension of the liquid (γ), the diameter of the rod it drips from (ρ) and the gravitational acceleration (g), m ~ γ*ρ/g, for a given rod and liquid all drops produced that way should have the same diameter. This is consistent with the features of the spots seen in Pollock's paintings.
PAINTING WITH JETS
The use of a trowel really gave Pollock a high degree of control over the form of his lines, as can be understood if we take a closer look at the mechanics of paint dispensing. Consider a rod of radius r dipped to a depth L and then pulled out of a container full of paint of viscosity μ, density ρ, and kinematic viscosity ν = μ/ρ as shown in Figure 3. The thickness of the collected liquid h depends on the speed uo at which the rod is pulled out of the liquid and it is determined by the interplay between the force of gravity, which pulls the liquid downwards, and viscous forces, which hold the liquid together: h ~ (v*uo/g)^(1/4). To maintain h constant against gravity, one can rotate the rod in exactly the same way that one can take honey out of a bowl without making a mess. If the loaded rod is kept stationary, however, gravity will cause a jet to form. The flow rate of this jet will depend on the system parameters via Q ~ ρ*uo^(3/2)*(v/g)^1/2. The artist had control over almost all of these parameters: the radius of his trowel, the speed at which he pulled it out of the paint container, its angular velocity - for maintaining a constant h when so desired - and the viscosity of the paint (which can be reduced through dilution with one or more solvents). By additionally changing the distance between the trowel and the canvas, he could adjust the thickness of the jet creating the impression of lateral acceleration on a stationary painting. An interesting phenomenon briefly explored by Pollock is folding and coiling instability, as shown in Figure 5. Three regimes have been identified to describe the mechanism behind this process: the inertial regime, where viscous forces and inertia are balanced; the viscous regime, in which gravity and inertia are negligible and the net viscous forces on each liquid segment are zero; and the gravitational regime, where viscous forces and gravity are balanced. In the painting shown (Figure 2) we can see an example of the use of coiling which seems to correspond to the inertial regime. This follows from the dimensions and periodicity ω of the drawn coils, which follows the relation ω ~ ν^(-1/3)*r^(-10/3)*Q^(4/3). Reasonable values for these quantities match what we observe. The use of two paints on this work gives us a chance to observe the effect of viscosity in coiling instability; while modulating patterns can be observed in red, the black ink was less viscous, was absorbed more by the canvas, and did not show coiling. The superposition of coiling with transverse motion, achieved as the coiling jet is translated over the canvas, yields yet more possibilities, depending on the relative magnitude of the translational speed U to the modulation frequency ω and the amplitude of oscillations R, St = U/(omega*R). When St<1 the coils are clearly imprinted; when St~1 the result is a line with periodically spaced cusps; as St exceeds 1 the result is a sinusoid that eventually approaches a straight line. All three effects have been employed in this painting.
PAINTING WITH SHEETS
Painting with sheets is a yet unexplored technique, most likely due to the further technical challenges it involves which might constrain the degree of control seeked by artists for freedom of expression. As a potential application of this technique, the authors propose the use of a can full of paint with a thin slit through which sheets of paint may flow with a continuous front, without breaking into jets due to surface tension inhomogeneities. The aesthetic appeal of this or analogous techniques is yet to be explored.
While science and art are often considered independent of each other, artists use material means and thus the forms of their work are directly influenced by the physical laws governing their behavior. It is up to the artist to learn how to manipulate his or her tools to their desire, and it is tempting for the scientist to inquire about the mechanism behind the artistic results. In the case of Pollock, empirically acquired intuition allowed the use of fluid mechanics towards the creation of artworks in ways that were only much later put in a quantitative frame by scientists. Could the reverse process also be fruitful? The author of this summary believes so.