Pine Research Group
Hydrodynamic Reversibility

FIG. 1. G.I. Taylor's film clip showing hydrodynamic reversibility.

Hydrodynamic reversibility in viscous liquids

It is well known that the flow of a slowly sheared viscous liquid is reversible. This is dramatically demonstrated in a film clip (Fig. 1) made by G.I. Taylor in which a colored droplet is introduced into a viscous liquid contained between two transparent concentric cylinders (an arrangement known as a Couette cell). When the inner cylinder is rotated through several revolutions, the colored droplet is sheared with the rest of the liquid and is stretched into a barely visible pink ribbon winding around the Couette cell (see Fig. 1 film clip). When the direction of the inner cylinder is reversed, the thin pink ribbon of fluid reforms the original spherical droplet, dramatically illustrating the reversibility of the flow.

Hydrodynamic reversibility in viscous suspensions

FIG. 2. Animation of oscillatory Couette flow with a particle suspension in the gap between the two cylinders concentric. [Quicktime required]

In a series of experiments, we investigate reversibility in non-Brownian particle suspensions. We employ a Couette cell filled with a viscous liquid similar to that used for the film clip in Fig. 1. However, we make one important change: we load the liquid with small (0.22 millimeter) spheres. The spheres are density matched to the liquid, to avoid settling, and index matched, so that they are invisible. We adjust the concentration of the particles so that they occupy about 30% of the total (liquid + particle) volume.

In order to follow the motion of the suspended particles, a very small fraction of the particles are dyed black (depicted as black dots in Fig. 2), rendering them visible while the vast majority of particles remain invisible. These are shown in the left hand panels in Figs. 3 & 4, which are actual pictures taken from our experiments. Alternatively, we introduce a fluorescent dye into the liquid in which the particles are suspended and excite it with a sheet of intense light. In this case, all the particles appear as dark dots on a bright background. These are shown in the right hand panels in Figs. 3 & 4.

To test whether the flow is reversible, we rotate the inner cylinder of the Couette cell a small distance back and forth as shown in Fig. 2, taking a picture each time the inner cylinder returns to its original position. If the flow is reversible, all the particles return to their original positions. In this case, the stoboscopic movie (one frame per cycle) of the particle positions is static. On the other hand, if the flow is not reversible, the particles do not return to their original positions. In this case, the stroboscopic movie shows particles not returning to their original positions: instead, they jump about.

Reversible Partical Motion

FIG. 3. Stroboscopic movie showing reversible particle motion. This is what is observed when the suspension of particles is not sheared too far, that is, if the inner cylinder is rotated back and forth only a small distance. Nothing appears to move as each particle returns to the same position every cycle. [Quicktime required]

Irreversible Partical Motion

FIG. 4. Stroboscopic movie showing irreversible particle motion. This is what is observed when the suspension of particles is sheared farther than some critical amount, that is, if the inner cylinder is rotated back and forth a relatively large distance. [Quicktime required]