Autocatalytic plume pinch-off

A localized source of buoyancy flux in a nonreactive fluid medium creates a plume. The flux can be provided by either heat, a compositional difference between the fluid comprising the plume and its surroundings, or a combination of both. For autocatalytic plumes produced by the iodate-arsenous acid reaction, however, buoyancy is produced along the entire reacting interface between the plume and its surroundings. Buoyancy production at the moving interface drives fluid motion, which in turn generates flow that advects the reaction front. As a consequence of this interplay between fluid flow and chemical reaction, autocatalytic plumes exhibit a rich dynamics during their ascent through the reactant medium. One of the more interesting dynamical features is the production of an accelerating vortical plume head that in certain cases pinches-off and detaches from the upwelling conduit. After pinch-off, a new plume head forms in the conduit below, and this can lead to multiple generations of plume heads for a single plume initiation. We investigated the pinch-off process using both experimentation and simulation. Experiments were performed using various concentrations of glycerol, in which it was found that repeated pinch-off occurs exclusively in a specific concentration range. Autocatalytic plume simulations revealed that pinch-off is triggered by the appearance of accelerating flow in the plume conduit.

Figure 1

A schematic of the apparatus. The reactant solution is contained in one of two different cylinders used for the experiments. These cylinders have lengths of 32 and 40.6 cm, and both have inner diameters of 8.9 cm. The capillary tube has an inner diameter of 2.7 mm.

Figure 2

(Color online) The morphology of autocatalytic chemical starting plumes in (a) water, and in glycerol concentrations of (b) 20%, (c) 30%, (d) 40%, and (e) 50%. All images are of plumes at a height of $\sim 20\text{cm}$ from the outlet. It took the plumes (a) 255, (b) 555, (c) 425, (d) 449, and (e) 681 s to ascend to this height before these images were captured.

Figure 3

(Color online) The height as a function of time for five plume heads produced by a 40% glycerol run in the 40.6 cm long cylinder. Lines indicate linear fits to the five consecutive data points with the maximum slope. Slopes of lines such as these were used to determine $v_{max}$ for each plume head.

Figure 4

(Color online) The average plume head Reynolds number $⟨{\text{Re}}_h⟩$ for glycerol solutions characterized by various Schmidt numbers, Sc. Diamond symbols indicate runs that did not pinch-off in the short cylinder apparatus. Circular points indicate that pinch-off occurred, with shaded (red) points indicating conditions under which two or more pinch-offs were observed.

Figure 5

(Color online) The aspect ratio $w_h/{\ell }_h$ for autocatalytic plumes in a 30% (dark circles, blue online) and 40% (light circles, orange online) glycerol solution. The horizontal gray line indicates the constant value of $w_h/{\ell }_h=1.24\pm 0.04$ for nonreacting forced plumes [7]. Here, $t=0$ corresponds approximately to when a vortex ring first forms in the head, not to the moment when the reaction front emerges from the capillary tube.

Figure 6

(Color online) The radius of curvature $R_c$ of the crest of an autocatalytic plume head as a function of time. The two straight lines are fits to the data before and after pinch-off. The inset shows the crest of an autocatalytic plume head and the best fit circle that describes its shape. The head was imaged at a height of 16.7 cm above the outlet, 448 s after the front emerged from the capillary.

Figure 7

(Color online) The cylindrical coordinate system used, with the concentration field for a plume produced by the simulation.

Figure 8

(Color online) The (a) concentration, (b) temperature, and (c) vorticity fields for an autocatalytic plume that has pinched-off. The concentration profile shows a plume with $c=1$ separated from the surrounding fluid with $c=0$ by a thin reaction front. The spatial domain for the simulation was $r_b=500\ell$ and $z_b=2000\ell$, only data in the region bounded by $r=300\ell$ and $z=1500$ is shown. The time after initiation is $42.5\tau$.

Figure 9

(Color online) (a) The height of first and second generation simulated plume heads as a function of time. (b) The width to length $w_h/{\ell }_h$ aspect ratio and (c) the radius of curvature $R_c$ of the crest of the first generation head. The shaded region in (c) shows the constant aspect ratio of nonreacting forced plumes [7]. Parts (a), (b), and (c) show simulation data that correspond to the experimental data presented in Figs. 3, 5, 6, respectively.

Figure 10

(Color online) A space-time diagram showing the development of the centerline velocity $v_c$ of a simulated plume. The units of $v_c$ are $\ell /\tau$.