Conduits of steady-state autocatalytic plumes

Plumes are typically formed when a continuous source of buoyancy is supplied at a localized source. We studied laminar plumes where buoyancy is supplied by an autocatalytic chemical reaction: The iodate-arsenous acid (IAA) reaction. The nonlinear kinetics of the IAA reaction produces a sharp propagating front at which buoyancy is produced by exothermicity and compositional change. When the reaction is initiated in an unconfined volume of reactant, a starting plume with a mushroom shaped head connected to the initiation point by a long conduit is formed. After the initial transient during the ascent of the head, we observed the emergence of a steady state in the conduit morphology and flow. Autocatalytic plumes were compared to nonreacting, compositionally buoyant plumes using the Gradient Echo Rapid Velocity and Acceleration Imaging Sequence (GERVAIS), an MRI velocimetric technique. Autocatalytic conduits had axisymmetric bimodal velocity profiles and cone-shaped morphologies, in contrast to the Gaussian profiles and cylindrical shapes of nonreacting conduits. The bimodal distribution for autocatalytic plumes is a consequence of the unique effect of entrainment in this system. Rather than the usual effect of entrainment in nonreacting plumes, where less buoyant fluid is incorporated into the plumes, entrainment in autocatalytic plumes provides a buoyancy flux along the entire conduit by means of chemical reaction, thereby delocalizing the buoyancy source.

Figure 1

(Color online) Top: Schematic diagram of the cylindrical reaction vessel placed inside the bore of the MRI spectrometer (shown in cross section). Bottom: Typical MRI velocity image of an autocatalytic chemical plume when the imaging region is $15\mathrm{cm}$ above the outlet of the capillary tube. The size of the imaging region in view is $64\times 64\mathrm{mm}$, and $v_z=0$ is indicated by the color of the imaging region surrounding the pipe.

Figure 2

(Color online) Sequence of images during the evolution of an autocatalytic chemical plume. During the ascent of the plume head toward the top of the container, as shown in (a) through (c), the plume head grows, and in (d) it pinches off, forming a free vortex ring. The point of pinch off proceeds to swell, nucleating a new plume head. As the steady flow of product solution moves upward by means of the conduit, a growing volume of product solution accumulates at the top of the vessel, as shown in (e) and (f). Using $t=0$ as the time at which the front first emerged from the capillary tube, the times at which the pictures were taken in (a) through (f) are $t=67$, 253, 371, 443, 1492, and $2302\mathrm{s}$, respectively. The distance from the capillary tube to the top surface of the fluid is $21.6\mathrm{cm}$; the inner diameter of the cylinder containing the plume is $8.9\mathrm{cm}$.

Figure 3

(Color online) Averaged axial velocity profiles derived from MRI velocity images for (a) a compositionally buoyant plume $10\mathrm{cm}$ from the capillary tube outlet produced by an injection flow rate of $2.0\mathrm{mL}∕\min$, and an autocatalytic plume (b) $10\mathrm{cm}$ from the outlet and (c) $15\mathrm{cm}$ from the outlet. $r$ indicates the distance from the plume axis, and $a$ is the radius of the glass tube. Vertical lines represent the location of the reaction front, or plume edge. The curve in (a) shows a Gaussian fit of the velocity data, and the curves in (b) and (c) show axisymmetric bimodal Gaussian fits. Gaussian fits were performed only for positive velocity values. Negative velocities are due to the broad downward return flow generated by the plume. The number of consecutive velocity images averaged for each profile were (a) 36, (b) 91, and (c) 128, where each velocity image was $3\mathrm{s}$ apart.

Figure 4

(Color online) Left: Typical morphology of a compositional and an autocatalytic plume, obtained from image analysis of experimental data, shown to scale. Right: Radius of the autocatalytic plume $(▵)$ and compositional plume $(○)$, and their lines of best fit, as a function of height from the capillary tube outlet.

Figure 5

Simple geometrical model of an autocatalytic plume conduit. The cone half-angle is $\theta$; the radius of the cone as a function of distance above $z=0$ is $\mu \left(z\right)$.