Mechanisms leading to the formation of double-diffusive layers during unidirectional solidification of aqueous ${\mathrm{NH}}_4\mathrm{Cl}$ solution

The phenomenon of unidirectional solidification of binary solutions leads to various flow patterns such as solute fingers, plumes, and double-diffusive layers (DDLs) due to density variations arising out of the coupled effects of thermal and solutal gradients. The present work reports experiments to elucidate the transport phenomena responsible for the formation of DDLs during unidirectional solidification of aqueous ${\mathrm{NH}}_4\mathrm{Cl}$ solution in a narrow solidification chamber. The spatiotemporally resolved flow and transported properties associated with the phenomenon have been determined through a combination of nonintrusive techniques. Dual-wavelength interferometry has been used for simultaneous measurement of temperature and salt concentration distributions. Various subprocesses such as convection transients, plume formation, and evolution of DDLs that result in the formation of the stepped structure of solutal-thermal gradients have been mapped through rainbow-schlieren deflectometry. Flow velocities have been quantified using PIV. Based on the whole-field measurements, plausible mechanisms responsible for the development and further evolution of DDLs have been identified. Direct experimental observations revealed the existence of counter-rotating rolls near the chamber sidewalls. Interaction of these convective rolls with the plumes originating from the mushy zone results in a downward inclination of DDLs (towards plume locations), thus giving DDLs a slanted shape instead of their horizontal orientations. The alternate sense of rotation of convective rolls in the adjacent DDLs has been explained through observations made using different experimental techniques. Experimental results are additionally supported with analytical scales of flow parameters such as plume velocity, diameter, the height of DDLs, the downward velocity of DDLs, etc.

Figure 1

Schematic setup of solidification chamber.

Figure 2

Optical configuration of rainbow-schlieren deflectometry setup.

Figure 3

Optical configuration of dual-wavelength interferometer.

Figure 4

Schematic diagram of PIV setup.

Figure 5

Rainbow-schlieren observations at different instants of time.

Figure 6

DDLs position at different time instants.

Figure 7

Thermocouples based temperature variation as a function of experimental run time.

Figure 8

Dual-wavelength interferograms during the experimental run time.

Figure 9

Variation of composition of binary solution on the top of the chamber during the experimental run time.

Figure 10

(a) Dual-color interferogram at $t=270\min$, (b) temperature field at $t=270\min$, (c) composition field at $t=270\min$, (d) dual-color interferogram at $t=320\min$, (e) temperature field at $t=320\min$, (f) composition field at $t=320\min$, (g) dual-color interferogram at $t=480\min$, (h) temperature field at $t=480\min$, and (i) composition field at $t=480\min$.

Figure 11

Velocity components (m/s) during the unidirectional solidification of water-28wt.% ${\mathrm{NH}}_4\mathrm{Cl}$ solution.

Figure 12

Vorticity components (1/s) during the unidirectional solidification of water-28 wt.% ${\mathrm{NH}}_4\mathrm{Cl}$ solution.

Figure 13

Convection roll formation in a zero gradient density field by exposing a lateral thermal gradient.

Figure 14

Schematic diagram showing formation of DDLs in a pre-existing vertically varying compositional field by exposing a lateral thermal gradient.

Figure 15

Schematic diagram to show different stages for the formation of DDLs: (a) Vertically stable compositional gradient with lateral cooling by plume, (b) initiation of convection rolls, (c) existence of convection rolls A and B, (d) formation of convection rolls C and D, (e) direction of movement of fluid inside convection rolls, (f) expanded DDLs, (g) representative schlieren observation, (h) representative interferometric observation, and (i) representative vorticity field with velocity vector.

Figure 16

Schematic diagram representing the physical processes before the onset of DDLs.

Figure 17

Plot of (a) $x$ and $y$ component of velocities ($V_x$ and $V_y$) and (b) density profile along the height of the fluid domain (the vertical sections considered to plot the profiles are indicated as dashed line in both the PIV and schlieren images shown in the inset of each figure).

Figure 18

Infinite fringe setting: (a) combined interferogram of red and blue, (b) corresponding red interferogram, and (c) corresponding blue interferogram.