Dissolution regimes of a horizontal channel in a gravity field

Buoyancy-driven dissolution of the solid phase is common in natural processes and subsurface applications, such as geomorphology, solution mining, and geological ${\mathrm{CO}}_2$ storage. When an external horizontal flow is imposed, the dissolution dynamics are controlled by the interplay between buoyancy-driven and forced convections. The reshaping of the solid surface due to this interplay is not well understood. Here, we fabricate a soluble microfluidic chip with a horizontal channel to investigate the pore-scale dissolution dynamics in a gravity field. We observe that the wave number and the surface roughness factor of the upper solid-liquid interface initially increases with the flow rate (Péclet number Pe) and then decreases, indicating two dissolution regimes, namely, Regimes I and II. Microparticle-image-velocimetry-based imaging reveals that the eddy evolution occurring in the flow-dissolution system controls the local dissolution rate and the geometry evolution of the solid-liquid interface. Through the quantification of the eddies (or troughs) for the whole channel, the number of the eddies increases with Pe in Regime I and decreases with Pe in Regime II, indicating that the buoyancy-driven convection is enhanced in Regime I and suppressed in Regime II by the forced convection. Finally, by performing a theoretical analysis of the density gradient, we obtain a scaled critical aperture, i.e., the critical aperture normalized by a characteristic length, for the onset of unstable dissolution of the solid-liquid interface. Such a scaled critical aperture is constant for both dissolution regimes. In this paper, we elucidate the crucial role of eddies in the flow-dissolution system in a gravity field. Moreover, we improve our understanding of the interplay between buoyancy-driven and forced convections in etching the solid surface.

Figure 1

Fabrication of soluble microfluidic channels. (a) A NaCl crystal chip is etched by the laser etching technology according to a horizontal smooth channel pattern with the initial aperture being 0.5 mm. (b) The NaCl crystal chip is fixed into the slot of a polydimethylsiloxane (PDMS) layer and is bonded by another smooth PDMS plate using a plasma cleaner (Harrick Plasma, PDC-002). (c) Two transparent acrylic bars are finally assembled to fix the chip firmly. (d) A microfluidic model with a soluble horizontal channel is created.

Figure 2

The microparticle-image-velocimetry (micro-PIV)-based flow-visualization system for imaging the dissolution of a horizontal channel in a gravity field. (a) Micro-PIV system, (b) charge-coupled device (CCD) camera coupled with the stereoscopic microscope, and (c) soluble microfluidic chip.

Figure 3

Experimental setup of microparticle image velocimetry (micro-PIV). The deionized (DI) water mixed with fluorescent particles with a diameter of ∼5 µm is injected into the channel by syringe pump B after the initial saturation of the channel. Since fluorescent particles can be excited by the green laser (∼532 nm), the movement of particles in channels can be captured by the charge-coupled device (CCD) camera, and the flow velocity field can be calculated by analysis software (DaVis 10.0). The entire experimental system is maintained at room temperature $\left(25\pm 0.5{}^{\circ }\mathrm{C}\right)$ with an air conditioner.

Figure 4

Image processing and the characterization of the flow velocity field. (a) The location of the field of view (FOV) of the visualized experiment. The red dashed box denotes the FOV of visualized experiments. (b) The raw grayscale image captured by the charge-coupled device (CCD) camera. The yellow box denotes the FOV of microparticle-image-velocimetry (micro-PIV) experiments. (c) The processed binary image. (d) The result of the local flow velocity field.

Figure 5

The definition of the initiation of dissolution (Pe = 126). (a) The channel filled with saturated NaCl solution before dissolution. (b) The beginning of dissolution ($t=0$ s). It is defined as the beginning of the recession of channel interfaces, which can be captured with the high-frame-rate charge-coupled device (CCD) camera. Note that the channel has nearly been filled with the dyed fresh water at this time. (c) The dissolution morphology of channel at $t=832$ s.

Figure 6

Observation of dissolution regimes of the microfluidic channels in a gravity field. Evolution of channel surface morphology with Pe increasing from 126 to 2512. The typical morphologies of channel surfaces are presented via the lines with different colors, corresponding to $\langle b\rangle =\langle b_0\rangle , 3\langle b_0\rangle$, and $6\langle b_0\rangle$. The corresponding times elapsed after dissolution are also denoted.

Figure 7

Characterization of dissolution regimes. (a) Variation of average wave number κ vs Pe ($t=t_{\mathrm{end}}$). Two dissolution regimes are distinguished. At low flow rates, the wave number increases with the flow rate in Regime I. In Regime II, the wave number is reduced by increasing Pe. (b) Definition of the analyzed area and identifiable amplitudes (${\sigma }_1, {\sigma }_2$, and ${\sigma }_3$) for Pe =1995. Waves with amplitudes $\sigma >\sim 150\mu \mathrm{m}$ are considered in the calculation. (c) Variation of the average amplitude of troughs σ vs Pe ($t=t_{\mathrm{end}}$). (d) Variation of the surface roughness factor (SRF) vs Pe ($t=t_{\mathrm{end}}$).

Figure 8

Flow-dissolution feedback loop, characterized by the eddies at the pore scale, and its effect on local dissolution. (a) Evolution of local recession rate of the upper surface from $t=4$ to 19 min for Pe = 794. (b) Evolutions of upper surface geometry together with the flow velocity distribution at the location of the first trough for Pe = 794 from $t=4$ to 19 min. The measured areas correspond to the dashed box location denoted in (a).

Figure 9

Conceptual description of the flow-dissolution feedback loop associated with the eddy evolution in a gravity field. Due to the buoyancy-driven convection, the first trough occurs and provides a space for lighter fresh water to accumulate (a). As the flooding proceeds, the trough area expands, and a counterclockwise eddy forms at this trough (b). As the flooding further proceeds, the nonuniform local dissolution rate amplifies, and the counterclockwise eddy flushes the dissolved salt from the top surface to the bottom on the left side (c). As more and more solid phase is dissolved on the left side of the trough, the upper surface tends to be smooth (d).

Figure 10

The role of eddy evolution in Regime I. (a) Number of troughs on the upper surface at the sample scale in Regime I. (b) Temporal evolution of local surface roughness factor (SRF) for Pe = 324 and 501. (c) Temporal evolution of local mass transport current density ($j$) for Pe = 324 and 501. (d) and (e) The local velocity field near surfs. #1 and #2 from eddy generation to fading. Locations of surfs. #1 and #2 are denoted by solid lines, and the eddies are also denoted. The colorbar from black to red shows the velocity magnitude.

Figure 11

The role of eddy evolution in Regime II. (a) Number of troughs on the upper surface at the sample scale in Regime II. (b) Temporal evolution of local surface roughness factor (SRF) for Pe = 794 and 1995. (c) Temporal evolution of local mass transport current density ($j$) for Pe = 794 and 1995. (d) and (e) The local velocity field near surfs. #3 and #4 from eddy generation to fading. Locations of surfs. #3 and #4 are denoted by solid lines, and the eddies are also denoted. The colorbar from black to red shows the velocity magnitude. The rightmost column features horizontal velocity distribution curves for the profiles marked with red and blue vertical lines in surfs. #3 and #4. The bottom row displays vertical velocity distribution curves for the profiles marked with yellow, green, and black horizontal lines in surfs. #3 and #4. The red dots indicate the center positions of the eddies. The width of the shaded areas represents ± standard deviation.

Figure 12

The critical aperture for the onset of instability of solid-liquid surface. (a) Variation of $b_c$ vs Pe. The schematic diagram shows the critical state when the first observable trough occurs. (b) The scaled aperture $b_c/b^{*}$ for all experimental conditions shows a constant prefactor being ${\alpha }_0=170\pm 15$ for both dissolution Regimes I and II Pe after being modified. However, under a nonflowing condition, such a prefactor is ∼50, highlighting the significant effect of forced convection.

Figure 13

The distribution of the flow velocity field in the channel. (a) Flow velocity field for Pe = 794 at $t=900$ s. (b) Flow velocity field for Pe = 794 at $t=1080$ s. (c) Flow velocity field for Pe = 324 at $t=840$ s. (d) Flow velocity field for Pe = 324 at $t=1200$ s. The colors correspond to the velocity magnitude.