Transport and removal of a passive tracer in porous media employing surface washing

TL;DR

This study investigates how a gravity-driven surface-washing film removes a passive tracer from a water-saturated porous plate. By depositing disodium fluorescein on the plate, allowing diffusion into the pore space, and then washing, the authors capture both qualitative surface distributions (via dye attenuation imaging) and quantitative effluent concentrations (via a calibrated fluorometer). They identify a three-stage mass-transfer process: rapid surface flushing of tracer near the surface, a slower diffusion-dominated interior phase, and an advection-dominated final stage when the tracer-rich region reaches the downstream boundary, with the third stage governed by the film and porous-media flow interaction. A parametric study reveals how film characteristics, plate permeability, initial tracer mass, and diffusion depth influence removal dynamics, yielding scaling insights (notably time rescaling with $\\sin(\\alpha)$) and practical guidance for optimizing surface-washing protocols in industrial and environmental contexts. The work also presents a low-cost, high-precision measurement approach and demonstrates qualitative imaging as a valuable complementary diagnostic tool for studying surface washing in porous media.

Abstract

This experimental study investigates the dynamics of surface washing to remove a passive tracer from a porous plate by a gravity-driven liquid film across its surface. A disodium fluorescein tracer is introduced at the surface of a water-saturated porous plate and allowed to diffuse into the plate for a number of hours before a film of water solution flows over its surface to extract and transport the tracer away. The removal rate of the tracer is monitored quantitatively by using fluorescence measurements to determine the concentration in the effluent from the washing process. These measurements are supplemented by dye-attenuation imaging, which provides mainly qualitative insights about the tracer's concentration distribution on the porous plate surface. Our findings reveal a three-stage mass-transport process consisting of an initial period of rapid removal of the tracer found within the surface roughness, followed by a period of slower removal, which appears to be limited by vertical diffusion, and a third stage of accelerated advection-dominated removal when the tracer-rich region that was transported downstream during the second stage reaches the downstream boundary of the porous plate. A parametric study explores the influence of the characteristics of the washing film, the permeability of the porous plate, the amount and initial spatial extent of the tracer on the porous plate and the tracer's diffusive penetration depth on the mass removal rates. Our insights offer practical guidance for optimising surface washing protocols for porous systems in industrial and environmental applications.

Figures (7)

• Figure 1: Schematics of the experimental setup. (a) Side view of the surface-washing apparatus. (b) The complete experimental setup, including a top view of the washing apparatus. Squares with P represent a gear pump.
• Figure 2: (a) Drawing of the cross-section view of the Tee-connector with the end of the fluorometer fitted in it. (b) A test of the fluorometer response after the instantaneous injection of a known mass of fluorescein in the funnel.
• Figure 3: Schematics and corresponding experimental images of the stages of a passive tracer removal from the porous plate during surface washing. Left: Schematics showing cross-section view of the porous medium and the surface film flow illustrating how the distribution of tracer (in yellow and orange) evolves in time and space during the different stages of the washing process. Right: Representative background-subtracted experimental images of the porous plate at each stage obtained from direct visualisation using light absorption to reveal the tracer distribution in situ the porous medium, during surface washing. Dark regions reveal higher concentration regions of the tracer within the porous plate.
• Figure 4: The dynamics of passive tracer transport out of the porous plate. (a) Tracer mass removed from the porous plate, $m_r$, normalised with the tracer mass deposited on the porous plate, $m_d$, against time, $t$. Data from effluent concentration measurements with the fluorometer. The three mass removal stages are shaded with different colours. (b) A typical image of the tracer patch, overlaid with the binary contour of the patch and the fitted ellipse. The major and minor axes of the ellipse are denoted by $a$ and $b$, respectively. (c) The distance travelled downstream by the centre of the ellipse fitted to the tracer patch with time. (d) The ratio of the major axis, $a$, over minor axis, $b$, of the ellipse fitted to the tracer patch plotted against time, $t$. In all the plots the black solid lines represent the mean calculated from 3 experiments and the shade spans vertically 2 standard deviations.
• Figure 5: The mass of the tracer removed from the porous plate against time for varying parameters. (a) Varying inclination angles, $\alpha$ ($\tau$ = 2 h, porous plate: 300--400 , $m_d$ = 0.5 mg). The symbols indicate the inflection point. Inset: Rescaled time axis with the sine of inclination angle, $\alpha$, which corresponds to the down-slope component of gravity. (b) Varying $\tau$, 2 and 18 h, for two different inclination angles, $\alpha$ (porous plate: 300--400 , $m_d$ = 0.5 mg). (c) Varying area of initial contamination, $A_0$, $A_1 = (5.54 \pm 0.48) \times 10^3$ and $A_2 = (3.07 \pm 0.51) \times 10^3$, for two plates with different permeability, made of 100--200 and 300--400 glass beads ($\tau$ = 18 h, $\alpha$ = 11.0 degrees). (d) Varying porous plate permeability using plates made of 100--200 and 300--400 glass beads ($\tau$ = 18 h, $\alpha =11.0$ degrees, $m_d$ = 0.2 mg). Time axis is rescaled with the travelling velocity of the tracer patch downstream, $u_p$. Inset: Patch travelled distance against time on two different plates. In all the plots the lines represent the mean from at least 3 experiments and the shade spans vertically 2 standard deviations.