# Using foams for the oxidative dissolution of copper particles: the transport of reactants is controlled by the foam structure

Anne R Rousseau, Phabie Paraison, Grégory Lefèvre, Cécile Monteux

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Anne R Rousseau, Phabie Paraison, Grégory Lefèvre, Cécile Monteux. Using foams for the oxidative dissolution of copper particles: the transport of reactants is controlled by the foam structure. Langmuir, 2025, 10.1021/acs.langmuir.5c00263. hal-05350470

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# Using foams for the oxidative dissolution of copper particles: the transport of reactants is controlled by the foam structure

Anne R. Rousseau<sup>1,2,3</sup>, Phabie Paraison<sup>1</sup>, Grégory Lefèvre<sup>2</sup>, Cécile Monteux<sup>1,*</sup>

## Abstract

We study the oxidation of micrometric copper particles in rotating aqueous foams by oxygen $O_2$ present in the gas bubbles and in the presence of protons $H^+$ in the continuous phase. Our goal is to understand the link between the reaction kinetics and the transfer of the three reactants present in three different phases in the foam by monitoring foam structure using simple experimental tools. Measuring the bubble size evolution and the foam liquid fraction enable us to obtain an insight into the transfer of $O_2$ by diffusion in the thin liquid films, while measuring the foam liquid fraction and using a pH sensitive dye enable us to observe the distribution of protons within the foams. Finally, the trapping of particles in the dry foams can be observed directly with a camera. We vary the rotating speed which influences the amount of liquid effectively incorporated inside the foams, which in turn controls the quantity of particles and protons within the foams. We prove that the foam structure controls the transfer of reactants and hence the reaction kinetics. Wetter foams ensure a steady transport of particles and protons, resulting in a steady increase of the amount of copper dissolved over time. In the drier foams, the $O_2$ transfer is faster so that the kinetics is faster than in wet foams at short times. Yet the transport of the particles and the continuous phase is hampered leading to a slower kinetics at longer times. These results will guide the design and handling of reactive foams when used as chemical reactors.

## Keywords

Foam, multiphase microreactor, leaching, oxidation, copper

## I. Introduction

Heterogeneous chemical reactions involving components of at least two phases (solid and gas, solid and liquid or two immiscible liquids) require to maximize the contact area between reactants to enhance mass-transfer and reaction kinetics. <fnref n="1" />⁻<fnref n="3" /> In the case where the two immiscible fluids are a gas and a liquid, foams and aerosols enable to obtain a high interfacial area between the dispersed and

<footnote n="1"><sup>1</sup>Sciences et Ingénierie de La Matière Molle, ESPCI Paris, PSL Research University, CNRS, Sorbonne Université, Paris 75005, France</footnote>

<footnote n="2"><sup>2</sup>Institut de Recherche de Chimie Paris (IRCP), Chimie ParisTech, PSL Research University, CNRS, Paris 75005, France</footnote>

<footnote n="3"><sup>3</sup>Agence de l'Environnement et de la Maîtrise de l'Energie (ADEME), 20 avenue du Grésillé, 49004 Angers, France</footnote>

<footnote>* Corresponding author -- cecile.monteux@espci.fr</footnote>
continuous phases. As an example, methane mixed with air could be partially oxidised into methanol at the interface of water microdroplets, because their contact initiate free radical reactions.⁴ Similarly, nitrogen could be converted into nitric acid at the interface of gas microbubbles generated in water, thanks to the strong electric field existing at the interface.⁵ In organic chemistry, foams stabilised by pH-sensitive nanoparticle catalysts have been recently used to perform oxygenation and hydrogenation of water-soluble species.⁶⁻⁹ Foamed systems exhibit enhanced activity in comparison with non-foamed systems thanks to a larger interfacial area, a higher gas exchange rate and a more efficient catalytic activity of the particles adsorbed at the air/liquid interface.⁷

In the present article, we use foams to oxidize and dissolve metallic particles as a possible step of hydrometallurgical processes. Hydrometallurgy has been used for decades to dissolve natural ores¹⁰ and recent developments aim at the recovery of metals present in secondary resources such as copper anode slimes¹¹ or waste electrical and electronic equipment¹². Large amounts of oxidizing agents are used, hence decreasing the amount of liquid reactants is a crucial issue to develop greener processes. Bubbling a reacting gas such as ozone¹³ or oxygen¹⁴,¹⁵ into the leaching solution has been recently shown to improve the leaching of copper and has the advantage to lower the environmental footprint of the process due to the decrease or replacement of soluble oxidant. In our group we have performed the oxidation of a copper plate rotated in a foam in the presence of protons¹⁶ (Equation 1). We have found that the fast oxygen transfer¹⁷ from the atmosphere to the foam allowed to dissolve eight times more copper than in an aqueous solution containing the same amount of liquid. Later this “leaching foams” concept was extended to the dissolution of silver plates¹⁸.

Equation 1

$$2 \text{ Cu(s)} + \text{O}_2 \text{(g)} + 4 \text{ H}^+ \text{(aq)} \rightarrow 2 \text{ Cu}^{2+} \text{(aq)} + 2 \text{ H}_2\text{O}$$

Furthermore, we studied and modelled the transfers of O₂ and H⁺ during the oxidation of an immobile copper cylinder in a foam using a forced drainage experiment where the continuous phase is injected through the foams at a controlled flow rate which enables to control both the advection velocity of the continuous phase as well as the foam liquid fraction. We found that the flux of O₂ through the foams, occurring by dissolution and diffusion of O₂ in the thin liquid films, decreases when the liquid fraction increases as the surface area of the films decreases and their thickness increases. The advective flux of protons increases with the advection flow rate. This model geometry enabled us to show that there is an optimum liquid fraction and flow rate to optimize the dissolved amount of Cu: at low flow rate and liquid fraction the reaction is limited by the transfer of H⁺ while at high flow rate and liquid fraction the reaction is limited by the transfer of O₂.
After establishing this proof of concept of leaching foams on metal plates and cylinder, the goal of the present article is to focus on a situation which is closer to recycling applications, where the metal is often encountered as micro particles, either grinded particles of hundreds of microns in size or as micron size particles in anodic slimes. In that case one has to care about the relative transfer of the particles and other reactants, H⁺ and O₂ inside the foams. In reference ¹⁵, Régnier et al. have studied the oxidation of copper particles as well as grinded PCB wastes in rotating foams using a Buchi rotavapor set up and studied the influence of the particle size on the dissolution. However, in their case, the liquid fraction was not controlled nor measured and the rotation velocity was not varied which did not allow the authors to decouple the influence of O₂, H⁺ and particle transfer inside the foams.

In the present article we study the oxidation of copper micrometric particles by oxygen, in rotating foams containing protons in the continuous phase. We built a homemade set up to control the rotation velocity of the foams and to control the amount of liquid in the rotating cell. Moreover, we study situations where either the amount of Cu or H⁺ is limiting the reaction. Using a camera, we measure the effective liquid fraction i.e., the amount of liquid effectively incorporated inside the foams as well as the bubble size. Moreover, we observe the position of the front of particles inside the foams. Furthermore, we obtain an indication of the local pH using a pH-sensitive dye in the continuous phase. This experimental study enables us to discuss the transport of the three reactants and relate it to the kinetics of reaction that we measure. We find that for wet foams the rotation velocity influences the foam's effective liquid fraction which in turn influences the transport of the three reactants. In the wet foams the O₂ transfer is slower. However the transport of the particles and protons is free in the liquid channels, which ensures a continuous supply of these two reactants. Hence the reaction kinetics varies linearly with time and increases with the H⁺ concentration. Drier foams favour oxygen transfer hence the reaction kinetics is faster at short times. However the reaction kinetics slows down at longer times as the transport of particles and protons is hampered.

# Experimental Section

## Materials.

Copper powder (spherical, APS 10 microns, 99.9% - from Alfa Aesar) was used as reference particles for leaching. The particles size was assessed using diffraction granulometry (Figure S1). Non-ionic surfactant polyoxyethylene(10) oleyl ether (Brij® O10 from Sigma) and 1 mol/L hydrochloric acid (Titripur® from SigmaAldrich) as well as 0.1 mol/L hydrochloric acid (Titripur® from SigmaAldrich) were used to prepare the leaching solutions. Foaming solutions contained both hydrochloric acid (at various concentrations between 0.02 mol/L and 1 mol/L) and Brij® O10 (0.5 mmol/L).
## Set-up.

A home-made polymethylmethacrylate (PMMA) rectangular column (internal section 33 mm x 33 mm; height 143 mm) was connected to a gear motor (12 Vc.c., 12.8 W, 14 rpm or 71 rpm from RS Pro). The rotation speed could be adjusted between 1 rpm and 50 rpm (see Figure 1). Except specified otherwise, the rotation speed was set to 17 rpm.

<figure><img src="image_2.png" /><figcaption>Figure 1. Experimental set-up for leaching particles in foams (a) foam preparation (b) rotating device (c) foam characterization</figcaption></figure>

## Foam preparation.

A volume of 30 mL of leaching solution was introduced in the column, followed by the introduction of 49 mg of copper particles. A porous frit (ROBU® micro filter candle, pore size = 16 – 40 µm) was then immersed in the liquid for 10 minutes. Afterwards, an air flow was forced into the liquid at a controlled pressure of 80 mbar, corresponding to a flow rate of approximately 20 mL/min, which enabled to produce bubbles. The air flow was stopped once the column was filled with foam.

We prepared two major types of foams containing two different volumes of liquid, either 6 mL or 30 mL corresponding to total liquid fractions of $φ_{tot} = 5\%$ (referred to as “dry foams” in the following) and $21\%$ (referred to as “wet foams” in the following) (see Table 1). As we shall see later, once in rotation, the effective liquid fraction $φ_l^{eff}$ in the foam may differ from the total liquid fraction $φ_{tot}$ in the column depending on the rotation speed. The wetter foam ($φ_{tot} = 21\%$) was prepared by introducing 30 mL of leaching solution in the column and subsequently bubbling air through a porous frit until the top of the column was reached by foam. It is worth noting that the dryer foam ($φ_{tot} = 5\%$) was also prepared by introducing 30 mL of leaching solution, in order to ensure that the porous frit stayed completely immersed during the foaming process. Yet, once the top column was reached by the foam, 24 mL of solution were withdrawn by using a needle inserted into the bottom liquid phase, letting space for air at the top of the column, as can be seen on Figure S2.
<table><caption>Table 1. Experimental details of leaching experiments.</caption><thead><tr><th>Liquid volume (mL)</th><th>Liquid fraction in the column φ<sub>tot</sub> (%v)</th><th>H<sup>+</sup> concentration (mol/L)</th><th>Mass of copper introduced (mg)</th><th>Reagent which total amount is limiting</th><th>Mass percentage of leachable copper (%w)</th></tr></thead><tbody><tr><td>30.0 ± 0.5</td><td>21</td><td>0.02</td><td>49 ± 2</td><td>H<sup>+</sup> (aq)</td><td>39 %</td></tr><tr><td>30.0 ± 0.5</td><td>21</td><td>0.05</td><td>49 ± 2</td><td>H<sup>+</sup> (aq)</td><td>98 %</td></tr><tr><td>30.0 ± 0.5</td><td>21</td><td>0.1</td><td>49 ± 2</td><td>Cu (s)</td><td>100 %</td></tr><tr><td>30.0 ± 0.5</td><td>21</td><td>0.5</td><td>49 ± 2</td><td>Cu (s)</td><td>100 %</td></tr><tr><td>6 ± 1</td><td>5</td><td>0.1</td><td>49 ± 2</td><td>H<sup>+</sup> (aq)</td><td>39 %</td></tr><tr><td>6 ± 1</td><td>5</td><td>0.5</td><td>49 ± 2</td><td>Cu (s)</td><td>100 %</td></tr><tr><td>6 ± 1</td><td>5</td><td>1.0</td><td>49 ± 2</td><td>Cu (s)</td><td>100 %</td></tr></tbody></table>

## Foam characterization.

To characterize the foam, a right-angle prism (Edmund Optics) was glued on the top face of the column with a drop of a mixture of 0.05 mol/L BrijO10 and 0.1 mol/L glycerol to obtain good optical contact. The prism was placed at 5 cm from the bottom of the column. A LED light panel was used to illuminate the column and a camera was placed perpendicularly to the other side of the right-angle prism to acquire the foam images. As the exposition time could not be reduced enough to acquire clear images during rotation, the rotation was stopped for a few seconds for each image acquisition.

**Local foam pictures analysis.** The acquired images were deformed by a $\sqrt{2}$ factor because of the right-angle prism geometry. Their length was consequently resized while their height stayed unchanged. The images were then binarized using a Python program inspired from the one given by Lamolinairie et al. 19 Examples of pictures before and after binarization can be found in Figure S3. The surface area $A_b(t)$ of bubbles was determined for different times from the binarized images and converted into the bubble radii $R(t) = \sqrt{A_b(t)/\pi}$, which represents the equivalent surface radii of the surface bubbles. Incomplete bubbles positioned at the edge of the image were excluded from these measurements. Mean bubble radius at the wall was then determined. This radius can be considered representative of the mean radius of bubbles within the foam for dry foams having a polydispersity index higher than 0.2 20, which is well the case for our foams. Indeed, the polydispersity index measured from bubble size analysis during microscopic observations after foaming was found to be around 0.4. Error bars plotted in Figure 5 (b) show standard deviation in mean bubble size determined when experiments were repeated (n = 2 for 21 % foam, 17 rpm; n = 3 for 5 % foam, 17 rpm), and do not account for bubble size polydispersity.

**Macroscopic foam pictures analysis.** Macroscopic pictures of the column in rotation were also extracted from videos taken with a high speed camera (Fastcam Mini from Photron, equipped with Computar MLH objective). The area occupied by the liquid $A_{liq}(t)$ below the foam as well as the one
occupied by the liquid and the foam $A_{tot}(t)$ were determined for different times using software ImageJ. From these measurements, a macroscopic effective liquid fraction was determined: $\phi_l^{eff}(t) = (V_{liq,ini} - A_{liq}(t) \times p)/(A_{tot}(t) \times p - A_{liq}(t) \times p)$ with $V_{liq,ini}$ the initial volume of liquid introduced in the column and $p$ the depth of the column. Examples of pictures used can be found in Figure S4.

## Dissolved copper quantification

**Sampling.** To avoid sampling heterogeneities in metal concentration within foams because of reactants transport, it was decided to recover the whole volume of solution for each measurement when measuring kinetics of reaction. Hence, kinetics measurements were performed by stopping the experiments at varying reaction times, to recover the whole solution and measure its copper content. Each data point is thus the result of a different experiment performed with a new foam. The pH of recovered solutions was measured. If pH stayed < 3, recovered solutions were directly filtered with 0.20 µm hydrophilic cellulose acetate syringe filters to retain residual copper particles. If pH was found to be > 3, atacamite, a solid form of oxidized copper, could be formed (Section 5 of SI for more details on copper speciation depending on pH). As pH was not measured for the data shown on Figure 2, the eventual formation of atacamite in dry foams, for which the limiting reagent was protons, was neglected in that case. However, for data shown in Figure 3 (b) for hydrochloric concentration of 0.1 mol/L, the sampling protocol was adapted to take atacamite into account from 45 minutes onwards. Thus, in that case, a known volume of 1 mol/L hydrochloric acid was added to the recovered solution in order to dissolve atacamite. Sample was then filtered with 0.20 µm hydrophilic cellulose acetate syringe filters to retain the residual non oxidized copper particles. Thus, data points obtained in Figure 3 (b) for hydrochloric concentration of 0.1 mol/L take into account the total amount of copper oxidized during the reaction, whereas data points shown in Figure 2 neglect atacamite. One can notice that results are consistent and stay within the repeatability range, proving that atacamite formation stays minor until 60 minutes.

**ICP-OES.** Inductively-Coupled-Plasma – Optical Emission Spectroscopy (ThermoScientific ICAP 6300 Duo) was used to measure the concentration of dissolved copper in samples. Wavelengths used for the determination of copper concentrations were 219.958 nm, 221.810 nm, 213.598 nm and 204.379 nm. Calibration curves were performed before every ICP-OES analysis (using commercial 1000 mg/L copper standard from Sigma Aldrich). Samples recovered from experiments were diluted in 1 mol/L nitric acid. Absorbance intensities were measured three times for each sample and averaged concentrations were determined from calculated concentrations for each wavelength.

**pH measurements.** pH measurements were done using pH meter Seven2Go from Mettler Toledo equipped with pH InLab® Viscous Pro ISM electrode. pH was measured to control the acidity
of the leaching solution before and after the leaching experiment, and used as an indicator of proton
consumption during the reaction, which in turn could be used to determine the amount of Cu²⁺ formed
according to stoichiometry presented in Equation 1.

Results & discussion

The rotation speed and the liquid fraction control the amount of copper dissolved and
the oxidation kinetics

We measured the amount of copper dissolved in one hour for two foams obtained after
introducing either 6 mL or 30 mL of the continuous phase for different rotation velocities. For these
two foams the total liquid fraction in the column, φ<sub>tot</sub> = V<sub>liq,tot</sub>/V<sub>foam</sub>, is equal to 5 % and 21 % respectively.
For these two liquid fractions, the HCl concentration was fixed at 0.1 mol/L, corresponding to situations
where the reaction was limited either by the amount of protons (φ<sub>tot</sub> = 5 %) or by the amount of
copper (φ<sub>tot</sub> = 21 %) (Table 1). Consistently the amount of copper dissolved was higher for the 21 %
foams as it contained a higher quantity of protons than the 5 % foam (Figure 2).

<figure><img src="image_3.png" /></figure>

Figure 2. Mean mass percentage of copper leached in one hour depending on the rotation speed for a foam containing ● 6 mL, φ<sub>tot</sub> = 5 % ; ● 30 mL, φ<sub>tot</sub> = 21 % of 0.1 mol/L leaching solution.
Experiments were performed in triplicate and each result is presented in pale colours ○ or ●. Dashed lines are a guide for the eyes. Horizontal lines indicate the maximal amount of leachable copper, which depends on the limiting reagent.

In the absence of rotation, the particles were not significantly dissolved in one hour as they
remained in the drained liquid below the foam and were not in contact with the oxygen present in the
air bubbles. Rotating the foams enabled to increase greatly the amount of copper dissolved and a
rotation velocity of 10-20 rpm enabled to optimize the amount of copper dissolved. For both foams, the amount of copper leached in one hour at 10-20 rpm was consistent with the expected maximal value. It is to be noted that, for the 5 % foam, this maximal value was determined considering that all the protons present in the solution reacted with copper to produce Cu²⁺ accordingly with Equation 1.

Turning to the reaction kinetics (Figure 3), we explored the same two liquid fractions, 21 % (Figure 3 (a)) and 5 % (Figure 3 (b)) with varying HCl concentrations at a rotation velocity of 17 rpm.

<figure><img src="image_4.png" /><figcaption>Figure 3. Copper leaching kinetics of (a) a wet foam (30 mL, $\varphi_{tot} = 21\%$) and (b) a dry foam (6 mL, $\varphi_{tot} = 5\%$) rotated at 17 rpm for various protons concentration in the leaching solution (♦ 0.05 mol/L; ● 0.1 mol/L; ▲ 0.5 mol/L; ■ 1.0 mol/L).</figcaption></figure>

For the wetter foam ($\varphi_{tot} = 21\%$), the mass fraction of leached copper showed a regular increase with time (Figure 3 (a)). The proton concentration impacted mostly the time needed to leach the maximal amount of copper: thus, a plateau was still not reached after 90 minutes for the less concentrated leaching solution [HCl] = 0.05 mol/L; it was reached in about 90 minutes when [HCl] = 0.1 mol/L and in about 60 minutes when [HCl] = 0.5 mol/L.

For the dryer foam ($\varphi_{tot} = 5\%$), the reaction kinetics quickly increased at short times, slowed down after 20 minutes and reaccelerated after 45 minutes (Figure 3 (b)). This three-step kinetics was observed for all leaching solutions investigated, at 0.1 mol/L, 0.5 mol/L and 1 mol/L and will be discussed later. It is worth noting that for the 5 % foam, the protons are the limiting reagent at 0.1 mol/L, leading to the formation of solid atacamite because of proton shortage. For Figure 3 (b) the quantification procedure has been adapted to take into account the formation of atacamite, as described in the Experimental section, which explains why the amount of copper leached after 60 minutes slightly differs between Figure 2 and 3 for 17 rpm and [HCl] = 0.1 mol/L.
<table><caption>Table 2. Kinetics rates at short times (slope measured during the first 20 minutes) depending on the foam total liquid fraction</caption><thead><tr><td>Protons concentration (mol/L)</td><td>Slope in wet foams (wt%/min)</td><td>Slope in dry foams (wt%/min)</td></tr></thead><tbody><tr><td>0.5</td><td>0.016</td><td>0.032</td></tr></tbody></table>

When comparing the two kinetics obtained in wet and dry foams for the same proton concentration and same limiting reagent, that is to say for [HCl] = 0.5 mol/L (triangles on Figure 3), one can see that kinetics at short times were quicker in the drier foams (Table 2). Indeed, about 60 % of copper was leached in 20 minutes in dry foams, whereas only 30 % of copper was leached in the same time in wetter foams. However, it takes about 60 minutes to leach the entirety of copper in wet foams, as opposed to 90 minutes in drier foams.

The results above show that the foams' liquid fraction controls the oxidation kinetics of copper, which means that it plays a role in reactants transport. Moreover, we find that there is a rotation velocity threshold that enables to increase the amount of copper dissolved. In the section below we examine how the rotation speed influences the effective liquid fraction, i.e. the amount of liquid effectively in contact with the air bubbles. We also investigate how the liquid fraction controls the transfer of oxygen, particles and protons.

## Effective liquid fraction, bubble size evolution and discussion about the O₂ transfer

As the liquid can drain out of the foam because of gravity or during the rotation, the macroscopic effective liquid fraction $\phi_l^{eff}$ inside the foams may be different from the total liquid fraction $\phi_{tot}$ defined earlier (initial liquid volume in the column divided by the column volume). We therefore report below the effective liquid fraction of the foams as a function of time and rotation velocity. These effective liquid fractions were measured from pictures taken with a high speed camera, that can be found in Figure S4.

We also measured the size evolution of the bubbles in the middle of the column using a prism, which is a way to assess coarsening. Coarsening is in turn a way to assess the gas transfer due to Laplace pressure gradients into the foams.

One can see in Figure 4 that the effective liquid fraction $\phi_l^{eff}$ varies with the rotation speed for the wet foams ($\phi_{tot} = 21 \%$). $\phi_l^{eff}$ increased from 4% to 21% when the rotation velocity increased from 0 to 17 rpm and remained constant above 17 rpm. Indeed, when the rotation was too slow, a large
amount of liquid in excess remained on the walls of the column and was not incorporated inside the foams. Thus, varying the rotation velocity leads to the variation of the effective liquid fraction which in turn controls the amount of protons and particles effectively incorporated in the foam. Hence, we expect an increase of the amount of protons and particles in contact with oxygen within the foam when the rotation velocity increases up to 17 rpm. This variation of the effective fraction could thus account at least partly for the increase of the leaching efficiency when the rotation velocity increases from 0 to 17 rpm.

<table><caption>Figure 4. Characterization of the wetter foam (30 mL, φ<sub>tot</sub> = 21 %) (a) effective liquid fraction 3 minutes after the beginning of rotation and (b) mean bubble radius depending on the rotation speed (4.5 rpm, 17 rpm or 48.5 rpm) during foaming (t<0) and rotation (t>0)</caption><thead><tr><th colspan="7">Wet foam φ<sub>tot</sub> = 21 %</th></tr><tr><th>Rotation speed</th><th>0 rpm</th><th>4.5 rpm</th><th>9.5 rpm</th><th>17 rpm</th><th>28 rpm</th><th>48.5 rpm</th></tr></thead><tbody><tr><th>φ<sub>l</sub><sup>eff</sup> (%)</th><td>4 %</td><td>15 %</td><td>19 %</td><td>21 %</td><td>21 %</td><td>21 %</td></tr><tr><th>Pictures</th><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

The time evolution of the effective liquid fraction as well as mean bubble radius were determined for wet (φ<sub>tot</sub> = 21 %) and dry (φ<sub>tot</sub> = 5 %) foams, both rotated at 17 rpm (Figure 5).
<figure><img src="image_5.png" /><figcaption>Figure 5. Characterization of the foam (a) effective liquid fraction and (b) mean bubble radius depending on their liquid content (● 6 mL, $\varphi_{tot} = 5\%$; ○ 30 mL, $\varphi_{tot} = 21\%$) during foaming ($t \le 0$) and rotation at 17 rpm ($t > 0$)</figcaption></figure>

Before starting the rotation, the effective liquid fractions were $\phi_l^{eff} = 2\%$ for $\varphi_{tot} = 5\%$ and $\phi_l^{eff} = 7\%$ for $\varphi_{tot} = 21\%$. Indeed, gravity caused the drainage of the liquid that accumulated at the bottom of the column below the foam. As the rotation started (17 rpm), the effective liquid fraction inside the two foams increased back to $\phi_l^{eff} = \varphi_{tot} = 5\%$ and 21% and remained almost constant over time.

The average bubble size, of the order of 100 µm, stayed constant over time for the wetter foams, while for the drier foams the bubble size increased from 100 to 350 µm in 90 minutes. Hence, we show here that bubbles coarsen faster in dryer foams 21, probably because their bubbles exhibit larger interfacial area 22,23 (Figure S3) and that the thin films between bubbles might be thinner. This in turn indicates that gas transfer, driven here by Laplace pressure, is eased in dry foams. However, Laplace pressure is not the only driving force of gas transfer at stake here. The chemical reaction indeed consumes O₂, which generates a partial pressure gradient. Gradients of partial pressure are expected to induce gas transfers, which can be order of magnitudes faster than the ones induced by gradients of Laplace pressure. 24 In both cases, the gas transfer is controlled by the dissolution of the gas into the
continuous phase and its subsequent diffusion from bubble to bubble through the thin liquid films. Thus, in both cases, gas transfer is expected to increase for higher bubble surface area and thinner films, and therefore for lower liquid fractions.

These bubble size evolution results and reasoning on gas transfer lead us to qualitatively expect that O₂ transfers more quickly in the dry foams to react with the particles in the liquid, which leads to a dissolution kinetics which is faster at short times for the dry foams than for wetter foams (Table 2).

In the next section we further show that the liquid fraction controls the transport of the particles and protons inside the foams.

## Insight into the transport of protons and particles within the foams

To obtain more insight into the transfer of protons in foams, we added a pH sensitive dye inside the foams which switched from pink to green when the pH rose from 1 to 7 (Figure 6). In order to be able to see colour changes, we decided to fix the proton molar quantity so that protons are the limiting reagent. Thus, HCl concentration was fixed to 0.02 mol/L for the wetter foam ($\varphi_{tot} = 21 \%$) and to 0.1 mol/L for the dryer foam ($\varphi_{tot} = 5 \%$). In both cases, the total quantity of protons was 0.6 mmole, so that maximum 39 %w of copper initially introduced could be leached (Table 1).

In the case of the 21 % foam at 0.02 mol/L ((Figure 6 (a)), no spatial heterogeneity in the protons concentration was observed, which means that both the particles and the protons were transported freely inside these wet foams. These observations correlate well with the fact that the reaction kinetics are rather linear with time for the 21 % foam and increases when the H⁺ concentration increases (Figure 3 (a)).

In the case of the 5 % foam at 0.1 mol/L (Figure 6 (b)), the pH quickly rose in one end of the foam column which corresponded to the area where the copper particles were trapped. Indeed, when $\varphi_{tot} = 5 \%$, the foam channels were not wide enough to allow for the transport of particles. Consequently, the particles accumulated at one end of the column and, at short times, the oxidation reaction consumed the protons locally. Interestingly, the local increase of pH at t = 15 minutes corresponded well to the transient slowing down of the kinetics described in Figure 3 (b) for the dry foam. In this regime, the reaction is probably limited by the diffusive transfer of H⁺. Yet, at t = 30 minutes, the pH seemed to decrease back close to its initial value at the tip of the column and became more spatially uniform, inducing an acceleration of the kinetics. At t = 70 minutes the pH increased homogeneously over the entire foam column. We will discuss in more detail this complex evolution of the pH in Section III.4.
<figure><img src="image_6.png" /><figcaption>Figure 6. Visualisation of proton concentrations using a pH indicator dye within (a) wet foam (30 mL, $\varphi_{tot} = 21 \%$) containing 0.02 mol/L HCl, and (b) dry foam (6 mL, $\varphi_{tot} = 5 \%$) containing 0.1 mol/L HCl, both rotated at 17 rpm. In both cases, molar quantity of protons is fixed to 0.6 mmole.</figcaption></figure>

Regarding the transport of particles in dry foams, we present pictures of the accumulated particles at velocities between 1 and 48.5 rpm (Figure 7 (a) and (b)). It can be clearly seen that the particles were trapped on one end of the column. As detailed below, the particles were trapped because the width of the foam channels was too small to allow for the transport of particles. According to reference ²⁵, the size of the foam channels, i.e. the Plateau borders, writes $r_{PB} = R_v\sqrt{\frac{\phi_l}{0.33}}$ with $R_v$ the radius of spheres having the same volume as the bubbles, and $\phi_l$ the foam's liquid fraction. More precisely the confinement parameter $\lambda = \frac{d_{particule}}{d_{lim}}$, with $d_{lim} = 2 r_{PB} (\frac{2}{\sqrt{3}} - 1)$ corresponds to the ratio between the particle size, and the size of the maximal circle that can be inscribed within the Plateau border cross-section. ²⁶ From the mean diameter of the bubbles $d_b$ and the foam liquid fraction $\phi_l$ we find that $d_{lim} = 9 \mu m$ during foaming ($2R_v = d_b = 151 \mu m$; $\phi_l = 5 \%$) and reached 40 $\mu m$ as bubbles grow ($2R_v = d_b = 719 \mu m$; $\phi_l = 5 \%$). Hence the confinement parameter was between 0.25 and 1, values for which it has been shown that particles transport is hampered ²⁶, consistently with our
observations. For 9.5 and 17 rpm the particles seemed to accumulate over a slightly larger zone, which
correlated well with the fact that the velocity at which the maximum amount of copper is dissolved in
the 5% foams was about 10 to 20 rpm. From 48.5 rpm on, the centrifugal force exerted on copper
particles is not negligible anymore compared to weight (Section 6 in SI for detailed calculation), which
might explain why the particles stay at the very end of the column.

<figure><img src="image_7.png" /><figcaption>Figure 7. Transport of copper particles in dry foams (a) Scheme of particles blocked within the Plateau borders of a dry foam (b) Pictures of the particles dispersion at the bottom of the dry foam depending on the rotation speed</figcaption></figure>

Discussing the relation between reactants transfer and reaction kinetics

Let us now rationalize the reaction kinetics observed in *Figure 3* (a) and (b) and Table 2. In the wet foams the kinetics varied almost linearly with time and increased with the H⁺ concentration. For these wet foams, the pH was spatially homogeneous and no clogging of the particles in the foam was observed. Therefore, in these wet foams both the particles and the protons were transported freely in the foams. More precisely, the sedimentation velocity of the particles is not sufficient to allow for the free transport of the particles in the foams (shown in Section 7 of the SI). Hence it is the free advection of the aqueous phase that drags the particles ²⁷ and enables the reaction to occur in a spatially homogeneous manner within the foams. However, for low rotation velocities some of the liquid may accumulate on the column walls and does not take part in the reaction, nor does it efficiently advect particles within foams. This leads to the existence of an optimum velocity of 17 rpm, which
corresponds to the velocity at which most of the protons and particles are incorporated inside the foams.

For the dry foams we have seen that the chemical reaction presented three different regimes: i. at short times a first regime with a quick production of cupric ions where the dissolution kinetics increased with the H⁺ concentration and was faster than for the wetter foams at high proton concentration, ii. a short plateau where the dissolution levelled off (between 20 and 30 minutes) and iii. an increase of the reaction kinetics at longer times.

As shown in Table 2, at high proton concentration (0.5 mol/L), the short time kinetics was two times faster for the dry foams than for the wet foams due to a faster oxygen transfer in dryer foams. However, the reaction kinetics slowed down after 20-30 minutes in the dry foams as the protons were consumed close to the particles, creating a growing depletion zone. This spatially heterogeneous increase of the pH means that the aqueous phase that contained the protons did not have time to be advected in a continuous manner within the dry foams. Indeed the drainage velocity in the 5 % foam can be estimated using foam drainage equations ²⁸ (Section 8 of the SI). We found that the liquid is advected over 0.1 mm during a half-rotation at 17 rpm, while the flow direction is reversed during the second half rotation. Hence the protons of the continuous phase are weakly advected during the rotations. Thus, protons transfer probably occurs through diffusion over increasingly high distances, so that the depletion zone is growing over time. This result enables us to understand the local increase of pH at short times and the induced deceleration of the reaction for dry foams between 20 and 30 minutes.

After 30 minutes, the pH rehomogenized spatially and decreased close to the particles leading to an acceleration of the kinetics. Such a homogenization of the pH cannot be accounted for by any diffusive process (Section 9 of the SI). The driving force for this homogenization will be the object of future work.

## Conclusion

We have reported the leaching kinetics of micrometric copper particles in rotating foams which are oxidized by protons present in the continuous phase and oxygen present in the air bubbles. In comparison to previous literature dealing with leaching foams, this study addresses new fundamental questions concerning the link between the reaction kinetics and the transport of the three reactants, Cu(s), O₂(g) and H⁺(aq) in situations where either the amount of Cu or H⁺ is limiting reagent and by controlling the foam liquid fraction.

To do so we have built a unique homemade set-up to control the rotation velocity of the particles as well as the amount of continuous liquid phase and air inside the cell. For the first time we
quantify precisely the time evolution of the bubble radius as well as the effective liquid fraction i.e.,
the amount of liquid effectively incorporated inside the foams. We obtain pictures of the clogging of
the particles inside the foams as well as indications of the local variations of pH and hence the H+
concentrations by using a pH sensitive dye. These experimental tools enable us to quantify the reaction
kinetics as a function of the liquid fraction and rotation velocity and to discuss the link between the
kinetics and the transport of the three reactants.

We found that there is an optimum rotation velocity that enhances the dissolution of copper.
Indeed, the rotation velocity controls both the liquid and particles repartition inside the foams. We
have also varied the total amount of liquid in the foam column and determined the impact of foam
structure on leaching efficiency. For dry foams hence low amounts of liquid (5 %), the reaction kinetics
is fast at short times due to a fast oxygen transfer through the thin liquid films. However, the transport
of the particles and of the H+ in the continuous phase is hampered because the particles clog the thin
foam channels and because the advection of the aqueous phase during rotation is negligible. It follows
that the H+ are consumed close to the particles at short times. Consequently, a depletion zone forms
close to the particles, hence the reaction kinetics slows down at intermediate times. At longer times
we observe a spatial homogenization of the H+ concentration leading to a further increase of the
copper leaching kinetics.

In contrast, in wetter foams the transfer of O₂ by diffusion through the films is slower.
However, both the protons and the particles can move freely inside the foams, which leads to a
dissolution rate that remains constant over time. Moreover the reaction rate increases with the proton
concentration.

Our study gives an insight on mechanisms at play during multiphasic chemical reactions
occurring in foams and sets the stage for a promising approach of leaching in hydrometallurgy, using
multiphase foam microreactors.

## Supporting Information.

Copper particles size distribution. Details on the foaming process for dry foams. Local pictures of the foam at the prism level. Macroscopic pictures of rotating foams. Speciation diagram of copper. Estimations of centrifugal force exerted on particles, particles sedimentation speed, advection velocity in dry foams and protons transport by diffusion in dry foams.
Acknowledgments

We thank Alesya Mikhailovskaya for her help with the foaming process, Ludovic Olanier for the column
design and Jean-Claude Mancer for 3D impression of parts of the set-up. We thank Florence Rouyer,
Isabelle Cantat, Arnaud Saint-Jalmes, Benjamin Dollet for useful discussions on particle transport, gas
transfer and foam drainage and permeability, as well as Olivier Diat and Damien Bourgeois, our
partners in the FOAMEX project, for many discussions on leaching kinetics. We thank Olga Kergaravat
as referent engineer from ADEME. This work was supported by the French Environment and Energy
Management Agency (ADEME), by French National Research Agency (FOAMEX, ANR-17-CE08-0016) as
well as by Foundation Simone et Cino Del Duca.

Credits

Anne R. Rousseau: writing, review & editing, investigation, data curation, conceptualization. Phabie
Paraison: investigation. Grégory Lefèvre & Cécile Monteux: writing, review & editing, supervision, data
curation, conceptualization.

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