Metal leaching using continuous stirred-tank reactors in end-of-life photovoltaic recycling

Abstract

The invention relates to methods and apparatus for the recovery of valuable materials from the recycling of photovoltaic panels. Particularly, the method comprises leaching photovoltaic cell particles with a leachant in a continuous stirred tank reactor.

Description

[0001]METAL LEACHING USING CONTINUOUS STIRRED-TANK REACTORS IN END- OF-LIFE PHOTOVOLTAIC RECYCLING This application claims priority from Australian Provisional Patent Application No. 2024901250 filed 1 May 2024, the content of which is incorporated herein by reference in its entirety. Field of the Invention The invention relates to methods and apparatus for the recovery of valuable materials from the recycling of photovoltaic panels. The invention will be described with reference to the recovery of silver (Ag) but it will be appreciated that the process is applicable to any leachable material. Background of the Invention The following discussion of the prior art is provided to place the invention in an appropriate technical context and enable the advantages of it to be more fully understood. It should be appreciated, however, that any discussion of the prior art throughout the specification should not be considered as an express or implied admission that such prior art is widely known or forms part of the common general knowledge in the field. Photovoltaics (PV) technology, which converts solar radiation into electricity, stands out as the most rapidly growing renewable energy. The global PV installation and electricity generation are reported to be 707.5 GW and 855.7 TWh respectively by 2020, within which crystalline silicon (c-Si) panels account for over 90%. There will be a significant challenge to manage large volumes of decommissioned PV panels when they reach the end of their 25–30-year lifetime. The cumulative mass of end-of-life (EoL) PV panels is predicted to be 60-78 million tonnes (Mt) and exceed nearly 10% of the total global electronics waste annually by 2050. Instead of landfills, EoL PV panel recycling, during which valuable materials e.g., silver, can be recovered, could be environmentally and economically beneficial. A typical recycling process consists of five steps: disassembly, delamination, material sorting, leaching and extraction (Figure 1a). Disassembly is the step to mechanically take apart the aluminium frame and back sheet from the PV panel. Delamination is the step to remove EVA layers and enable glass and solar cells to be separated, where thermal, chemical and mechanical are the three mainstreams. Material sorting, including technologies like screaming, density separation, electrostatic separation and optical separation, can separate the materials into different groups, where the solar cell can be effectively collected and concentrated. Leaching is applied to the metal-rich fraction (solar cell) after material sorting to dissolve valuable materials e.g. silver. The following extraction process adopts the chemical method to recover critical materials e.g. silver, from the leachate for reproducing photovoltaic raw materials. Glass and aluminium are the most commonly recycled materials in the present market, while other components are frequently disposed of in landfills due to the limited applicable recycling technologies. However, most valuable metals in the solar cell, especially silver (1% in c-Si solar cells, which is much larger than 0.0005% in natural silver ore), are theoretically recyclable (Figure 1b). Thus, silver recovery should be operated and added in the solar panel recycling. It is an object of the present invention to overcome or ameliorate at least one of the disadvantages of the prior art, or to provide a useful alternative. It is an object of at least one preferred form of the present invention to provide a method of recovering a recyclable substance from a photovoltaic cell with improved mixing. It is an object of further preferred forms of the present invention to a method of recovering a recyclable substance from a photovoltaic cell with improved heat and / or mass transfer efficiency. It is an object of yet further preferred forms of the present invention to a method of recovering a recyclable substance from a photovoltaic cell with improved efficiency Summary of the Invention In a first aspect, the invention provides a method of recovering a recyclable substance from a photovoltaic cell comprising crushing the cell to provide photovoltaic cell particles and leaching the photovoltaic cell particles with a leachant in a continuous stirred tank reactor, thereby to provide a solution of the recyclable substance in the leachant, and wherein the reactor is a vertical cylinder comprising an axially located first impeller mounted on and driven by an axial drive shaft. The recyclable substance may be any leachable substance of value found in a photovoltaic cell. In some embodiments, the recyclable substance is silicon, aluminium, silver, or copper. Preferably, the recyclable substance is silver. In some embodiments, the leachant is an acid. In some embodiments, the acid has a concentration of about 0.1M to about 10M in the leachant, for example, about 0.1M to about 0.5M, about 0.5 M to about 1 M, about 1 M to about 1.5 M, about 1.5 M to about 2 M, about 2 M to about 2.5 M, about 2.5 M to about 3 M, about 3 M to about 3.5 M, about 3.5 M to about 4 M, about 4 M to about 4.5 M, about 4.5 M to about 5 M, about 5 M to about 5.5 M, about 5.5 M to about 6 M, about 6 M to about 6.5 M, about 6.5 M to about 7 M, about 7 M to about 7.5 M, about 7.5 M to about 8 M, about 8 M to about 8.5 M, about 8.5 M to about 9 M, about 9 M to about 9.5 M, about 9.5 M to about 10 M, about 0.1 M to about 2 M, about 2 M to about 4 M, about 4 M to about 6 M, about 6 M to about 8 M, about 8 M to about 10 M, about 0.1 M to about 5 M, about 5 M to about 10 M, about 0.1 M, about 1 M, about 2 M, about 3 M, about 4 M, about 5 M, about 6 M, about 7 M, about 8 M, about 9 M, or about 10 M. Any suitable leachant may be used, one example is nitric acid. Any suitable concentration may be used having regards to leaching ability, safety and convenience, for example, the leachant may be at least about 3M nitric acid, or about 4M. The leaching process may be carried out at any suitable temperature having regards to reaction kinetics, safety and convenience, for example, the leachant may be carried out wherein the leachant temperature is at least about 40°C. In some embodiments, the leachant temperature is about 40°C to about 100°C, for example, about 40°C to about 50°C, about 50°C to about 60°C, about 60°C to about 70°C, about 70°C to about 80°C, about 80°C to about 90°C, about 90°C to about 100°C, about 40°C to about 60°C, about 60°C to about 80°C, about 80°C to about 100°C, about 40°C, about 50°C, about 60°C, about 70°C, about 80°C, about 90°C, about 100°C. The crushed photovoltaic particles may be crushed to any suitable size, for example 0.5 to 1.0mm by any suitable means (crusher or ball mill). In some embodiments, the crushed photovoltaic particles are introduced through an aperture at an upper portion of the continuous stirred tank reactor. In some embodiments, the aperture is located at between about upper 0% to about upper 50% of a height of the continuous stirred tank reactor, for example, about 0% to about 10%, about 10% to about 20%, about 20% to about 30%, about 30% to about 40%, about 40% to about 50%. The skilled person would understand that upper 0% is the top of the continuous stirred tank reactor, and upper 50% is the halfway height of continuous stirred tank reactor. In some embodiments, the crushed photovoltaic particles are introduced either before or after the leachant is added to the continuous stirred tank reactor. In the disclosed embodiment, the axial drive shaft which descend into continuous stirred tank reactor to the is driven by a rotation controller (such as direct drive motor or geared motor) located above the continuous stirred tank reactor, however any suitable drive mechanism may be used, e.g. a chain driven shaft with a controller alongside the continuous stirred tank reactor or a shaft driven from below the continuous stirred tank reactor or by some other means such as a magnetically controlled motion. In some embodiments, the continuous stirred tank reactor further comprises a temperature control mechanism. In further embodiments, the temperature control mechanism is a water jacket adapted to circulate heated or cooled water around the leachant. In some embodiments, the continuous stirred tank reactor has an inlet port for the introduction of fresh leachant. In some embodiments, the continuous stirred tank reactor has an extraction port for the removal of loaded leachant. In some embodiments, the continuous stirred tank reactor has an openable aperture at a lower portion for removal of spent crushed photovoltaic particles. In some embodiments, the openable aperture is located at between about lower 0% to about lower 50% of a height of the continuous stirred tank reactor, for example, about 0% to about 10%, about 10% to about 20%, about 20% to about 30%, about 30% to about 40%, about 40% to about 50%. The skilled person would understand that lower 0% is the bottom of the continuous stirred tank reactor, and lower 50% is the halfway height of continuous stirred tank reactor. In some embodiments, the continuous stirred tank reactor has a port located above an upper level of the leachant for removal of gas. In preferred embodiments the first impeller is located at a lower portion of the continuous stirred tank reactor, for example, the first impeller is located within the lower 10% of the continuous stirred tank reactor or within the lower 10%-20% of the continuous stirred tank reactor. Within this specific range, the leachant and particles can be more effectively mixed compared with other single impeller locations. In some embodiments, the first impeller is located within the lower 10% of a height of the continuous stirred tank reactor. In some embodiments, the first impeller is located within the lower 10%-20% of a height of the continuous stirred tank reactor, for example about 10% to about 12%, about 12% to about 14%, about 14% to about 16%, about 16% to about 18%, about 18% to about 20%. In another preferred embodiments, there is an axially located second impeller mounted on the axial drive shaft. This second impeller is located above the first impeller. The second impeller is located at or below a halfway height of the continuous stirred tank reactor. In some embodiments, the continuous stirred tank reactor and / or the drive shaft and / or first and / or second impellers are all formed from leachant resistant material, for example, the continuous stirred tank reactor and drive shaft is formed from stainless steel and / or has a PTFE sleeve. Preferably, the first and second impellers are formed from PTFE. Any suitable conventional impeller design may be used. Each of the two impellers may be of any design and have two, three four or five blades, the blades may be straight or curved and may have an external brace ring. A simple flat two bladed impeller located at desired locations is sufficient to stop the particles from sinking in an easy way. The skilled person would appreciate that the impeller may have any suitable number of blades in any suitable shape. In any event, for any particular given impeller design, the most effective location for that impeller is in the lower portion of the tank, e.g. the lower 10% or lower 10-20% of the tank. In some embodiments, the impeller speed is chosen so as to fluidize any particle bed in the continuous stirred tank reactor. Typically, the impeller speed will be in the range about 100- about 800 rpm, such as about 300-about 800 rpm or about 500- about 800 rpm, for example, about 100 to about 200 rpm, about 200 to about 300 rpm, about 300 to about 400 rpm, about 400 to about 500 rpm, about 500 to about 600 rpm, about 600 to about 700 rpm, about 700 to about 800 rpm. In some embodiments, the extraction time is chosen to maximise recovery of loaded leachant. The leaching takes place at an initially rapid rate and then slows. For example, depending upon the volume of material to be processed, it may be more efficient to extract 10x batches to 90% than to extract x batches to 99%. Leaching time inversely proportional to impeller speed. Typically, the extraction time is at least 5 min at 100 rpm impeller speed and at least 2.5 min at 500 rpm impeller speed. Definitions In describing and claiming the present invention, the following terminology will be used in accordance with the definitions set out below. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments of the invention only and is not intended to be limiting. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one having ordinary skill in the art to which the invention pertains. Unless the context clearly requires otherwise, throughout the description and the claims, the words “comprise”, “comprising”, and the like are to be construed in an inclusive sense as opposed to an exclusive or exhaustive sense; that is to say, in the sense of “including, but not limited to”. As used herein, the phrase “consisting of” excludes any element, step, or ingredient not specified in the claim. When the phrase “consists of” (or variations thereof) appears in a clause of the body of a claim, rather than immediately following the preamble, it limits only the element set forth in that clause; other elements are not excluded from the claim as a whole. As used herein, the phrase “consisting essentially of” limits the scope of a claim to the specified elements or method steps, plus those that do not materially affect the basis and novel characteristic(s) of the claimed subject matter. With respect to the terms “comprising”, “consisting of”, and “consisting essentially of”, where one of these three terms is used herein, the presently disclosed and claimed subject matter may include the use of either of the other two terms. Thus, in some embodiments not otherwise explicitly recited, any instance of “comprising” may be replaced by “consisting of” or, alternatively, by “consisting essentially of”. Other than in the operating examples, or where otherwise indicated, all numbers expressing quantities of ingredients or reaction conditions used herein are to be understood as modified in all instances by the term “about”. The examples are not intended to limit the scope of the invention. In what follows, or where otherwise indicated, “%” will mean “weight %”, “ratio” will mean “weight ratio” and “parts” will mean “weight parts”. The term ‘substantially’ as used herein shall mean comprising more than 50% by weight, where relevant, unless otherwise indicated. The recitation of a numerical range using endpoints includes all numbers subsumed within that range (e.g., 1 to 5 includes 1, 1.5, 2, 2.75, 3, 3.80, 4, 5, etc.). Further, unless expressly stated to the contrary, “or” refers to an inclusive or and not to an exclusive or. For example, a condition A or B is satisfied by any one of the following: A is true (or present) and B is false (or not present), A is false (or not present) and B is true (or present), and both A and B are true (or present). The terms “preferred” and “preferably” refer to embodiments of the invention that may afford certain benefits, under certain circumstances. However, other embodiments may also be preferred, under the same or other circumstances. Furthermore, the recitation of one or more preferred embodiments does not imply that other embodiments are not useful and is not intended to exclude other embodiments from the scope of the invention. It must also be noted that, as used in the specification and the appended claims, the singular forms “a”, “an” and “the” include plural referents unless the context clearly dictates otherwise. As used herein, with reference to numbers in a range of numerals, the terms “about,” “approximately” and “substantially” are understood to refer to the range of -10% to +10% of the referenced number, preferably -5% to +5% of the referenced number, more preferably -1 % to +1 % of the referenced number, most preferably -0.1 % to +0.1 % of the referenced number. Moreover, with reference to numerical ranges, these terms should be construed as providing support for a claim directed to any number or subset of numbers in that range. For example, a disclosure of from 1 to 10 should be construed as supporting a range of from 1 to 8, from 3 to 7, from 1 to 9, from 3.6 to 4.6, from 3.5 to 9.9, from 8 to 10, and so forth. Although exemplary embodiments of the disclosed technology are explained in detail herein, it is to be understood that other embodiments are contemplated. Accordingly, it is not intended that the disclosed technology be limited in its scope to the details of construction and arrangement of components set forth in the following description or illustrated in the drawings. The disclosed technology is capable of other embodiments and of being practiced or carried out in various ways. Description of the Drawings Figure 1. Shows (a) structure of PV panels with multilayers and their relevant recycling technologies; (b) structure of solar cells with valuable silver presented. Figure 2. Shows silver leaching efficiency during the process under different impeller speeds (a) before 300 s (b) before 3600 s. Figure 3. Shows the linear relationship between ln (k) and ln(ω). Figure 4. Shows a SEM surface morphology analysis of the silver electrode on solar cells after HNO3 treatment under different times for impeller speed at 100 rpm: 1 min (a-b); 2.5 mins (c- d) and 5 mins (e). Figure 5. Shows a schematic illustration of the PIV set-up consisting of LED light, high-speed camera, computer and the reactor. Figure 6. Shows comparisons between PIV observation and CFD-DEM simulation of particle behaviour at different impeller speeds: (a) 100 rpm and 3.0 s; (b) 500 rpm and 1.5s; (c) 800 rpm. Figure 7. Schematic illustration of the CSTR system for silver leaching experiment. Figure 8. Comparisons between experimental results and CFD-DEM simulations of silver leaching efficiency at different impeller speeds as a function of time. Figure 9. Is an illustration (a) and statistical analysis (b) of solar cell particle spatial distribution at t = 5.0 s for impeller speeds at 100 rpm, 500 rpm and 800 rpm respectively. Figure 10. Is an illustration (a) and statistical analysis (b) of the fluid velocity profile at t = 5.0 s for different impeller speeds at 100 rpm, 500 rpm and 800 rpm respectively. Figure 11. Is an illustration (a) and statistical analysis (b) of AgNO3 mass fraction distribution at t = 5.0 s for different impeller speeds at 100 rpm, 500 rpm and 800 rpm respectively. Figure 12. Shows optimization CSTR design from #1 to # 2 with lower impeller position and doubled impeller layers. Figure 13. Is an illustration (a) and statistical analysis (b) of solar cell particle spatial distribution at t = 5.0 s for impeller speeds at 100 rpm, 500 rpm and 800 rpm respectively in CSTR #2. Figure 14. Is an illustration (a) and statistical analysis (b) of the fluid velocity profile at t = 5.0 s for different impeller speeds at 100 rpm, 500 rpm and 800 rpm respectively in CSTR #2. Figure 15. Is an illustration (a) and statistical analysis (b) of the fluid velocity profile at t = 5.0 s for different impeller speeds at 100 rpm, 500 rpm and 800 rpm respectively in CSTR #2 Figure 16. Shows the average silver leaching rate in CSTR #1, #2 and #3 for different impeller speeds at 100 rpm, 500 rpm and 800 rpm respectively till leaching time to 5s. Figure 17. Illustration (a) and statistical analysis (b) of solar cell particle spatial distribution at t = 5.0 s for impeller speeds at 100 rpm, 500 rpm and 800 rpm in CSTR#3 respectively Figure 18. Illustration (a) and statistical analysis (b) of the fluid velocity profile at t = 5.0 s for impeller speeds at 100 rpm, 500 rpm and 800 rpm in CSTR#3 respectively. Detailed Description of the Invention Chemical leaching is the most efficient and economically feasible method for metal recovery in mineral processing and thus can be used for recovering silver from solar cells after receiving the separated solar cells from the mechanical and thermal delamination processes. Nitric acid (HNO3) is commonly used as a suitable reagent for silver leaching due to its low cost, high reactivity and low reaction temperature. Based on chemical leaching in mineral processing, the leaching efficiency may be related to the chemical reagents and their concentrations, reaction temperature, and reactant mixing state, and they should be investigated and quantified for solar cells. On the other hand, stirring tanks are the most widely used reactors due to their simple construction, ease of operation and effective homogenous mixing. Previously, experiments in the laboratory system have been conducted to explore efficient ways to recover silver from solar cells (Table 1). Most recently, the numerical simulation method has emerged as a popular method to understand and further design silver leaching from the solar cell for low-cost and low-risk compared to experiments. The Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) is one popular choice, where the fluid and solid phases are modelled by CFD and DEM respectively. Other investigations have conducted CFD-DEM studies of silver leaching from solar cell particles in a lab beaker. However, the previous experimental and numerical studies on silver leaching from solar cells are still at a very early stage and limited their applicability in Lab-scale systems, such as beakers. Table 1. Previous experimental works on silver leaching from PV panels. Leaching process Scale / system 15% HF, 4–1 H2SO4·H2O solution, 40 wt% HNO3Lab / NA 1- 27 °C 1–3 M HCl or H2SO4 or HNO3 and NaOH, 1:5 of Lab / Beaker sample / solution in volume 3M HNO3, temperature 50-60 °C Lab / NA 1-10 mol / L HNO3, temperature 25 to 60 °C Lab / Erlenmeyer flask 1M H2SO4, 3 M HNO3, and 30% H2O2, temperature 25-60 °C Lab / NA 5 ml HNO3 (70 wt%), 0.5 mL of HF (40 wt%), 1:10 of Lab / NA sample / solution in volume 2 M HNO3, temperature 80 °C Lab / NA 5g HNO3, 4M KOH, temperature 80 °C Lab / Beaker 65 wt% HNO3, 50 wt% H2O2, 37 wt% HCl Lab / Digestion vessel For the industry scale metal leaching process, the continuous stirred-tank reactor (CSTR) is the most widely used reactor system due to its simple construction, ease of operation and effective homogenous mixing. However, their use in end-of-life (EoL) photovoltaic (PV) recycling is not well understood. The specific structure of PV cells presents quite specific challenges in recycling and how that recycling yields and properties are influenced by the hydrodynamics in the reactor In order to adequately tackle the problems associated with the design, optimization and scale- up of CSTR, the hydrodynamics inside the reactor and its effectiveness in leaching efficiency should be well understood before their application in industry-scale PV recycling, which is largely affected by the impeller speed. The present invention relates to configurations of CTSR’s that are suitable for the leaching of valuable by products such as silver from EoL PV cells. In this invention, a surprisingly effective method for silver recovery from solar cells using a CSTR system. Based on the experiments, the inventors developed kinetics model and characterised by SEM the evolving surface morphology of crushed PV cells during the leaching process. A CFD-DEM particle-scale model is integrated with the kinetics model and validated against the fluid-flow pattern and silver leaching performance results from lab measurements. The validated CFD-DEM model is then applied to understand the particle-scale behaviour of silver leaching in the CSTR system in terms of hydrodynamics and AgNO3 distribution under different impeller speeds was investigated. The key and innovative concepts / methods incorporated in this study are: (i) an impeller speed-oriented kinetics model development; (ii) kinetics model incorporated CFD-DEM model development; (ⅲ) particle-scale understanding of the hydrodynamics and AgNO3 distribution in CSTR reactor and ultimately improved silver leaching performance in optimised CSTR reactor design. Results and Discussion Experimental results Silver leaching efficiency under different impeller speed Chemical reaction 1 is the main reaction in the silver acid leaching process: 2HNO3 + Ag(s) → AgNO3(l)+NO2+H2^^ (1)The leaching efficiency η is defined as: ^^^^^^ ^^^^ = · massand ^^^^^^is the mass concentration with a value of 1.39% for crushed solar cell particle sizeranging from 0.5-1.0 mm. The ^^^ = ^^ ∙ ^^ is the mass of silverin the leaching solution, where ^ ^^^^V is the volume of HNO3 solution with a value of 800 ml. ^^^^^^is the Ag+concentration in the leaching solution collected under different reaction conditions, the values were obtained by the Inductively Coupled Plasma-Optical Emission Spectroscopy (ICP-OES) test. Table 2 below shows the Experimental conditions of the silver leaching process in the CSTR, where the rotator (impeller) speed was tested between 100 and 800 RPM. Table 2 Experimental conditions of the silver leaching process in the CSTR. Solid phase Value Unit Solar cell particle size 0.5-1.0 mm Density 2516 kg / m3Weight 50 g Ag mass concentration 1.34 wt% Liquid phase Value Unit Mass concentration of HNO325 wt% Density 1150 kg / m3Volume 800 ml Operating conditions Value Unit Rotator speed 100-800 rpm Temperature 40 ℃ Time 0-60 min Figure 2 shows the silver leaching efficiency with time under impeller speed from 100 to 800 rpm over different times. Figure 2(a) shows leaching in the first 300s, while 2(b) shows leaching up to 3600s. Overall, the leaching efficiency was proportional to time with a different increasing rate at different impeller speeds. Two stages could be observed: stage 1 was a rapidly increased reaction rate where the chemical reaction was in control (0-75 s); stage 2 was a slow reaction rate where the diffusion was in control (75-300 s). During stage 1, the impeller speed at 800 rpm had the fastest reaction rate with a slope of 0.51, where the values for the impeller speed at 500 rpm, 300 rpm and 100 rpm are 0.48, 0.43 and 0.4, respectively. For stage 2, the reaction proceeded at a slow rate for all impeller speeds and approached the steady status with leaching performance at about 62 %, 57 %, 50 % and 44 % for impeller speeds at 800 rpm, 500 rpm, 300 rpm and 100 rpm respectively. The above results reveal that silver leaching from crushed solar cell particles is a vibrant process, beginning with intense chemical reaction control and followed by gentle diffusion control. Note that the larger impeller speeds offer more frequent crushed solar cell particle and HNO3collisions, resulting in faster chemical and diffusion reactions. The time effect’s contribution to silver leaching efficiency reduced significantly after 300s, where the efficiency increasing rates were 0.0046, 0.0053, 0.005 and 0.0053 % / s for impeller speed at 100, 300, 500 and 800 rpm respectively. Kinetics model development In this study, the silver leaching kinetics model in acid is developed based on the shrinking core model (SCM). Equation 3 is applied to describe the chemical reaction control during silver acid leaching: 2 1− (1 − ^^)3 = ^^^^^^ (3)^^^^is the kinetic parameter. The experimental results in Figure 2 were fitted to the form of SCM through Equation 3. To express the effect of impeller speed (ω) on the activation energy (E), a modified Arrhenius equation is applied, as follows: ^^^^ = ^^^^^^−^^ / ^^^^(4) where R = 8.314 J mol-1K-1(universal gas constant), and T = 313.15 K or 40C (temperature applied in this study). While λ is the exponential factor. Equation 4 can be transformed into the following equation:ln(^^^^) = −^^(5)^^^^+ ^^ln(ω)The dependence of ln(^^^^) on ln(ω) is shown in Figure 3. The experimental results fit well with the modified Arrhenius equation with R2=0.96. The influence of HNO3 concentration and temperature effects are found in linear relationships. Also, the amount of silver reduces as the reaction proceeds. In our kinetic model, d0is assumed as the particle diameter when reshaping the total silver in each silicon particle to a spherical particle, and d is the equivalent diameter of the remaining silver. The final impeller speed- oriented silver leaching kinetics model in the CSTR system is expressed as follows: ^^ 2 ^^ c is the HNO3 mass concentration. Note that the best applicable conditions of Equation 6 in terms of the impeller are ω = 100-800 rpm. The effect of temperature has a linear relationship with the reaction rate. Surface morphology characterization To further study the effect of impeller speed on the silver leaching process, Figure 4 shows the silver electrode shape variation on the solar cell surface under the impeller speed of 100 and 500 rpm. For impeller speed at 100 rpm, silver electrodes had severe cracks when the leaching time reached 1min where the diameter was about 12.9 µm (Figure 4a). With the leaching time increased to 2.5 mins, the silver electrode diameter decreased to around 8.59 µm (Figure 4b) and the silver electrode disappeared from the solar cell particle surface with the leaching time further increased to 5 mins (Figure 4c). Compared with the case for impeller speed at 100 rpm, the silver electrode breakage and disappearance process was accelerated for impeller speed at 500 rpm. As shown in Figure 4d, the silver electrode diameter was about 9.65 µm when the leaching time was 1 min. It disappeared when the leaching time was 2.5 mins (Figure 4e) and 5 mins (Figure 4f). The SEM results showed that the process of silver electrode separation from the solar cell particle was accelerated at a larger impeller speed, which explained why the silver acid leaching efficiency increased with an increased impeller speed . CFD-DEM simulations results Fluid-particle flow patterns Particle image velocimetry (PIV) is a non-invasive optical measurement technique. In this study, a high-speed video camera with a resolution of 512 pixels × 512 pixels was used to record the fluid-solid concurrent flow behaviour. A fixed field of view of 542 mm × 542 mm was recorded, and thus a pixel corresponds to 0.94 mm physical distance. One LED floodlight was positioned at the left side of the CSTR to illuminate the particle movement. A high-speed camera, X- Stream VISION XS-4, was positioned frequency of 500 Hz. In the experiments, water was taken as the fluid phase. The chip-like particles with length × width × height of 3 mm × 3 mm × 1 mm and density of 1500 kg / m3were used. Figure 5 shows the experimental platform as well as the data collection system. Independent PIV experiments were conducted using chip-like particles (imitation of the crushed solar cell particles) to validate this CFD-DEM model of fluid-particle flow pattern in CSTR under different impeller speeds. A total amount of 65 g of chip-like particles and 1L water were used. The specific experimental and simulation settings are available in Table 3. Figure 6 shows the comparison between PIV observations and CFD-DEM simulations of fluid-particle patterns for impeller speed at 300 rpm, 500 rpm and 800 rpm respectively. For impeller speed at 300 rpm, most particles accumulated at the bottom of the CSTR and few particles were suspended above the impeller. A dense particle bed was formed with a height of about 50 mm, which was reproduced by the CFD-DEM simulation with a deviation of 16 % (Figure 6a). With increased impeller speed to 500 rpm (Figure 6b), the particle bed height decreased to around 23 mm since the particles used to accumulate near the bottom of the impeller were suspended under larger centrifugal force; this tendency was also captured by the CFD-DEM where the particle bed decreasing to about 19 mm with a deviation of 17.4 % to PIV observation. While further increasing the impeller speed to 800 rpm (Figure 6c), the particle bed almost disappeared with few particles accumulated at the bottom of CSTR. This phenomenon was also reproduced by CFD-DEM where particles were suspended along the vertical direction of CSTR. Therefore, the model validity was confirmed given the flow-particle patterns under different impeller speeds. Note that the deviations of particle bed height between the PIV observations and CFD- DEM simulations may come from the particle shape effect, where spheres with a diameter of 2.7 mm were applied in the CFD-DEM model instead of chip-like particles. The Experimental and numerical parameters used for the fluid particle flow pattern validation are shown in table 3 below. Table 3 Experimental and numerical parameters used for the fluid particle flow pattern validation. Solid phase Experiment Simulation Unit Particle size chip-like (3×3×1) sphere (2.6 diameter) mm Particle density 1500 1500 kg / m3Total weight 65 65 g Friction coefficient NA 0.16 NA Restitution coefficient NA 0.926 NA Fluid phase Experiment Simulation Unit Fluid viscosity 1.0 × 10-31.0 × 10-3Pa*s Fluid density 998 998 kg / m3Temperature 20 20 ℃ Operating conditions Experiment Simulation Unit Reactor 1L STR 1L STR NA Rotator speed 300;500;800 300;500;800 rpm Silver leaching efficiency The CFD-DEM model with the impeller speed oriented kinetic model is further verified by comparing the numerical results of the silver acid leaching efficiency against the experiments for impeller speeds of 100 rpm, 500 rpm and 800 rpm at different times respectively. The experiments and numerical settings for this validation are presented in Table 4. The experimental system for the silver leaching experiments is shown in Figure 7. As shown in Figure 8, the CFD-DEM model reproduced the silver acid leaching efficiency increasing tendency for both impeller speeds at 100 rpm, 500 rpm and 800 rpm as a function of time. The impeller speed effect on silver acid leaching efficiency was also captured by the CFD-DEM model, where the efficiency increased with increased impeller speed. The average deviations of 8.0 %, 19.9 %, and 3.0 % were obtained between the CFD-DEM simulation and experiment results for impeller speeds at 100 rpm, 500 rpm and 800 rpm respectively, quantitatively indicating the high accuracy of the CFD-DEM model with the impeller speed oriented kinetic model in simulating silver acid leaching process. Note that the particle used in the CFD-DEM model was uniformly distributed, and the average particle size value (0.75 mm) of the experimental size range (0.5-1.0 mm) was applied. Table 4 Experimental and numerical parameters in the silver acid leaching efficiency validation. Solid phase Experiment Simulation Unit crushed solar cell sphere (0.75 Particle size mm particles (0.5-1.0) diameter) Particle density 2516 2516 kg / m3Total weight 50 50 g Friction coefficient NA 0.3 NA Restitution coefficient NA 0.95 NA Ag mass concentration 1.34 1.34 wt% Fluid phase Experiment Simulation Unit Fluid viscosity 8.9 × 1048.9 × 104Pa*s Fluid density 1150 1150 kg / m3HNO3mass concentration 25 25 % Temperature 40 40 ℃ Operating conditions Experiment Simulation Unit Reactor 1L STR 1L STR NA Rotator speed 100;500;800 100;500;800 rpm Understanding of silver leaching process in CSTR Hydrodynamics Figure 9 illustrates the particle spatial distributions along with statistical analysis at t = 5s with impeller speeds of 100 rpm, 500 rpm and 800 rpm respectively. Figure 9a depicts the particle spatial distributions inside the CSTR and clearly shows particle accumulation at the bottom and different particle patterns close to the impeller for three impeller speeds, which is consistent with the results shown in Figure 6 observed by the Particle image velocimetry (PIV) set up (Figure 5) and as discussed in more detail below. For impeller speed at 100 rpm, a dense particle bed was formed at the bottom with additional particles suspended around the impeller. When the impeller was increased to 500 rpm, the particle bed height decreased where the particles around the wall were fluidized and the previously suspended particles around the impeller were pushed above due to the increased centrifugal force. For speed at 800 rpm, the particle bed were almost fluidized, where a V-shape particle stream was observed between the CSTR bottom and impeller. This occurred due to the increased vertical velocity associated with an augmented impeller speed, during which the aerodynamic drag forces intensified and began to oppose the gravitational forces, resulting in an expansion of volume as the particles dispersed. For a quantitative analysis of the particle behaviour, Figure 9b shows the statistical spatial distribution of solar cell particles at different impeller speeds. Overall, most particles were distributed in the range of Yaxis = 0-0.05 m, which was the region between the STR bottom and impeller with values of 84 %, 60 % and 44.6 % for impeller speeds at 100 rpm, 500 rpm and 800 rpm respectively. The second stream of particles was located in the range of Yaxis = 0.05-0.1 m, where the case of 500 rpm dominated with values of 25 % and 8.8 %, 23 % for 100 rpm and 800 rpm respectively. The last mainstream particles could be found in the region where the Y axis is 0.1-0.15, where the case of 800 rpm started to dominate with values of 30.7 % and 3.22 %, 11.26 % for 100 rpm and 500 rpm respectively. The above qualitative and quantitative results all indicate that the tendency of particle accumulation at the CSTR bottom decreases with increased impeller speeds. For impeller speeds of 100 rpm, 500 rpm and 800 rpm at t = 5.0 s, Figure 10 presents the cross- section view of the fluid velocity distribution, aiming to explain the above particle behaviour. With increased impeller speed, the fluid velocity increased greatly and comparatively high- velocity zones started to appear near the CSTR wall (Figure 10a). More specifically, the fluid initiated an upward motion along the wall as a result of directly colliding with the impeller rotating at a speed of 500 rpm. As the impeller speed increased to 800 rpm, the fluid continuously circulated around the wall but intermittently descended toward the centre, creating a V-shaped pattern. This formation suggests a robust fluid circulation, moving from the periphery towards the wall and subsequently descending to the centre. In Figure 10b, the statistical fluid velocity (vertical) distributions are presented for different impeller speeds. Generally, the fluid velocity predominantly ranged from -0.8 to 0.6 m / s. The percentage of velocity exhibited a peak, followed by a decline as the fluid velocity transitioned from downward to upward movement. The peak fluid velocity (Vf, peak) was 0.05 m / s for all three impeller speeds, where the peak percentage values were 42.7 %, 35.1 % and 23.6 % for 100 rpm, 500 rpm and 800 rpm respectively. For the velocity region from -0.75 to -0.15 m / s, the percentage values were 44.8 %, 47.7 % and 40.4 % for 100 rpm, 500 rpm and 800 rpm respectively. For the velocity region of 0.15-0.55 m / s, the percentage values were 12.5 %, 32.2 % and 36 % for 100 rpm, 500 rpm and 800 rpm respectively. The findings suggest a prominent transition in fluid velocity from downward to upward as the impeller speed increased from 100 rpm to 800 rpm, which is consistent with the result that fewer particles are accumulated at the CSTR bottom with larger impeller speeds. AgNO3distribution The spatial distribution of AgNO3for impeller speeds of 100 rpm, 500 rpm and 800 rpm at t = 5.0 s is presented in Figure 11. Obvious AgNO3 regions were observed at the CSTR bottom but all three impeller speeds demonstrated that silver leaching from solar panel particles mainly took place in this region due to the accumulated solar cell particles where more particle surface area could serve as the reaction site, but the mass fraction decreased with increased impeller speed (Figure 11a) due to the bottom particle fluidization. Specifically, a dense AgNO3 region characterised as V-shape was formed at the bottom for impeller speed at 100 rpm. When the impeller was increased to 500 rpm, the intensity of AgNO3for regions close to the wall decreased but increased in the middle of CSTR. While for speed at 800 rpm, the AgNO3 mass fraction at the bottom was further decreased but increased along the wall in the Y direction of CSTR forming a vortex in the middle. Furthermore, Figure 11b presents a quantitative analysis of the AgNO3 mass fraction distribution. Overall, AgNO3 was distributed in the range of Yaxis = 0-0.05 m with values of about 0.0014, 0.0011 and 0.0008 for impeller speeds at 100 rpm, 500 rpm and 800 rpm respectively, which was consistent with the particle behaviour results shown in Figure 7. While for the position above the impeller (Y axis > 0.05 m), the AgNO3 mass fraction for impeller speed for 800 rpm remained the largest, such as the values were 1.95, 2.35, 2.99, 4.2 times of that of 100 rpm at Y axis = 0.1, 0.15, 0.2, 0.25 respectively. The above qualitative and quantitative results all indicate that the AgNO3would present a homogeneous distribution in CSTR instead of accumulation at the bottom at a larger impeller speed. CSTR design optimization In previous designs, the particle accumulations at the bottom are obvious, especially at low impeller speeds. A flow pattern would be optimised by improving the mixing and reducing the dead zone. In this study, an improved CSTR design with a lower impeller position and doubled impeller layers (Figure 12) was proposed and the particle behaviour and silver leaching yield distribution in the improved reactor were numerically studied by the CFD-DEM model. Improved hydrodynamics Figure 13 illustrates the improved particle spatial distributions along with statistical analysis at t = 5s with impeller speeds of 100 rpm, 500 rpm and 800 rpm respectively in CSTR #2. Similar to the case in CSTR #1, particle accumulation at the bottom and different particle patterns close to the impeller were observed for three impeller speeds; while there were two main differences: (1) the number of accumulated particles was decreased significantly and (2) three particle streams presented at the bottom, above impeller layer one and impeller layer two for impeller speeds at 500 rpm and 800 rpm (Figure 13a). For a quantitative analysis of the improved particle behaviour, Figure 13b shows the statistical spatial distribution of solar cell particles at different impeller speeds. For impeller speed at 100 rpm, the distribution of the particles showed a very similar pattern to the case in CSTR #1, where most particles were distributed in the range of Yaxis = 0-0.05 m with a value of 82.6 %. While increasing the speed to 500 rpm, the particle fluidization intensity increased greatly, with the evidence that the value in Yaxis = 0-0.05 m was 1.78 times smaller and the value in Yaxis = 0.15-0.2 m was 16.3 times than the case in CSTR #1. Further increasing the speed to 800 rpm, particles were beginning to approach the top of CSTR #2 with the value of 32.6 in Yaxis = 0.2-0.25 m, which was not the case neither for lower speed in CSTR #2 or CSTR #1. The above qualitative and quantitative results all indicate that the tendency of particle accumulation at the CSTR bottom decreases and fluidization to the CSTR upper part increases greatly with lower impeller location and double impeller layers design. In Figure 14, the cross-section view displayed the improved vertical fluid velocity distribution for impeller speeds of 100 rpm, 500 rpm and 800 rpm at t = 5.0 s respectively in CSTR #2. Similar to the case in CSTR #1, the fluid velocity increased greatly and comparatively high- velocity zones started to appear near the wall; while the main difference was that high-velocity zones above impeller layer one and impeller layer two for impeller speeds at 500 rpm and 800 rpm were observed in CSTR #2 (Figure 14a). Meanwhile, improved statistical distributions of vertical fluid velocity in CTSR #2 were presented in Figure 14b. The distribution of fluid velocity exhibited a broader range, ranging from -1.0 to 0.8 m / s, in comparison to CSTR #1. However, it maintained a consistent pattern, with the percentage of velocity reaching a peak before decreasing as the fluid velocity transitioned from downward to upward. The peak fluid velocity (Vf, peak) was 1.0 m / s for all three impeller speeds, which was two times larger than the case in CSTR #1. For the velocity region from 0.1 to 0.5 m / s, the percentage values were 59 %, 56.5 % and 56.8 % for 100 rpm, 500 rpm and 800 rpm, which were 4.7, 1.8 and 1.6 times larger than the case in CSTR #1. The results indicate the upward fluid flow tendency is increased in CSTR #2 with a lower impeller location and double impeller layer design for all three impeller speeds, where this phenomenon is more obvious at lower impeller speeds. Improved AgNO3distribution The improved spatial distribution of AgNO3 for different impeller speeds at t = 5.0 s in CSTR #2 is presented in Figure 15. Notable AgNO3regions were also observed at the bottom of CSTR #2 for impeller speeds at 100 rpm and 500 rpm but the intensity was smaller than the case in CSTR #1 (Figure 11a). While for impeller speed at 800 rpm, there were two clear individual AgNO3 distribution regions in CSTR #2 which were located between the two impeller layers and above the top impeller layer respectively (Figure 15a). Furthermore, Figure 15b presents a quantitative analysis of the improved AgNO3 mass fraction distribution. For impeller speeds at 100 rpm and 500 rpm, AgNO3 was still mainly distributed in the range of Yaxis = 0-0.001 m with values of about 0.0009 and 0.0003 and intensity decreased with increased Y axis, which was similar to the case in CSTR #1. While for impeller speed at 800 rpm, the AgNO3mass fraction increased to a peak at the Y axis = 0.1 m with a value of 0.00017 and then decreased with the increased Y axis, which was different from the case in CTSR #1. The above qualitative and quantitative results all indicate that the AgNO3would present a more homogeneous distribution and its mass fraction would increase in the upper part instead of accumulation at the bottom of CSTR with a lower impeller location and two impeller layer design. Improved silver leaching rate Figure 16 shows the average silver leaching rate in CSTR #1 and #2 at different impeller speeds. In CSTR #1, the average silver leaching rate increased with increased impeller speed, where the values were 7.3 % / s, 12.96 % / s and 16.73 % / s for speed at 100 rpm, 500 rpm and 800 rpm respectively. Comparatively, CSTR #2 with an optimized impeller design obtained a higher rate at each impeller speed, which was about 1.13 times larger than that of CSTR #1. Firstly, particles were randomly distributed along the Y axis approaching the top of CSTR #2 with an optimized impeller design instead of mainly accumulating at the bottom (Figure 13), which would result in an average larger surface area of the particle that could serve as the silver leaching reaction sites. Then, the optimized impeller design in CSTR #2 could better generate a velocity distribution with larger values at the same impeller speed (Figure 14), which would result in more energetic collisions between acid solution and solar cell particles. This way, the improved leaching rate is the result of more frequent and qualified collisions between acid solution and solar cell particles. CSTR design comparison CSTR#3 is a comparison design based on the results obtained from the modelling and experimental results derived from CSTR#1 and CSTR#2, which aims to indicate that the single impeller located at the lower portion of the CSTR is an easy way to impede particles from sinking. Compared with CSTR#2, the single impeller of CSTR#3 is located at about 33% (0.1 mm) of the CSTR. Figure 17 illustrates improved particle spatial distributions along with statistical analysis at t = 5s with impeller speeds of 100 rpm, 500 rpm and 800 rpm respectively in CSTR #3. Similar to the case in CSTR #1, particle accumulation at the bottom and different particle patterns close to the impeller were observed; while there was one main difference that particle accumulation above the impeller layer was also clear in CSTR#3. Figure 17b shows the statistical spatial distribution of solar cell particles at different impeller speeds. Similar to CSTR#1, most particles were distributed in the range of Yaxis = 0-0.05 m with a value of nearly 90 %. The main difference compared with CSTR#1 is that about 35% of particles are also accumulated around the impeller. The above qualitative and quantitative results all indicate that the tendency of particle accumulation in CSTR#3 is larger than the design of CSTR#1 with a lower impeller position. In Figure 18, the cross-section view displayed the improved vertical fluid velocity distribution for impeller speeds 100 rpm, 500 rpm and 800 rpm at t = 5.0 s respectively in CSTR #2. Similar to the case in CSTR #1, the fluid velocity is random is distributed increased and comparatively high-velocity zones appear near the wall; while the main difference is that the range of high-velocity zones is smaller compared with CSTR #1 (Figure 18a). Meanwhile, the statistical distributions of vertical fluid velocity in CTSR #3 are presented in Figure 18b. Similar to CSTR#1, the distribution of fluid velocity exhibited a broader range, ranging from -0.8 to 0.8 m / s. While the main difference is that the downward fluid velocity is the dominated in CSTR#3, where the percentage value for velocity region from -0.8-0 m / s is about 62% (Figure 18b). The results indicate the downward fluid flow tendency in CSTR#3 is larger than that of CSTR #1 with a lower impeller location, which would impede the particle suspension. That is, the simulation results comparing CSTR #1 and #3 demonstrate the surprising benefits of locating the impeller at the lower portion of the CSTR, which is consistent with the results shown in Figure 16. Discussion The results above illustrate contribution in relation to two aspects: (i) impeller speed-oriented kinetics model development in CSTR system for silver acid leaching; (ⅱ) optimized CSTR design and their performance prediction by CFD-DEM model. Note that the kinetics model primarily focuses on the impeller speed effect, which is the critical parameter affecting the hydrodynamics in CSTR. In the CFD-DEM simulations, solar cell particles are treated as spheres and have uniform size distributions. While crushed solar cell particles often exhibit irregular, chip-like shapes and wide variations in size distribution in practical scenarios. These deviations can significantly impact both underlying hydrodynamics and the resulting silver leaching performance. To offer a comprehensive understanding of silver leaching in the CSTR system, the development of a more inclusive kinetics model that accounts for variations in both reactor flow and chemical reaction (acid type and concentration, temperature and solid-liquid ratio) conditions is needed, which requires extensive experimental data input. Additionally, the development and implementation of models accounting for irregular particles with different sizes in the CFD-DEM model can further improve the simulation accuracy. Lastly, the design and optimization of the CSTR system conducted using the CFD-DEM model is lab-scale. The numerical understanding of the underlying hydrodynamics and silver leaching performance may be limited to lab-scale operations, which means that the outcomes might vary if the CSTR system scales up to the industry operation. Overall, further research on the silver leaching in CSTR system should be carried out to develop a comprehensive kinetics model and improve the CFD-DEM mode accuracy and capability at a larger scale by incorporating sub-models. Conclusion The results in this section may assist to understand and optimise the silver recovery from crushed c-Si solar cell particles in the CSTR system from the point of view of silver recovery efficiency by integrating experimental and numerical investigations. In detail, the impeller speed-oriented silver leaching kinetics model was developed from a set of experiments. This kinetic model was integrated into a CFD-DEM model, which was well validated against experimental measurements of fluid-particle flow pattern and silver leaching efficiency. Then the validated model was applied to understand the silver leaching process in the CSTR system and also predicted the performance of an optimized CSTR design with improved impeller location and double impeller layer. The key conclusions are as follows: (1) The silver leaching efficiency exhibited a time-dependent relationship for impeller speeds at 100 rpm, 500 rpm and 800 rpm, characterized by different increasing rates in distinct time intervals. Two stages emerged: stage 1 denoted a rapid increase in reaction rate, governed by chemical reaction (0-75 s); stage 2 represented a slower reaction rate where the diffusion was in control (75-300 s). Larger impeller speed demonstrated increased silver leaching efficiency. A kinetics model tailored to impeller speed (Equation 6) was proposed: ^^ 2 ^^ ^^ (2) Independent PIV experiments were conducted using chip-like particles (imitation of the crushed solar cell particles) to validate this CFD-DEM model of fluid-particle flow pattern in CSTR under different impeller speeds with a maximum deviation of 17.4 %. Meanwhile, the CFD-DEM model was further verified by comparing the numerical results of the silver acid leaching efficiency against the experiments for different impeller speeds with a maximum deviation of 19.9 %. (3) For the hydrodynamics in CSTR #1, most particles were distributed in the range of Yaxis = 0-0.05 m, which was the region between the CSTR bottom and impeller; the dominant fluid motion transitioned from a downward to an upward direction as the impeller speed increased from 100 rpm to 800 rpm with peak fluid velocity (Vf, peak) of 0.05 m / s. Meanwhile, AgNO3was mainly distributed in the range of Yaxis = 0-0.05 m at all three impeller speeds. (4) For the hydrodynamics in CSTR #2, the tendency of particle accumulation at the CSTR bottom decreased and fluidization to the CSTR upper part increased greatly; the upward fluid flow tendency was increased for all three impeller speeds, where this phenomenon was more obvious at lower impeller speeds. AgNO3 would present a more homogeneous distribution and its mass fraction would increase in the upper part instead of accumulating at the bottom of CSTR. Comparatively, CSTR #2 with an optimized impeller design obtained a high leaching rate at each impeller speed, which was about 1.13 times larger than that of CSTR #1, which was the result of more frequent and energetic collisions between acid solution and solar cell particles. Methods Experimental settings Pure commercial c-Si solar cells were used in this study. Crushed solar cell particles were prepared in two steps. Firstly, the solar cell was crushed in a ball mill (MM40, Retsch company) and sorted by size ranging from 0.5-1.0 mm using a sieve shaker (AS450 control, Retsch company). HNO3 was selected as the solvent. The silver acid leaching experiments were conducted by using a benchtop CSTR system, which comprised an electric water bath heater, peristaltic pumps, temperature indicator and a custom reactor, as shown in Figure 7. Firstly, the HNO3 solution was pumped into the reactor using the peristatic pump B. Secondly, pump A circulated the warm water (45-50 °C) from the water bath into the reactor jacket to heat HNO3, where the overhead stirrer also started working. The temperature of the HNO3 solution was monitored by a temperature indicator. Once the temperature of the HNO3 solution reached around 40 ℃, the crushed solar cell particles would be loaded into the reactor through the funnel. Each experiment was carried out twice, ensuring results accuracy and the temperature was kept around 40±2 ℃. CFD-DEM method The CFD model is applied to characterize the fluid phase, where local- averaged Navier-Stokes (NS) equations are resolved with information stored at the centre of cells. The DEM model is used to describe the particle phase, applying Newton’s laws of motion to obtain the trajectory and velocity of each particle. The drag forces models are applied to couple momentum transfer between fluid and particle phases. To address heat transfer within the reacting flow, three sub-models are used: heat conduction among particle-particle, heat convection between fluid-particle, and reaction-generated heat. The CFD-DEM model was constructed upon the general public software Multiphase Flow with Interphase eXchanges (MFIX). The governing equations of the CFD-DEM are listed in Table 5. Detailed explanations of the governing equations can be found in our previous studies. Note that the reaction kinetics of silver acid leaching was developed based on the results of experiments as described above. Table 5. List of governing equations of the CFD-DEM model ^^ ^^^^⋅ ^^,^^ ⋅ −Mass conservation ^^(^^^^^^^^^^^^) ^^ ^^ Nomenclature Ag Silver BFB Bubbling fluidized bed c-Si Crystalline silicon CFD Computational Fluid Dynamics CSTR Continuous flow stirred-tank reactor DEM Discrete Element Method EoL End of life ICP-OES Inductively Coupled Plasma-Optical Emission Spectroscopy FB Fixed bed GW Gigawatt LSD Liner-spring-dashpot Mt Mission tonnes HNO3 Nitric acid NS Navier-Stokes Photovoltaic PV PIV Particle image velocimetry Re Reynold number SEM Scanning Electron Microscopy TFM Two-Fluid-Model ^^^^Particle surface area ^^^^,^^Heat capacity of fluid phase ^^^^Particle diameter ^^^^,^^Fluid force exerting on particle i ^^^^,^^Gravity of particle i ^^^^^^Pressure gradient force ^^^^^^^^^^Drag force ^^^^^^^^ , ^^^^^^^^Normal and tangential forces ^^^^,^^Rolling friction torque ^^^^Number of the fluid phase species ^^^^Fluid pressure ^^^^^^Energy exchange term Inter-phase heat convection ^^^^^^^^^^Particle-particle heat conduction^^^^ℎ^^^^Reaction heat ^^^^^^^^^^^,^^^^^^^, ^^^^^^^^^^^^^^^,^^^^^Heat conduction between fluid-fluid and fluid-particle, respectively ^^^^^^Mass source of solid phase due to reactions ^^^^^^Mass source of fluid phase due to reactions ^^^^^^, ^^^^^^^^Representative of the length of the fluid layer between two particles ^̅^^^Stress tensor ^^^^Temperature ^^^^,^^Tangential torque ^^^^, ^^^^Particle and fluid temperature ^^^^,^^Volume of particle i ^^^^Volume of computational cell ^^^^Velocity of particle i ^^^^Mass fraction ^^ Drag coefficient Greek symbols ^^^^Void fraction ∆^^^^^^Heated caused by chemical reactions ^^^^Thermal conductivity ^^^^Fluid density ^^^^Fluid velocity ^^ ^^^^^^ ^^Thermal conductivity , Dynamic and second coefficient of viscosityOther embodiments of the present invention as described herein are defined in the following paragraphs: 1. A method of recovering a recyclable substance from a photovoltaic cell comprising crushing the cell to provide photovoltaic cell particles and leaching the photovoltaic cell particles with a leachant in a continuous stirred tank reactor, thereby to prove a solution of the recyclable substance in the leachant, and wherein the reactor is a vertical cylinder comprising an axially located first impeller mounted on and driven by an axial drive shaft. 2. The method according to paragraph 1 wherein the recyclable substance is silicon, aluminium, silver, or copper. 3. The method according to any one or more of the preceding paragraphs wherein the recyclable substance is silver. 4. The method according to any one or more of the preceding paragraphs wherein the leachant is nitric acid. 5. The method according to any one or more of the preceding paragraphs wherein the leachant is at least 3M nitric acid. 6. The method according to any one or more of the preceding paragraphs wherein the leachant temperature is at least 40C. 7. The method according to any one or more of the preceding paragraphs wherein the crushed photovoltaic particles are introduced through an aperture at an upper portion of the continuous stirred tank reactor. 8. The method according to any one or more of the preceding paragraphs wherein the axial drive shaft is driven by a rotation controller located above the continuous stirred tank reactor. 9. The method according to any one or more of the preceding paragraphs wherein the continuous stirred tank reactor further comprises a temperature control mechanism. 10. The method according to any one or more of the preceding paragraphs wherein the temperature control mechanism is a water jacket adapted to circulate heated or cooled water around the leachant. 11. The method according to any one or more of the preceding paragraphs wherein the continuous stirred tank reactor has an inlet port for the introduction of fresh leachant. 12. The method according to any one or more of the preceding paragraphs wherein the continuous stirred tank reactor has an extraction port for the removal of loaded leachant. 13. The method according to any one or more of the preceding paragraphs wherein the continuous stirred tank reactor has an openable aperture at a lower portion for removal of spent crushed photovoltaic particles. 14. The method according to any one or more of the preceding paragraphs wherein the continuous stirred tank reactor has a port located above an upper level of the leachant for removal of gas. 15. The method according to any one or more of the preceding paragraphs wherein the first impeller is located at a lower portion of the continuous stirred tank reactor. 16. The method according to any one or more of the preceding paragraphs wherein the first impeller is located within the lower 10% of the continuous stirred tank reactor. 17. The method according to any one or more of the preceding paragraphs wherein the first impeller is located within the lower 10%-20% of the continuous stirred tank reactor. 18. The method according to any one or more of the preceding paragraphs further comprising an axially located second impeller mounted on the axial drive shaft. 19. The method according to any one or more of the preceding paragraphs wherein the second impeller is located above the first impeller. 20. The method according to any one or more of the preceding paragraphs where the second impeller is located at or below a halfway height of the continuous stirred tank reactor. 21. The method according to any one or more of the preceding paragraphs wherein the tank and first and second impellers are formed from leachant resistant material. 22. The method according to any one or more of the preceding paragraphs wherein the continuous stirred tank reactor is formed from stainless steel and / or has a PTFE sleeve. 23. The method according to any one or more of the preceding paragraphs wherein the first and second impellers are formed from PTFE. 24. The method of any one or more of the preceding paragraphs wherein the first impeller has two, three four or five blades. 25. The method of any one or more of the preceding paragraphs wherein the second impeller has two, three four or five blades. 26. The method according to any one or more of the preceding paragraphs wherein the impeller speed is chosen to fluidize any particle bed in the continuous stirred tank reactor. 27. The method according to any one or more of the preceding paragraphs wherein the impeller speed is in the range 100-800 rpm. 28. The method according to any one or more of the preceding paragraphs wherein the impeller speed is in the range 300-800 rpm. 29. The method according to any one or more of the preceding paragraphs wherein the impeller speed is in the range 500-800 rpm. 30. The method according to any one or more of the preceding paragraphs wherein extraction time is chosen to maximise recovery of loaded leachant. 31 The method according to any one or more of the preceding paragraphs wherein extraction time is at least 5 min at 100 rpm. 32 The method according to any one or more of the preceding paragraphs wherein extraction time is at least 2.5 min at 500 rpm.

Claims

CLAIMS 1. A method of recovering a recyclable substance from a photovoltaic cell comprising crushing the cell to provide photovoltaic cell particles and leaching the photovoltaic cell particles with a leachant in a continuous stirred tank reactor, thereby to provide a solution of the recyclable substance in the leachant, and wherein the reactor is a vertical cylinder comprising an axially located first impeller mounted on and driven by an axial drive shaft.

2. The method according to claim 1, wherein the recyclable substance is silicon, aluminium, silver, or copper.

3. The method according to claim 1 or claim 2, wherein the leachant is nitric acid, preferably at a concentration of at least 3M.

4. The method according to any one of the preceding claims, wherein the leachant temperature is at least 40°C.

5. The method according to any one of the preceding claims wherein the crushed photovoltaic particles are introduced through an aperture at an upper portion of the continuous stirred tank reactor.

6. The method according to any one of the preceding claims wherein the axial drive shaft is driven by a rotation controller located above the continuous stirred tank reactor.

7. The method according to any one of the preceding claims wherein the continuous stirred tank reactor further comprises a temperature control mechanism, preferably the temperature control mechanism is a water jacket adapted to circulate heated or cooled water around the leachant.

8. The method according to any one of the preceding claims wherein the continuous stirred tank reactor has an inlet port for the introduction of fresh leachant, and / or an extraction port for the removal of loaded leachant.

9. The method according to any one of the preceding claims wherein the continuous stirred tank reactor has an openable aperture at a lower portion for removal of spent crushed photovoltaic particles.

10. The method according to any one of the preceding claims wherein the continuous stirred tank reactor has a port located above an upper level of the leachant for removal of gas.

11. The method according to any one of the preceding claims wherein the first impeller is located at a lower portion of the continuous stirred tank reactor.

12. The method according to claim 11 wherein the first impeller is located within the about lower 10% of a height of the continuous stirred tank reactor.

13. The method according to claim 11 wherein the first impeller is located within the about lower 10%-20% of a height of the continuous stirred tank reactor.

14. The method according to any one of the preceding claims further comprising an axially located second impeller mounted on the axial drive shaft.

15. The method according to claim 14 wherein the second impeller is located above the first impeller.

16. The method according to claim 15 where the second impeller is located at or below a halfway height of the continuous stirred tank reactor.

17. The method according to any one of the preceding claims wherein the impeller speed is chosen to fluidize any particle bed in the continuous stirred tank reactor.

18. The method according to claim 17 wherein the impeller speed is in the range 100-800 rpm, or 300-800 rpm, or 500-800 rpm.

19. The method according to any one of the preceding claims wherein extraction time is chosen to maximise recovery of loaded leachant.

20. The method according to any one of the preceding claims wherein extraction time is at least 5 min at 100 rpm, and / or at least 2.5 min at 500 rpm.

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