The Physical Characterization and Terminal Velocities of Aluminium, Iron and Plastic Bottle Caps in a Water Environment

: Aluminium, iron and plastic are materials which are extensively used at both industry and individual levels. However, signiﬁcant amounts of aluminium, iron and plastic end up in the environment. Speciﬁcally, bottle caps made of these materials are often thrown away, with or without bottles, and appear among the common plastic debris entering the world’s oceans and beaches. More than 20 million bottle caps and lids have been identiﬁed during beach-cleaning campaigns over the last 30 years. To recover bottle caps from the shores, conventional technologies can be used. In this paper, the physical properties of used metal and plastic bottle caps were examined and related to the settling and rising velocities of the caps, as well as their drag coefﬁcients and hydrodynamic modes in water environments, with respect to gravity separation. The sample contained aluminium, iron, high-density polyethylene (HDPE), low-density polyethylene (LDPE), and polypropylene (PP) bottle caps. The ﬁndings revealed that the density differences between the bottle caps resulted in the terminal settling velocities of aluminium and iron particles, which were signiﬁcantly higher than the rising velocities of the plastic caps. The results allowed us to design a ﬂowsheet for bottle cap recovery from beach coasts in order to reduce environmental impact and produce add-on plastic and metal products.


Introduction
Aluminium, iron and plastic are materials which are extensively used at both industry and individual levels [1,2]. Although iron and aluminium are known as metals for alloy production with a variety of applications (construction, electronics, transportation, etc.), they appear with plastic in a number of consumer goods. In particular, the materials are used to produce bottle caps, which seal glass or plastic bottles filled with either drinking liquids (soft drinks, beverages) or nondrinking liquids (water, oil, medical liquids, cosmetics, process fluids, etc.). Globally, a substantial increase in demand for bottled goods has resulted in a significant growth in bottle production rates and the consumption of aluminium, steel and plastics [3,4].
Meanwhile, there is a lack of primary aluminium and iron production due to the exhaustion of mineral deposits and a reduced amount of metals available from ores, which increases production costs. Furthermore, the world demand for aluminium, iron and plastic exceeds their production rates, resulting in a shortage of these materials across the world which could potentially lead to a deficit of these materials in the future [5]. Therefore, the production of aluminium, iron and plastic from secondary raw materials is a positive sustainable development option. The process is beneficial from both an economic and environmental point of view [6][7][8][9][10][11].
Despite this, a significant amount of aluminium, iron and plastic end up in landfills, waste-water streams, and the environment. For example, the bottle caps made of these materials are often thrown away with or without bottles, appearing in mixed garbage, where W a is the weight of the particle in the air, W w is the weight of the particle in the water, and ρ w is the density of the water. For the particles whose densities were less than water, the additional weight loads were added to achieve plunging the particles into the water to the bottom of the cell, and to make it possible to measure the volume and calculate the density of the particle.

SEM Analysis and FTIR Spectroscopy
An elemental composition of metal particles was analysed by means of a scanning electron microscope (SEM) VEGA3 (TESCAN, Brno, Czech Republic) [52,53]. Prior to SEM analysis, the metal particles were treated with sandpaper to remove any paint and plastic coatings from the surface of the particles.
Fourier transform infrared spectroscopy (FTIR) was used to identify the type of plastic particles used [54]. The particles were ground and then the powder samples were analysed by means of a FTIR spectrometer Nicolet 380 (Thermo Fisher Scientific Inc., Waltham, MA, USA).

Settling and Rising Tests
Particle settling and rising tests were performed in a cylindrical glass column which was installed vertically. Figure 1 shows a sketch of the glass column.  Figure 1. A sketch of apparatus used in rising (a) and settling (b) tests. 1-glass column; 2-rubber plug; 3-stripe; 4-water tank; 5-particle.  The inner diameter of the column was 5.5 cm. Two horizontal stripes were marked on the outside of the column, with one on the top end and the other one on the bottom side of the column to monitor the settling/rising points at the beginning and end of each test. The procedure for the particle settling tests was as follows: the lower end of the column was plugged with a rubber stopper, and then water was poured into the column to the upper edge of the column. The particle was immersed in the water from the upside of the column, and then allowed to settle due to gravity. Settling time was measured as the time required for the particle to settle from the upper to the lower stripe. The technique for the particle rising tests was similar; however, the upper end of the column was plugged with the stopper, while the lower end of the column was immersed in the tank filled with water. The particle was introduced through the lower end of the column and then the free rising of the particle was studied. Particle rising time was measured as the time required for the particle to ascent from the lower to the upper stripe. In each test, the particle was soaked in water for 5 min to achieve sufficient contact of the particle with the water, and then placed in the centre of the lower or upper part of the column. Following this, the particle moved along the central line of the column to prevent particle and wall contact, the so-called "wall effect".   Figure 1. A sketch of apparatus used in rising (a) and settling (b) tests. 1-glass column; 2-rubber plug; 3-stripe; 4-water tank; 5-particle.  Our observations revealed that the plastic and metal particles had appearances as shown in Figure 2a. However, some plastic particles had an untypical shape, as shown in Figure 2b (third from the left). In order to assess the particle size and shape, the mean diameter of each particle (dm) and the diameter to height ratio (r) were calculated as follows:

Physical Characteristics of the Particles
where Dmin and Dmax are the minimum and maximum diameters of each particle, and h is the height of the particle. The aspect ratio of each particle was calculated as the maximum diameter of the particle divided by its height: Our observations revealed that the plastic and metal particles had appearances as shown in Figure 2a. However, some plastic particles had an untypical shape, as shown in Figure 2b (third from the left). In order to assess the particle size and shape, the mean diameter of each particle (d m ) and the diameter to height ratio (r) were calculated as follows: where D min and D max are the minimum and maximum diameters of each particle, and h is the height of the particle. The aspect ratio of each particle was calculated as the maximum diameter of the particle divided by its height: The physical characteristics of the particles are summarized in Table 1. In general, the mean diameters of the plastic and metal particles were similar and within the range of 1.9-2.43 cm. The maximum diameter of the plastic particles was between 2.3 cm and 3.1 cm, while for the particles of Metal 1 and 2 this value was about 2.8 cm and 2.5 cm, respectively. Meanwhile, there was a difference in the aspect ratio of the particles. For the plastic particles, the aspect ratio was between 1.8 and 2.8; for Metal 1 particles this increased to 4.7, which was significantly higher than for Metal 2 and plastic particles. Moreover, the plastic particles and the particles of Metal 2 exhibited predominant cylindrical shapes with rare stripes, and had a similar aspect ratio.
The findings revealed a non-sphericity of the metal and plastic particles. Recent studies have introduced a number of factors describing the non-sphericity of particles and methods to estimate their size [34,36,37]. Among these, the equivalent diameter (d e ) is commonly used to characterize the size of non-spherical particles. The equivalent diameter is determined as the diameter of a sphere of the same volume as the particle of interest: where V is the volume of the particle, which can be measured experimentally or calculated as the mass of the particle divided by its density. The masses and densities of the particles were measured experimentally, as stated in Section 2.1. Further calculations of equivalent diameters were made based on experimentally measured volumes of plastic and metal particles. The equivalent diameters of plastic particles were in the range of 1.29-1.75 cm, while Metal 1 and 2 particles exhibited d e values of about 1.0 and 1.03-1.14 cm. Hence, the equivalent diameters of the plastic particles were higher than the metal particles.
Moreover, the studies showed differences between the equivalent and mean diameter values. In general, the mean diameters of the particles were higher than the equivalent diameters. More specifically, the mean diameters of plastic particles were 1.3-1.6 times higher compared to the equivalent diameters. A slight increase in dm/de ratio was observed for the metal particles, which ranged from 1.9 to 2.1.
Our observations showed that the density of the plastic particles was between 0.61 and 0.95 g/cm 3 , while Metal 1 particles demonstrated a density up to 4.43 g/cm 3 , which was 4.6 and 7.2 times higher than that of the plastic particles. The density of Metal 2 particles was 1.67-1.97 g/cm 3 , which was more than two times less than the Metal 1 particles, and double the plastic particles.
To further understand the reasons for the differences in the densities of the metal particles, SEM analysis was carried out. Figure 3 demonstrates the SEM images and the elemental compositions of the metal particles. The elemental composition of the metal particles revealed two types of metals. Metal 1 particles were made of iron (99.0%) with slight additives of aluminium (0.7%) and silicon (0.3%), while Metal 2 particles were composed of aluminium (98.4%), silicon (0.6%), manganese (0.5%), and iron (0.5%). Apparently, the identification of Si in the caps can be attributed to the treatment of the caps with sandpaper. The results were consistent with the previously measured densities of the metal particles. However, the metal caps had inside plastic coatings, which reduced the densities of the particles as compared to those of pure aluminium (2.7 g/cm 3 ) and iron (5.0 g/cm 3 ).
As for the plastic particles, a predominant number of them used in the study were The elemental composition of the metal particles revealed two types of metals. Metal 1 particles were made of iron (99.0%) with slight additives of aluminium (0.7%) and silicon (0.3%), while Metal 2 particles were composed of aluminium (98.4%), silicon (0.6%), manganese (0.5%), and iron (0.5%). Apparently, the identification of Si in the caps can be attributed to the treatment of the caps with sandpaper. The results were consistent with the previously measured densities of the metal particles. However, the metal caps had inside plastic coatings, which reduced the densities of the particles as compared to those of pure aluminium (2.7 g/cm 3 ) and iron (5.0 g/cm 3 ).
As for the plastic particles, a predominant number of them used in the study were marked with a '2' universal recycling symbol. This means that they were produced of highdensity polyethylene (HDPE). Moreover, for unmarked particles, further FTIR analysis was carried out to identify the particle composition. Figure 4 shows the IR spectra produced from the unmarked particles.  A small absorption band at 1377 cm −1 (Figure 4a) indicated that a majority of unmarked particles were produced from low-density polyethylene (LDPE) [54,55], and a few were made of polypropylene (PP) (Figure 4b). The results of plastic identification and the measured densities of the particles were consistent with the literature data for HDPE (0.940-0.970 g/cm 3 ), LDPE (0.910-0.940 g/cm 3 ) and PP (0.89-0.92 g/cm 3 ) [56].
To summarise, the bottle caps were of irregular shape with differences in density. The densities of the plastic particles were lower than water (1.0 g/cm 3 ), while the densities of the iron and aluminium particles were significantly higher than that of water. Following the physical characteristics of the particles, the plastic particles can float in a water environment, while the metal ones settle. Moreover, having three different types of particle (plastic, aluminium and iron) enabled us to evaluate the role of different particle characteristics such as density, size and shape. Hence, further studies are required to analyse the behaviour of particles in media and to measure the velocities of particles rising or settling in a water environment.

Particle Settling Velocity
The downward force of gravity acting on a particle is defined as follows: where m and V are the mass and the volume of the particle; g is the gravity acceleration; and ρp is the density of the particle. The particle is also affected by the upward buoyancy force of Archimedes: where ρl is the density of the liquid in which the particle is immersed. Furthermore, the settling particle experiences a drag force from the liquid due to the viscosity and pressure gradient [57]: A small absorption band at 1377 cm −1 (Figure 4a) indicated that a majority of unmarked particles were produced from low-density polyethylene (LDPE) [54,55], and a few were made of polypropylene (PP) (Figure 4b). The results of plastic identification and the measured densities of the particles were consistent with the literature data for HDPE (0.940-0.970 g/cm 3 ), LDPE (0.910-0.940 g/cm 3 ) and PP (0.89-0.92 g/cm 3 ) [56].
To summarise, the bottle caps were of irregular shape with differences in density. The densities of the plastic particles were lower than water (1.0 g/cm 3 ), while the densities of the iron and aluminium particles were significantly higher than that of water. Following the physical characteristics of the particles, the plastic particles can float in a water environment, while the metal ones settle. Moreover, having three different types of particle (plastic, aluminium and iron) enabled us to evaluate the role of different particle characteristics such as density, size and shape. Hence, further studies are required to analyse the behaviour of particles in media and to measure the velocities of particles rising or settling in a water environment.

Particle Settling Velocity
The downward force of gravity acting on a particle is defined as follows: where m and V are the mass and the volume of the particle; g is the gravity acceleration; and ρ p is the density of the particle. The particle is also affected by the upward buoyancy force of Archimedes: where ρ l is the density of the liquid in which the particle is immersed. Furthermore, the settling particle experiences a drag force from the liquid due to the viscosity and pressure gradient [57]: where ψ is the drag coefficient. The force balance for the settling particle implies that: A particle immersed in stagnant water is expected [38,57] to fall with a particular acceleration for a short period of time to reach a constant velocity, which is called the terminal settling velocity of the particle. Rearranging Equation (8) gives the expression for the terminal settling velocity of the particle: However, the drag coefficient of non-spherical particles is typically unknown. Therefore, from an experimental point of view, the drag coefficient can be calculated based on the measurements of the settling velocities of the particles of interest:

Particle Rising Velocity
Different from the metals, the plastic particles were characterized by a rising motion in the water consistent with the measured densities of the plastic particles shown in Table 1. Similarly to particle settling, the force balance for the plastic particles rising in water is expressed as follows: From Equation (11), the drag coefficient of the rising plastic particle can be expressed as: where v is the rising velocity of the particle. Moreover, for the particles rising or settling in the liquid, the Reynolds number (Re) was calculated to assess the hydrodynamic regime: where v is the particle velocity and µ is the viscosity of the medium. Particles moving in the liquid were generally accepted to move in the following hydrodynamic regimes: laminar (Re < 1), turbulent (Re > 1000), and transitional (Re = 1-1000) [57,58].
Froude number is commonly used to estimate the effects from the inertia force of gravity, and can be calculated as follows [58]: Equations (10) and (12)- (14) were used to calculate the ψ, Re and Fr values for the plastic, aluminium and iron particles used in this study. Figure 5 shows the experimental results of the settling velocities for the aluminium and iron particles, and the rising velocities for the plastic particles in stagnant water.

Analysis of the Results of Particles Settling and Rising in Water
Recycling 2022, 7, x FOR PEER REVIEW 10 of 16 Figure 5 shows the experimental results of the settling velocities for the aluminium and iron particles, and the rising velocities for the plastic particles in stagnant water. The observations revealed differences in the velocities of the particles immersed in water. The iron particles showed the maximum velocities (17.6-17.7 cm/s), while the settling velocities of the aluminium particles were about 11.5-12.0 cm/s. For the plastic particles, the rising velocities ranged from 2.1 to 6.1 cm/s. Moreover, the settling velocities of the iron and aluminium particles were 2.9-8.4 and 2.0-5.5 times higher than the rising velocities of the plastic particles. This significant contrast in the velocities of the metal and plastic particles can be attributed to the differences in their densities and equivalent diameters.

Analysis of the Results of Particles Settling and Rising in Water
The equivalent diameters of the plastic particles were between 1.29 and 1.75 cm with a mean equivalent diameter of 1.55 cm. The equivalent diameters of the aluminium and iron particles were less than the plastic ones, and ranged from 0.97 to 1.15 cm with mean values of 1.1 cm and 1.0 cm, respectively. Moreover, the sample of plastic particles was characterized by a high discrepancy of de.
The results were consistent with the further calculations of the drag coefficients. Figure 6a shows the drag coefficients which were calculated for plastic, iron and aluminium particles moving in the water. Figure 6b demonstrates the effect of the Reynolds number on ψ. The observations revealed differences in the velocities of the particles immersed in water. The iron particles showed the maximum velocities (17.6-17.7 cm/s), while the settling velocities of the aluminium particles were about 11.5-12.0 cm/s. For the plastic particles, the rising velocities ranged from 2.1 to 6.1 cm/s. Moreover, the settling velocities of the iron and aluminium particles were 2.9-8.4 and 2.0-5.5 times higher than the rising velocities of the plastic particles. This significant contrast in the velocities of the metal and plastic particles can be attributed to the differences in their densities and equivalent diameters.
The equivalent diameters of the plastic particles were between 1.29 and 1.75 cm with a mean equivalent diameter of 1.55 cm. The equivalent diameters of the aluminium and iron particles were less than the plastic ones, and ranged from 0.97 to 1.15 cm with mean values of 1.1 cm and 1.0 cm, respectively. Moreover, the sample of plastic particles was characterized by a high discrepancy of d e .
The results were consistent with the further calculations of the drag coefficients. Figure 6a shows the drag coefficients which were calculated for plastic, iron and aluminium particles moving in the water. Figure 6b demonstrates the effect of the Reynolds number on ψ.
The findings showed that the drag coefficients ranged from 1.0 to 4.2 for plastic, from 2.9 to 3.9 for aluminium, and from 5.4 to 5.5 for iron particles, with an exception observed for three plastic particles with a ψ of 12.9, 23.2 and 25.8. The high values of the drag coefficients for a few plastic particles can be attributed to their irregular shapes and having a larger surface exposed to the water compared with the other particles. Although the equivalent diameters of iron and aluminium particles were similar (d e~1 .0) cm, the drag coefficients of the iron particles were 1.4-1.8 times higher than those of the aluminium ones. This can be due to differences in the aspect ratio, shape and density of the particles. The findings showed that the drag coefficients ranged from 1.0 to 4.2 for plastic, from 2.9 to 3.9 for aluminium, and from 5.4 to 5.5 for iron particles, with an exception observed for three plastic particles with a ψ of 12.9, 23.2 and 25.8. The high values of the drag coefficients for a few plastic particles can be attributed to their irregular shapes and having a larger surface exposed to the water compared with the other particles. Although the equivalent diameters of iron and aluminium particles were similar (de~1.0) cm, the drag coefficients of the iron particles were 1.4-1.8 times higher than those of the aluminium ones. This can be due to differences in the aspect ratio, shape and density of the particles.
It follows from the Reynolds numbers that the rising plastic particles in water were characterized by a transitional hydrodynamic mode with Re values varying from 269 to 959. Meanwhile, high Reynolds numbers of the iron (Re = 1692-1711) and aluminium (Re = 1186-1342) particles showed that they were settled under turbulent conditions. Moreover, increasing Re resulted in the decrease in drag coefficients from 12.9 to 2.6 for plastic and from 3.9 to 2.9 for aluminium particles. The effect of Re on the ψ of the iron particles was insignificant. Figure 7 shows the Froude number plotted against the velocity of the particles and the Reynolds number. It follows from the Reynolds numbers that the rising plastic particles in water were characterized by a transitional hydrodynamic mode with Re values varying from 269 to 959. Meanwhile, high Reynolds numbers of the iron (Re = 1692-1711) and aluminium (Re = 1186-1342) particles showed that they were settled under turbulent conditions. Moreover, increasing Re resulted in the decrease in drag coefficients from 12.9 to 2.6 for plastic and from 3.9 to 2.9 for aluminium particles. The effect of Re on the ψ of the iron particles was insignificant. Figure 7 shows the Froude number plotted against the velocity of the particles and the Reynolds number. The findings showed that the drag coefficients ranged from 1.0 to 4.2 for plastic, from 2.9 to 3.9 for aluminium, and from 5.4 to 5.5 for iron particles, with an exception observed for three plastic particles with a ψ of 12.9, 23.2 and 25.8. The high values of the drag coefficients for a few plastic particles can be attributed to their irregular shapes and having a larger surface exposed to the water compared with the other particles. Although the equivalent diameters of iron and aluminium particles were similar (de~1.0) cm, the drag coefficients of the iron particles were 1.4-1.8 times higher than those of the aluminium ones. This can be due to differences in the aspect ratio, shape and density of the particles.
It follows from the Reynolds numbers that the rising plastic particles in water were characterized by a transitional hydrodynamic mode with Re values varying from 269 to 959. Meanwhile, high Reynolds numbers of the iron (Re = 1692-1711) and aluminium (Re = 1186-1342) particles showed that they were settled under turbulent conditions. Moreover, increasing Re resulted in the decrease in drag coefficients from 12.9 to 2.6 for plastic and from 3.9 to 2.9 for aluminium particles. The effect of Re on the ψ of the iron particles was insignificant. Figure 7 shows the Froude number plotted against the velocity of the particles and the Reynolds number. In general, increasing the velocity of the particles resulted in the growth of the Froude number, as shown in Figure 7a. The highest Fr values were observed at the maximum settling and rising velocities of the particles. However, the Froude number values were less than 1.0, indicating the subcritical mode of the particles moving in the water, in which the effects of gravity dominated over inertia. In particular, for the plastic particles, an increase in rising velocity from 2.1 to 6.1 cm/s resulted in the growth of the Froude number from 0.06 to 0.16 (2.7 times). The aluminium and iron particles were characterized by relatively stable Froude number values (Fr Al = 0.36 and Fr Iron = 0.57) at settling velocities of 12 cm/s and 18 cm/s, respectively. Moreover, the Fr Al /Fr plastic ratio was in the range of 2.6-6.2, while Fr Iron /Fr plastic was between 3.9 and 10.2. Although the study showed a linear dependency between Fr and Re, there was an insignificant scatter for plastic particles, as shown in Figure 7b.
The results of study are summarized in Table 2. The study revealed density and velocity differences between the plastic and metal caps, and hence, a gravity separation can be applied [32]. Based on the results of the physical characterization of the particles and their settling and rising velocities in water, a simplified process flowsheet for the separation of caps from sand shores is proposed (Figure 8). The proposed procedure is as follows. Finally, three products are generated, namely, sand fraction, plastic caps, iron caps, and aluminium caps.
The proposed flowsheet has the following advantages: it incorporates the recovery of sand fraction in the beginning of the process; it involves environmentally friendly processes and conventional gravity separation equipment; and, finally, high productivity and throughout capacity can be achieved.  Figure 8. A simplified flowsheet for cap separation from sand shores using dense medium (a) and magnetic (b) separation in the final stage of the process operation.
Sand shores, containing aluminium, iron and plastic caps are screened to obtain undersized products of −10(5) mm (sand fraction) and −30 + 10(5) mm. The latter is then separated by gravity concentration using the sink-float process and conventional gravity separators or classifiers [23]. To prevent the adverse effects of bottle cap contamination with dirt and sand on separation efficiency, a washing operation can be implemented before gravity separation (e.g., a screening operation). An overflow element of the sink-float separation retains the plastic caps, while the aluminium and iron ones are concentrated in the underflow product. The sink fraction is then subjected to a dense medium separation (DMS). The appropriate density of separation medium (ρ m ) is considered to be between 2 and 4 g/cm 3 . Under these conditions, aluminium particles will float, while iron particles will sink. The ratio of the settling to rising velocities of the particles can be expressed as follows: where v St is the settling velocity of iron particles and v Al is the rising velocity of aluminium particles. Moreover, the calculations show that, if ρ m = 3.0-3.1 g/cm 3 (k = 1), then aluminium particles will rise at the same velocity as the iron particles will settle. Alternatively, a magnetic separation can be used instead of DMS. Finally, three products are generated, namely, sand fraction, plastic caps, iron caps, and aluminium caps.
The proposed flowsheet has the following advantages: it incorporates the recovery of sand fraction in the beginning of the process; it involves environmentally friendly processes and conventional gravity separation equipment; and, finally, high productivity and throughout capacity can be achieved.

Conclusions
1. The physical characteristics of plastic and metal bottle caps were measured, and the composition of the particles was analysed. SEM analysis showed that there were two types of metal caps: aluminium and iron. The results of FTIR spectroscopy indicated that plastic particles were mainly represented by HDPE and LDPE, while a few particles were made of PP. Although the particles showed comparable equivalent diameters-1.29-1.75 cm (plastic), 1.03-1.15 cm (aluminium) and 0.97-1.1 cm (iron)-the aspect ratio of the iron particles was significantly higher compared to the aluminium and plastic particles; 2. The study exhibited differences in the densities of the particles. The densities of the plastic particles ranged between 0.752 and 0.956 g/cm 3 , while aluminium and iron particles observed significantly higher densities of 1.66-1.97 g/cm 3 and 4.43 g/cm 3 , respectively. A slight reduction in the densities of the metal particles can be attributed to the inside plastic coatings of these particles; 3. The differences in physical characteristics resulted in plastic particles floating and metal particles sinking in a water environment. The experimental tests obtained terminal settling velocities for the aluminium (12 cm/s) and iron (18 cm/s) particles, which were significantly higher than the rising velocities of the plastic particles (2.1 to 6.1 cm/s). The results made it possible to obtain new data regarding the drag coefficients of aluminium, iron and plastic particles moving in water; 4. Based on the results of the physical characterization of the particles and their settling and rising velocities in water, a simplified process flowsheet for the recovery of plastic and metal bottle caps from sand coasts was proposed. In addition to solving the significant problem of sea-shore cleaning and reducing environmental impact, the flowsheet allows the user to obtain three valuable products for further processing: the concentrate (plastic particles), the middlings (iron particles), and the tailings (aluminium particles).
Further studies should focus on large sample investigation and the management of other materials streams containing bottle caps.

Conflicts of Interest:
The author declares no conflict of interest.