3.1. Two-Phase Flow Characterization
To understand the coupling regime between the solid phase and the fluid phase, it is essential to calculate the characteristic parameters of the fluid and solid phases.
First, we present the fluid phase characteristic parameters (
Table 3). Nine hydraulic configurations (or cases) were obtained by combining tank height and number of opened outlet ducts. The Reynolds number, Re, was computed as follows: Re = Q/(W
td
f)d
f/ν (where Q is the flow rate, W
t = 0.45 m the channel width, d
f = 2.5 × 10
−2 m the channel passage height (
Figure 1a) and ν the kinematic viscosity of water). Re increases with the flow rate and ranges between 1950 and 3400. Re values suggest the flow regime within the separator is in the transitional regime, approaching the turbulent regime.
The characteristic time of the fluid phase is defined as τf = df/Uf (where Uf = Q/(Wtdf) is the fluid characteristic velocity). It decreases as the flow rate increases. Its maximum value (0.32 s) is obtained for the lowest flow rate (case #1), while the minimum value (0.18 s) for the largest one (case # 9).
The characteristic parameters of the solid phase are the solid phase volume fraction, αs, the particle Reynolds number, Rep, and the solid phase relaxation time, τs.
The solid phase volume fraction, defined as the ratio of the total volume of the dispersed phase and the total volume of the mixture [
14], is equal to 5.2 × 10
−5.
For all cases, Re
p = d
p|U
p − U
f|/ν (where d
p is the particle characteristic dimension, U
p and U
f the particle and fluid velocity respectively) results as being to the order of 10
2–10
3 (see
Table 4 for samples belonging to the size class I and
Table 5 for samples belonging to the size class II).
The solid phase relaxation time τ
s = ρ
sd
p2/(18 μf) (where ρ
s is the solid phase density, μ the dynamic viscosity and f = (1 + 1/6 Re
p2/3) a drag coefficient) is the time a solid particle employs to respond to changes of the fluid phase velocity. The relaxation time is strongly influenced by the particle size. In fact, larger particles take longer to respond to changes of the fluid velocity, while smaller particles respond quicker (
Table 4 and
Table 5).
According to [
14], the coupling regime among solid particles with Re
p to the order of 10
3 in a mixture with a solid phase volume fraction to the order of 10
−5 is expected to be two-way. Hence, a reciprocal influence between the phases does exist. A further important parameter to define the coupling regime between the two phases is the Stokes number (St), defined as St = τ
p/τ
f, where τ
p is the particle relaxation time and τ
f the flow field characteristic time [
15]. St was computed only for those cases where the characteristic time of the fluid phase assumes extreme values, i.e., for case #1 when the characteristic time of the fluid phase assumes its maximum value and for case #9 when it assumes the minimum value. Stokes numbers are reported in
Table 6 for samples belonging to the size class I and
Table 7 for samples belonging to the size class II. The Stokes number is smaller than 1 for all the cases investigated signifying that the solid phase relaxation time is smaller than the characteristic time of the fluid phase. Being the difference between the velocity of the solid and fluid phases small, the coupling among the two phases is large.
3.2. Mono-Material Separation Tests
Mono-material tests shown in this contribution were conducted employing samples of 12.42 × 10
−6 m
3 solid volume. The results obtained are observed against tests conducted with samples of 6.21 × 10
−6 m
3 solid volume [
13] (
Figure 4,
Figure 5 and
Figure 6). Since the fluid flow rate was kept constant, the comparison makes it possible to evaluate the effectiveness of the hydraulic separator as a function of the solid volume fraction treated within the device. Increasing the solid phase volume treated within the device and keeping unchanged the fluid flow rate, the solid phase volume fraction α
s increases from 2.6 × 10
−5 to 5.2 × 10
−5. As already stated in
Section 3.1, for α
s to the order of 10
−5 and particle Reynolds number to the order of 10
3, a two-way coupling among the phases takes place. Two-way coupling presupposes that there is a mutual influence between the two phases, i.e., a reciprocal exchange of forces. Those forces, usually referred to as two-way coupling forces, are directly proportional to the solid phase volume fraction and to the difference between the velocity of the fluid and solid phases and inversely proportional to the squared solid particles diameter. It is worth noting that tests were repeated more than one time to verify reproducibility of the results.
The sedimentation efficacy, η, defined as the ratio between the amount of material settled within the apparatus and the material treated within the separator, makes it possible to understand whether and how the increase of the solid phase volume fraction, i.e., the two-way coupling forces, influences the separation efficacy. Each plot of
Figure 4,
Figure 5 and
Figure 6 shows η of the plastic sample for both solid volumes, i.e., 6.21 × 10
−6 m
3 (blue bars) and 12.42 × 10
−6 m
3 (red bars). Additionally, η is plotted for increasing fluid flow rate.
Figure 4a shows that PC 2-WF, belonging to the size class I, is completely expelled from the apparatus except for case #1 and 12.42 × 10
−6 m
3 of solid particles input to the device, being in this case roughly 5% the amount of material that settles in the separator chambers. PC 2-WF, belonging to the size class II, behaves as the PC 2-WF that belongs to size class I (
Figure 5a) and is completely expelled from the apparatus in all cases except case #1. For this sample, the amount of polymer settled within the device slightly increases, doubling the volume of the sample. For the same fluid flow rate (case #1) and both solid volume fractions, a higher sedimentation efficacy is observed for the samples with solid particles belonging to the larger size class. Samples of PC 3-RF, belonging to both size classes, are completely expelled from the experimental apparatus for all hydraulic configurations but for case #1. For case #1, the test conducted with a solid volume of 6.21 × 10
−6 m
3 of PC 3-RF belonging to the size class I (
Figure 4b) shows that the polymer settles in a higher percentage (11.4%) than in the other case (3.4%). The analogous behavior was observed for PC 3-RF belonging to the size class II with different percentages, 19% instead of 12.4% (
Figure 5b). Then, PC 3-RF shows a different behavior respect to PC 2-WF since increasing the concentration of solid material, the percentage of material settling within the apparatus decreases. The different behavior of PC samples is related to the shape of the particles, which influences the sedimentation efficacy. PC 2-WF particles have a flat surface and a very jagged perimeter while PC 3-RF particles have a flat, more regular surface. PC 1-V is completely expelled from the separator for all cases except for cases #1 and #4 (
Figure 6a). In both of these cases, by increasing the volume of solid particles, sedimentation is disadvantaged. Therefore, due to their regular shape, the behavior of PC 1-V granules is more similar to PC 3-RF than to PC 2-WF.
PET 6-WF belonging to the size class I (
Figure 4c) is completely expelled from the apparatus for flow rates larger than 1.08 L/s (case #3). For case #1 and 6.21 × 10
−6 m
3 of solid volume treated within the device, 88% of the polymer settles within the separator chambers, whereas 90.3% of the solid volume settles after doubling the sample. A similar behavior was observed for case #4, when 43.3% and 57.5% of material settles within the apparatus when 6.21 × 10
−6 m
3 and 12.42 × 10
−6 m
3 of solid volume are treated within the device respectively. For case #7, the opposite behavior is observed. In fact, the percentage of material settling within the apparatus decreases (from 28.1% to 18.7%) as the amount of material treated within the apparatus is doubled. For case #2, the percentage of material settling within the apparatus is almost the same regardless of the volume treated within the apparatus. Insignificant or null quantities of polymer settle within the apparatus for case #5 and both solid volumes. For case #1, roughly 95% of PET 6-WF belonging to size class II settles within the hydraulic channel regardless of the volume treated within the apparatus (
Figure 5c). For case #4, the test carried out with 6.21 × 10
−6 m
3 of solid phase volume shows a larger percentage of polymer settling within the apparatus (80.8%) than the other test. Analogously, by increasing the flow rate (case #7), the percentage of material settling within the apparatus is larger (62.4% instead of 10.5%) for a smaller amount of solid volume treated within the apparatus. Also, for case #2, when 6.21 × 10
−6 m
3 of solid volume is treated within the device, the percentage of material settling within the apparatus is larger than in the other case, i.e., 25.7% instead of 11.9%. Further increasing the flow rate, an opposite behavior is observed, i.e., a larger percentage of material settles when a larger amount of material is treated within the apparatus. For the two solid volumes treated within the apparatus and for the hydraulic configuration denoted case #1, roughly the same percentage of PET 4-RF belonging to the size class I settles (82% and 83.6%;
Figure 4d). For case #4, a smaller percentage of the sample settles within the apparatus when smaller quantities of polymer are treated within the device (39.7% rather than 47.6%). The opposite behavior is observed for case #7. In this case, a smaller percentage of sample was collected in the separator chambers when 6.21 × 10
−6 m
3 of solid volume was treated within the device (32.7% rather than 27%). For case #2, roughly the same percentage of material settles for both solid volumes investigated. The behavior of PET 4-RF belonging to the size class II is analogous to the one described for the material belonging to the lower size class (
Figure 5d). The PET sample of virgin material (PET 2-V) behaves similarly to waste or regenerated PET samples (
Figure 6b). For case #1 and both solid volumes treated within the apparatus, the polymer completely settles. For case #4, for tests employing 6.21 × 10
−6 m
3 of solid volume, 92% of the sample settles whereas, doubling the solid volume treated within the device, 95% of plastic material remains within the apparatus. For case #7, a similar percentage of material settles for both the solid volumes. For case #2, the amount of material settling within the device seems to depend on the solid volume treated. In this case, 32.7% and 23.6% of polymer can be collected within the device for 6.21 × 10
−6 m
3 and 12.42 × 10
−6 m
3 solid volume samples respectively. The polymer is completely expelled from the apparatus for cases #5, #3, #8, #6, and #9 and both solid volumes. All PET samples show that for a low fluid phase velocity, the increase of the solid volume fraction determines the increase of the sedimentation efficacy. In fact, increasing the volume of solid particles treated within the device, the fluid phase slows down and the sedimentation processes is favored. For large flow rates, the fluid phase velocity increases as well as drag effects on the particles. Then those particles reach the outlet ducts in larger amounts determining a reduction of the sedimentation efficacy.
PVC 4-WP belonging to the size class I (
Figure 4e) completely settles within the device for low values of the fluid flow rate (cases #1, #4, #7). For case #2, more than 43% of polymer settles for both solid volumes. For cases #5 and #3, tests conducted treating 6.21 × 10
−6 m
3 of solid particles show a lower percentage of material settling within the device with respect to tests with 12.42 × 10
−6 m
3 of solid particles (
Figure 4e). Instead, for cases #8, #6, and #9, a larger percentage of solid particles settle within the device for the 6.21 × 10
−6 m
3 volume tests than for the 12.42 × 10
−6 m
3 volume ones. For cases #1, #4, #7, and #2, PVC 4-WP belonging to the size class II (
Figure 5e) completely settles within the device. For cases #3 and #8, the percentage of material settling within the device is higher than 95% and slightly larger when a lower amount of polymer is treated within the device. For case #6, 78% of the sample settles within the device when 6.21 × 10
−6 m
3 of solid particles are treated while 67% of the polymer can be collected in the separator chambers when the solid volume is doubled. For case #9, the larger is the amount of polymer treated within the device, the higher is the percentage of material settling within the device (49% instead of 25%). For cases #1, #4, and #7, the same percentage of PVC 6-RP belonging to the size class I (
Figure 4f) settles in the separator chambers for both solid volumes treated within the device. For cases #2 and #5, a higher percentage of polymer settles within the device for the test with the larger amount of solid volume (77.9% instead of 70.5% and 12.7% instead of 9.4%). For cases #3 and #8, the opposite occurs. For case #9, the polymer is completely expelled from the device. For cases #1, #4, #7 and #2, PVC 6-RP belonging to the size class II (
Figure 5f) almost completely settles in the device. For cases #5, #3 and #8, the percentage of material settling within the device is higher for the tests conducted with samples of smaller volume. The opposite behavior was observed for cases #6 and #9. For case #1, PVC 1-V almost completely settles in the separator chambers for both volumes treated within the device (
Figure 6c). For cases #4 and #7, a remarkable difference between the percentages of material that settles within the chambers as a function of the amount of material treated within the device was observed. In fact, the tests conducted inserting 6.21 × 10
−6 m
3 of solid particles show a significantly higher percentage of settled material with respect to the tests where the amount of treated material was doubled. For cases #2 and #5, an opposite behavior was observed. In fact, as the fluid flow rate increases, a higher percentage of material settles within the separator chambers when 12.42 × 10
−6 m
3 rather than 6.21 × 10
−6 m
3 of solid particles are treated within the device. For low flow rates, PVC 2-V completely settles in the separator chambers for both volumes treated within the device (
Figure 6d). For cases #7 and #2, a slightly larger percentage of solid particles settles within the chambers in the tests with 6.21 × 10
−6 m
3 of polymer treated within the device. The opposite occurs for cases #5, #8, and #6. Therefore, for low values of the flow rate (lower than 1 L/s), no remarkable differences in the percentage of PVC sample settling within the device were observed for both solid volumes investigated. For slightly larger values of the flow rate, between 1 L/s and 1.13 L/s, the increase in the amount of solid material introduced into the separator results in a reduction of the sedimentation efficacy, since the interaction between the solid and the fluid phases is more effective and the fluid phase tends to drag the solid particles towards the outlet ducts. For values of the flow rate larger than 1.13 L/s, increasing the amount of material treated within the device, a higher percentage of solid particles tend to settle within the apparatus.
For case #1, a small percentage of PLA 2-WF belonging to the size class I (
Figure 4g) settles in the separator chambers in the test with 6.21 × 10
−6 m
3 of polymer treated within the device. The increase of the solid volume determines the increase of the sedimentation efficacy. The bio-plastics is almost completely expelled from the apparatus for flow rates larger than 0.84 L/s. For cases #1 and #4, a remarkable percentage of PLA 2-WF belonging to the size class II settles in the separator chambers when a lower amount of polymer is treated within the device (45.8% instead of 35.2% and 8.9% instead of 3.3% respectively). An opposite behavior was observed for case #7, being the percentage of settled material equal to 22.1% when 12.42 × 10
−6 m
3 of bio-plastics are treated within the device and almost equal to 0% for half volume. For cases #1, #4 and #7, PLA 1-V (
Figure 6e) completely settles within the separator chambers. For case #2, the percentage of PLA 1-V settling in the separator is remarkable for both volumes (roughly 96%). For cases #5, #3, and #8, a smaller percentage of bio-polymer settles for the smaller solid volume case (6.21 × 10
−6 m
3). The sample is completely expelled from the apparatus for flow rates larger than 1.24 L/s.
For case #1, the larger is the amount of MATER-BI 2-WF belonging to the size class I treated within the device, the larger is the percentage of settled material (85% instead of 79.2%;
Figure 4h). A similar behavior was observed for cases #4 and #7 (26.1% instead of 16.7% and 3.3% instead of 1.2% respectively). Instead, the opposite behavior was observed for case #2. For case #1, MATER-BI 2-WF belonging to the size class II settles in analogous percentages for both volumes of material treated within the device (
Figure 5h). Increasing the flow rate (cases #4, #7 and #2), larger percentages of MATER-BI 2-WF belonging to the size class II settle in the separator chambers when 12.42 × 10
−6 m
3 of solid volume are treated within the device rather than 6.21 × 10
−6 m
3. For cases #1 and #4, a considerable percentage of MATER–BI 1-V (
Figure 6f) settles in the separator chambers for both solid volumes treated within the device. For cases #7 and #2, the sedimentation efficacy is remarkable (higher than 17%) and larger when larger amounts of bio-polymer are treated. The sedimentation efficacy is lower than 4% for flow rates larger than 1.08 L/s.