3.1. Gravimetric Measurements of the Particulate Material
To characterize the deposited particle mass on the fibers, experiments were terminated at a pre-defined TIF. Subsequently, a gravimetric analysis was conducted. Then, a new experiment was started. Experiment times varied between 3 and 210 min, depending on the flow velocity and feed rate of the aerosol generator (see
Section 2.2). All experiments shown were carried out with the aerosol generator described in
Section 2.2, whose dispersion technology is based on VDI 491-3 and ISO 5011. Continuous control of the ring loading is intended to exclude the possibility of ring loading failure and thus inconstant dispersion conditions. Any deviations in the deposited mass can thus also be attributed to inconsistencies in the dispersion or to the occurrence of electrostatic effects, whereas the latter is counteracted by neutralizing the aerosol with an
Kr.
Gravimetric analysis of the particle material on the 16 mm long array (5 fibers) is presented in
Figure 8. For experiments executed at a face velocity of 0.15 m/s, no deposition was detected below a TIF of
. Similarly, for experiments conducted at airflow velocities of 0.25 m/s and 0.1 m/s, no loading was detected below
. At high TIF, however, the mass on the fiber array increases continuously with increasing TIF at airflow velocity below 0.25 m/s, reaching a maximum of 5.5
in the experiments at 0.1 m/s.
The investigation revealed particle deposition on the fibers in experiments with compact morphology. Increased deposition occurred at airflow velocities greater than 1 m/s (Stokes greater than 5.1). Particles with large diameters, which represent the high-mass fraction of the particle distribution (PD), were most probably deposited by inertia. After reaching a TIF of , the increase in mass slowed down because of the poor growth of compact-shaped structures. The structure likely grows in the direction of flow and is compacted by incoming particles. Hence, the collector size increases slightly only. In the experiments with the compact structures (1.8 m/s and 1.2 m/s), increases in particle mass on the array are observed at similar TIF. Given that the TIF is a time-dependent metric and each data point is a result of three measurements, the probability of a random increase in mass due to discontinuous dispersion is negligible with the duration of the experiments.
In the experiments at 0.65 m/s, the deposited mass increased considerably above TIF . First, the deposited mass was below that of experiments with a complete compact structure. Shortly after the TIF , a sharp increase in the deposited mass on the fiber array is observed, indicating the complete closure of the structure and the resulting enlargement of the collector area. The increasing collector area increased the probability of separation, which might increase the impact coefficient. The steep increase in mass with increasing TIF was observed in all replicate experiments. The deposited mass was nearly 22.6 fiber length (five times 16 mm loaded fiber length) in the experiments at 0.65 m/s. At TIF greater than , the interspaces between the fibers were blocked. Unfortunately, measuring the pressure drop in a fiber array is not feasible. To gain a better understanding of the phenomena, different factors, such as accumulation of particulate material, size, and number of bridges and pores, were considered.
3.2. Accumulation of Particulate Material before Clogging
To distinguish the different phases of the separation process on the fiber array and to quantify the deposition kinetics during classical filtration, evaluation points were introduced at selected TIF. The position of the evaluation points is based on the overall course of an experiment with an airflow velocity of 0.65 m/s. In such an experiment the fiber interspaces are completely clogged, and no bridges are detected at a TIF of
(relative accumulated particulate material in the spacing
). The TIFs corresponding to the evaluation points are shown in
Table 2.
Image analysis was used to quantify the growth kinetics of particle structures in the fiber interspaces by measuring the increase in particle material in the inner fiber interspaces of the array.
Figure 9 shows the relative accumulated particle material in the fiber interspaces over the increase in TIF up to a TIF of
at different airflow velocities. None of the experiments revealed complete blocking at these TIF values. The airflow velocities ranged from 0.1 to 1.8 m/s. The development of accumulated particle material in the interspaces remained constant over the entire experiment. The evaluation started at the smallest TIF where the fibers became visible. The growth rate represents the rate at which the fiber interspace was occupied by particulate material. The fiber array first was in the depth filter phase, followed by the transition phase as in normal filters.
The average growth rates between the second and the third evaluation points were determined by using a linear fit (black fit) for each curve, with a coefficient of determination above 0.99. Regardless of the applied airflow velocity, the experiments passed the run-in phase and were in the surface phase or at the beginning of the transition phase.
Analysis of experimental conditions revealed trends and mechanisms in particle growth kinetics within the fiber interspaces. Dendritic particle growth was observed at flow velocities ranging from 0.1 to 0.65 m/s. As shown in
Figure 10, dendritic structures develop in the region of interception in the experiment at a flow velocity of 0.15 m/s.
The same phenomenon had been found before in a computational simulation by Payatakes and Tien [
34].
Figure 11 shows the rate for particle accumulation on an array plotted against the flow velocity and Stokes number, which is extracted from linear fit in
Figure 9. The rate reflects structure growth in the interspaces and on the fibers. An increase in the particle structure within or outside of the image plane cannot be detected. Compact structures formed in the experiments at 1.2 and 1.8 m/s result in a low growth rate compared to the low airflow velocity experiments. The smallest growth rate of dendritic structures was observed at 0.1 m/s, while growth at 0.15 and 0.25 m/s was 27% higher than in the experiments with an airflow velocity of 0.1 m/s. In the experiment with a flow velocity of 0.65 m/s, the growth was 49% higher. The particle loading rate in
Figure 11 is on a higher level because particles accumulated opposite to the direction of flow.
Kanaoka et al. (1986) observed a change in the orientation of particle deposition from upstream to cross-stream on the side of each fiber as the Stokes number decreased towards zero and the Péclet number increased towards infinity [
3]. The masses deposited on the fiber at flow velocities 0.1 m/s, 0.15 m/s, and 0.25 m/s were approximately the same at the same value of TIF (see
Figure 8). Therefore, the higher growth rate at 0.15 m/s and 0.25 m/s compared to 0.1 m/s in
Figure 9 cannot be attributed to an increased deposition rate.
Instead, the particle bounce parameter
defined by Kasper et al. may explain the observed horizontal widening of structures in the direction of the image plane [
31]. As particle velocity or diameter increases, the rebound parameter
increases, leading to re-arrangement and eventually to bouncing and dislodging of previously deposited particles [
35]. In addition to the effect of interception, re-arrangement might occur, initiated by the accumulation of particles that widen the structures at the horizontal level.
While previous studies cited in this work have used a narrow particle size distribution or monodisperse material, whereas this study used a polydisperse particle size distribution, which leads to overlapping deposition effects.
Therefore, the interception effect for small particles and the inertia effect for large particles overlap. When considering the rebound parameter, the effects for impinging particles and particles that detach before deposition overlap at the same flow rate for each particle size. The predominantly dendritic particle deposition observed at flow rates below 0.65 m/s changes to a compact deposition on the fiber surface at flow rates of 0.65 m/s and higher. The loading rate between the fibers decreases with increasing flow rate above 0.65 m/s. This indicates that particles hardly adhere in cross-stream or detach after adhesion at the highest Stokes numbers.
3.3. Development of Structures before and in the Clogging Phase
It is outlined in
Section 3.2 that as the TIF increases, more particles accumulate in the interspaces between the fibers. The complete closure of the interspaces between fibers was not observed at values of TIF up to
. To analyze bridge growth up to the CP, three experiments were conducted with different flow velocities at higher terminal TIF values. The flow velocity covered the range of deposition patterns (dendritic, transition, and compact morphology). The final TIF value reached
after a long experimental time. For one set of parameters, complete clogging was achieved.
Figure 12 displays the complete evolution of the structures up to the predefined evaluation points.
In all experiments, a particle layer was initially visible on the fiber at Evaluation Point 1. In the tests an incident flow velocity of 1.8 m/s, deposition at the stagnation point of the fiber was clearly visible. At Evaluation Point 2, the characteristic separation of particles was observed in all experiments. The morphology of the particle structure was a function of airflow velocity. In the experiments with a flow velocity of 0.25 m/s, dendritic structures with small arms appeared in the interspaces between the fibers. In the experiments with an airflow velocity of 0.65 m/s, growth of dendritic structures was observed, too. However, more particulate material is separated at the stagnation point of the fiber, as shown by the presence of a thick layer of particle material. In the experiment with an airflow velocity of 1.8 m/s, the unobstructed fiber interspaces were clearly visible. The particulate material just separated on the zenith/top of the fiber. At the third evaluation point, deposition of particulate material in the interspaces of the fiber was visible though the compact structure seems to bend into the interspaces. Merging particle structures across the interspaces were found at the sites where the fiber bends.
In the experiments with airflow velocities of 0.65 m/s, and 0.25 m/s, increased growth of the dendritic structures into the interspaces of the fiber was observed at this evaluation point. The images of the experiments at 0.65 m/s reveal a few gaps in the particle structure visible at Evaluation Point 3, where the fibers have dents and are slightly separate from each other. These gaps only close as the number of bridges decreased towards Evaluation Point 4. In addition, impacts on the already clogged particle structure were found and attributed to large particles which hit the particulate structure. Compared to the total area, these impacts are small in size. In the experiments with an airflow velocity of 0.25 m/s, the dendritic structure grew into the interspaces of the fiber. The dendritic arms were much more pronounced compared to the experiments with an airflow velocity of 0.65 m/s. The compact structure of the fiber merged (formation of bridges) across the interspaces of the fibers. The contact points of merging particle structures from different fibers were found to be much wider for the compact structures than for the dendritic structures. The clogging point will be reached soon when the free interspaces between the fiber are closed completely. For all experiments with different airflow velocities, an increased separation of particles at the outer fibers of the array is observed with increasing loading at Evaluation Point 4. Thus, in the experiments with the airflow velocity of 1.8 m/s, the structure at the outer fiber becomes a little bit bulky. The edges of the structure remain sharp and smooth. However, the growth of the structure on the outer two fibers is observed in the tests with incident flow velocities of 0.25 m/s and 0.65 m/s, too. Due to the separation mechanism, the structure has more small arms and dendrites on the outer fiber surface. The reason for this increased separation is the change of the flow around the fiber which is a result of particle separation in the interspaces of the fibers. This effect was predicted in the calculations of Müller et al. [
4]. As described in
Section 2.3, only the inner interspaces of the array are considered during evaluation. The limit on using just 5 parallel fibers is because the used motors are not able to stretch more polymer fibers at once due to the restrain force that the fibers encounter.
In
Figure 13, the fraction of accumulated particulate material and the total number of bridges are plotted as a function of TIF for each flow velocity. The experiment was conducted three times, and the data were analyzed using MATLAB.
For the highest flow velocity ( m/s), the graph shows a continuous growth of the fraction of accumulated material in the transition phase, with a small decrease in growth rate for a TIF above . This section comes with an increase in the standard deviation. At the same time, the number of bridges levels off at around 10 for the experiments with a flow velocity of 1.8 m/s. In contrast, the experiments with a flow velocity of 0.25 m/s and the dendritic structure on the fibers show a continuous increase in the number of bridges starting at a TIF of approximately . This effect is due to the growth of the structure vertical to the flow direction, which tends to close the interspaces between the fibers. In these experiments, the fraction of accumulated material increases from the start of the experiment with a steeper slope than in the experiments with a compact deposit at a flow velocity of 1.8 m/s. The relative accumulated particulate material starts to decrease slightly as bridge growth becomes dominant at a TIF of . In the experiments conducted at an airflow velocity of 0.65 m/s, the relative accumulation of particulate material within the fiber spacing displayed the most rapid increase. The accumulation continuously increased from the start of the experiment until complete closure of the filter occurred with minimal pore sizes.
Significantly, the experimental conditions that involved an airflow velocity of 0.65/exhibited the lowest standard deviation among the observed results. With increasing TIF, the number of bridges increases continuously at TIF of
to a maximum of approximately 100 bridges. Initially, dendritic growth is observed with well-developed bridge formation and the maximum number of bridges. The maximum value of bridges occurs just before Evaluation Point 3. It is important to note that the generation of bridges and the separation of particles at the fiber generally are processes that involve a certain random component. This fact is highlighted by the high standard deviations. Once the maximum is reached, the number of bridges decreases as the array becomes more clogged and the pores and interspaces between the fibers continue to fill and multiple small bridges merge into broader structures. A cake of particulate material forms on the array, as illustrated in
Figure 12.
The boundary line reflecting the deposition pattern is presented in
Figure 14. The boundary line is characteristic of the respective type of deposition morphology or mechanism. For the dendritic structures in the experiments with airflow velocities of 0.25 m/s and 0.65 m/s, a jagged and long boundary line can be observed. The boundary line of the experiments with a compact deposit is similar to the original fiber. The boundary line of the experiment at 0.65 m/s is initially jagged but becomes straighter with increasing TIF. In comparison, the boundary line of the experiment at 0.25 m/s is more jagged. Once complete closure of the interspaces is achieved, the boundary line disappears, as shown here by the experiments at airflow velocity 0.65 m/s.
Figure 15 presents a quantitative analysis of the length of the boundary line (horizontal, parallel to fiber axis) relative to the initial boundary line of the fiber for the three different morphologies (dendritic, transition from dendritic to compact, compact) of particulate structures. At an airflow velocity of 0.65 m/s, the ratio first increases slightly above 1 due to the dendritic separation of particles. Just before the second evaluation point, the ratio starts to decrease due to the formation of the first bridges. After the second evaluation point, the curve continues to decrease due to the formation of bridges and clogging of the interspace between the fibers. At the end of the experiment, the ratio reaches the value of 0 for the experiment with 0.65 m/s. At an airflow velocity of 1.8 m/s, by contrast, the ratio of the boundary lines remains constant at almost 1 due to the horizontal increase in compact structure. However, a reduction below 1 is observed between Evaluation Points 3 and 4, caused by the formation of bridges and the subsequent shortening of the boundary line at the end of the experiment (see
Section 3.4). As observed earlier, the boundary line of the dendritic structure is more jagged, resulting in a larger ratio than for the compact and transition structures. The ratio remains above one after the third evaluation point.
3.4. Size of Pores and Bridges
The pressure in a filter drops due to friction between gas molecules and fibers or deposited particle structures. Particle structure growth on the collector can lead to an increased blockage area (fiber + particulate material) and reduced free cross-sectional area for flow.
Section 3.2 emphasized that particle structures grow at varying rates and extend into interspaces of the fibers. While previous studies focused on the pressure drop as a function of process parameters, the impact of structural morphology on particle separation/accumulation and the CP has yet to be investigated in sufficient detail. Observing particle deposition on a single fiber or array of fibers is not sufficient to characterize pressure loss in the filtration process. The particulate material is deposited on the fibers. The fiber interspaces start to clog when more particulate material is separated onto a pre-existing particulate structure under a large angle to the stagnation point (refer to
Section 3.3). Particle bridges as illustrated in
Figure 12, develop with progressing filtration time between/across the fiber interspaces due to the growing of particle structures on neighboring fibers. As described above, the formation of bridges reduces the unobstructed flow area of the initial “pore” between the two fibers and generates two new pores on either side of the bridge. The number and dimensions of formed bridges depend on airflow velocity and the deposition mechanism as well as on the fiber’s structural morphology.
Figure 16 shows the development of maximal size (parallel to fiber axis) and number of bridges with three characteristic airflow velocities as a function of the TIF. This figure follows the principle of a heatmap. The total number of bridges (in the following pores) in each section is visualized using a grayscale code.
At a flow velocity of 0.25 m/s, the first small bridges (71–81 ) develop just before the second evaluation point. At first, the number of bridges simply increases to an average size of 50 . Then, starting at TIF of , more small bridges are formed while existing bridges grow together to form larger ones. At Evaluation Points 3 and 4, the number of medium-sized bridges (50–60 ) does not increase any further, while the large bridges continue to grow.
As shown in
Figure 13, the curve for the increase in particulate material in the interstitial spaces flattens somewhat at a TIF of
. At Evaluation Points 3 and 4, the structures are not fully closed yet (see
Figure 12 and
Figure 17). The size of bridges reaches a maximum of 281
.
At an airflow velocity of 0.65 m/s, bridge formation occurred earlier than at 0.25 m/s. The size of the first bridges formed in the two sets of experiments was similar. There was a significant growth of bridges between Evaluation Point 2 and Evaluation Point 3, with a considerable number of large bridges (larger than 121 ) and small bridges (ranging between 41 and 71 ) being formed. The bridges continued to grow towards Evaluation Point 3, reaching a maximum size of 441 . The number of bridges, however, was smaller than that at 0.25 m/s. The number of small bridges continued to decrease towards Evaluation Point 4, while bridges of medium size (between 121 and 201 ) increased in size due to particle accumulation.
In the experiments at an airflow velocity of 1.8 m/s, the formation of bridges sized 41–81 occured shortly before Evaluation Point 3 and continued to increase with increasing TIF. The total number of bridges in this size range increased, too. The maximum bridge size reached 401 before Evaluation Point 4, which is twice the size of the bridge observed at 0.25 m/s. The total number of bridges ranged from 8 to 14 and was lower than in the other experiments. This might be due to the fact that the structure between and on the fiber is growing more in the direction of the airflow. As a dendritic structure has more side arms in the horizontal direction that can reach structures on other fibers, the chance of bridge formation is higher.
As discussed in
Section 2.3, bridges typically result in the formation of new pores. At the beginning of the filtration process, there are empty spaces between neighboring fibers that gradually become filled with deposited particles.
Figure 18 presents the size and number of those pores at the corresponding TIF for three different airflow velocities. They are measured using the hydraulic diameter as a metric for pore size. The free fiber interspaces are detected at the start of each experiment and appear as a single large pore per fiber pair. At a TIF of
are the unobstructed interspaces between the fibers. As the loading process continues, the size of the interspaces between the fibers narrows. Subsequently, the hydrodynamic diameter starts to decrease. A newly created bridge splits into a large pore into two new pores. The experiments at an airflow velocity of 0.25 m/s exhibit an initial steady decrease in pore size with a constant number of pores from the beginning of the experiment. This indicates a stable growth of the particle structure within the interspace of the fibers. Immediately after Evaluation Point 1, corresponding to a TIF of
, the number of pores increases steadily. After the evaluation point, there is a marked increase in the number of smaller and medium-sized pores, particularly in the size range of 21–41
, which may include small holes within the dendritic structure (observed in
Figure 12). After Evaluation Point 4, mainly small pores are formed, while large pores above 100
become less frequent. Just before the fourth evaluation point, additional large pores may form in the deposited structure due to small demolition and fracturing. Moreover, it is possible that formed dendritic arms of the structures may detach and expose void areas between the fibers.
Further particle loading would lead to clogging in the interspaces of the fiber array. The number of small pores continues to increase, which suggests further growth and clogging of already existing pores. The exact TIF at which clogging occurs at this airflow velocity is not known.
Figure 12 presents images of the growing structure including pore formation.
Figure 17 illustrates the pores and bridges and their aspect ratios. In fiber sections with a slightly smaller fiber spacing the structure recedes more quickly with large pores/spaces and closing fast and almost completely.
At an incident flow velocity of 0.65 m/s, an initial linear decrease in pore diameter at a constant pore number is observed again. The deposited structure, as shown in
Figure 12, exhibits a morphology transitioning from dendritic to compact. Pore growth in the size ranges of 41–61
and 21–41
starts just before the second evaluation point. Further development of smaller pores and simultaneous reduction of larger pores indicates the gradual closure of large pores and growth of the structure between the second and third evaluation points. After Evaluation Point 3, the number of small pores continues to increase as the structure slowly closes completely.
Large pores with hydrodynamic diameters of 81–121
occur before Evaluation Point 4. These are actually holes in the previously closed particle structure, which were created by larger particles. The holes are closed by particulate material as the filtration process continues (see
Figure 18). Although some pores are still present at the end of the loading process, the combination of different results (accumulated particulate material, number of bridges, and pores) shows that the structure has reached the clogging phase.
When the airflow velocity increases by 1.8 m/s, a compact particle structure is formed on the fiber array in agreement with the investigation by Kanaoka et al. [
3]. As depicted in
Figure 18 on the lower left, the pores persist up to large values of TIF. The hydraulic diameter decreases to 241–261
because the structure grows in the direction of the stagnation point, rather than horizontally. Large pores form right after the start of the experiment and exist up until Evaluation Point 4. Before the third evaluation point, additional pores develop in the range below 100
. They are formed parallel to the bridges (see
Figure 16). The number of individual pores remains very low in the experiment with 1.8 m/s compared to 0.65 m/s and 0.25 m/s. Pores in the size range of 3–21
are found in all experiments. The presence of pores until the end of the experiment, along with the observation of large elongated pores between the fibers, suggests that the structure is not fully closed. These results, together with the findings presented in
Section 3.3, support the notion that the structure is not in a completely clogged state. The structures merge due to their length, as reflected by the horizontal bridge size data.