Study of the Oil Mist Filtration Performance: Pressure Drop Characteristics and Filter Efficiency Model

Oil mists, which are colloids composed of solid core particles surrounded by oil, are commonly removed from air by fibrous filters. However, unlike the filtration of pure solid or pure liquid particles, mist filtration is not yet fully understood. This study performed a series of experiments to investigate filter performance throughout a clogging process and evaluated the influence of oil content on the variance of pressure drop and filter efficiency. A model was developed for predicting the efficiency of the colloid particles and used to explain how the variance of the oil content changed the efficiency. Results showed that the filter became saturated, showing a constant pressure drop and efficiency, after a relatively short period of fluctuation. The particles with higher oil content used less time to reach the equilibrium state, and had a lower pressure drop and higher efficiency. The amounts of oil coated on the solid cores influenced both the particle diameters and the saturation of filters. Filter efficiency can notably increase with decreasing saturation until saturation was less than 0.5, and the efficiency of particles that were most affected were those with diameters of approximately 30 nm and 500 nm.


C c
Cunningham correction factor (-) D Particle diffusion coefficient (m 2 s -1 ) E int Single fiber efficiency for interception (-) E imp Single fiber efficiency for impaction (-) E diff Single fiber efficiency for diffusion (-) E f Combined single fiber efficiency (-) E e Overall capture efficiency (-) k Boltzmann's constant (J K -1 ) Ku Kuwabara hydrodynamic factor (-) m f Fiber mass (kg) Pe Peclet number (-) R Ratio of particle diameter to the fiber diameter (-) S e

INTRODUCTION
Oil mists exist in the air of numerous places, such as in machining factories, in areas exposed to automobile exhaust, and in kitchens (Dennekamp et al., 2001;Popovicheva et al., 2014;Zhang et al., 2016).The particles of oil mists can be called colloid particles; they usually form as a certain amount of oil coated on a solid core (Bredin et al. 2012).Much research has reported that a high level of exposure to oil mists may cause adverse health effects (Calvert et al., 1998;Hsu et al., 2012;Lee et al., 2015).An effective and widely used method to remove particles is filtration.Whereas filtration for solid particles had been intensively investigated (Thomas et al., 2001;Chen et al., 2015), fewer studies have been conducted on the filtration of oil mist.Because the oil mist filtration often show notable difference in performance to that of the solid particles (Boundy et al., 2000;Tekasakul et al., 2008), understanding the loading behavior of the filer media is necessary.
In general, the loading process of an oil mist can be divided into three stages: initial stage, transitional stage, and quasiequilibrium stage.Experimentally, Sun and Chen (2002) published an investigation on the filtration loading characteristics of oil mists at the initial stage.Hsiao and Chen (2015) developed previous research (Sun and Chen, 2002) by illustrating that filter pressure and efficiency values tend to vary in the transitional stage.However, few publications have addressed filter performance over an entire filtration processes; the last stage of filtration, by and large, has not been investigated.Because a filtration system can be expected to remain in its quasiequilibrium stage over a long life span (Mead-Hunter et al., 2013), it is crucial to investigate the pressure and efficiency of filters in the quasiequilibrium stage.In addition, theoretical study on the oil mist filtration was very limited.To our knowledge, the efficiency model for oil mists (colloid particles) has not been developed yet.However, because the filter performance of the oil mists show similarity to that of the pure liquid particles when the contained oil is more than 50% (Hsiao and Chen, 2015), we could expect to build a new model based on the existing model for pure liquid particles with some modifications on parameters represent the difference of oil mist filtration to pure liquid filtration.Hsiao and Chen (2015) revealed the performance of a filtration system for colloid particles can be different because of the presence of solid cores.Mead-Hunter et al. (2012) suggested the solid core ratio could change the viscosity of an oil mist and could affect the saturation of a filter, altering the efficiency of that filter.Although the model for the pure liquid particles can predict changes in the efficiency of a filter caused by changes in the saturation of pure liquid particles, because the change of saturation caused by the presence of solid cores in an oil mist is different from changes of saturation in a pure liquid mist, that model is not applicable here.To calculate the efficiency of a filter that processes a mist containing solid particles, further research should be conducted.The efficiency of a filtration system could vary constantly in numerous practical situations.To maintain the filter performing steadily at high efficiency, the influences of the variation of major factors on the filter performance should be studied.Researchers have shown that one of the reasons for the variation of efficiency is the changes of the oil content (Mead-Hunter et al., 2012).A variation of oil content simultaneously alters both the major size and the filter saturation of an oil mist.Numerous investigators (Thomas et al., 2001;Contal et al., 2004) have studied the influence of a single variable on the efficiency of a filter because the widely studied change of the efficiency for solid particle or pure liquid particle is usually due to the change of a single variable.In contrast, few researchers have estimated the influences of phenomena with multiple variables varied simultaneously, such as the situation for oil mists.
Therefore, the aims of this study were to understand the performance of mist filtration over an entire filtration process, develop a model and evaluate the influence of oil content on pressure drop and filter efficiency.It is hoped that our study would contribute to effective removal of oil mists.

Experimental Set-up
The schematic of our apparatus is shown in Fig. 1.The filtration chamber was made of polymethyl methacrylate; it measured 1000 mm × 28 mm × 28 mm in length, width, and height.A Sinclair-Lamer monodisperse aerosol generator (MAG 3000, PALAS, Germany) generated oil-coated particles, with sodium chloride as the cores and di-2ethylhexyl sebacate (DEHS) as the oil.The particles were transported by filtered nitrogen to the filtration chamber at a flow rate of 3.5 L min -1 , which was controlled by a rotameter integrated in the generator.After passing through a test filter, the particles were filtered and exhausted by a vacuum pump (VT 4.4,Berker,Germany), also at a flow rate of 3.5 L min -1 , controlled by a mass flow meter.Additionally, because it was likely that liquid would drain from the surface of the fibrous filter after that filter became saturated, a thin tube was connected close to the rear of the filter; that tube guided the drained liquid to a tightly attached vessel.
The experimental measurements were expected to obtain the real-time pressure drop, the real-time aerosol distribution, and the saturation.A differential pressure transducer (TRD-FD3051DP2A22AB4M5, Tianjin Redzonce Instrument, Fig. 1.Schematic of the experimental system.China) was used to record the pressure changes between the flows upstream and downstream from the filter.To measure the particle distribution, an aerodynamic particle sizer (APS) (Model 3321, TSI, USA) was applied to measure all particles with diameters between 0.5 µm and 10 µm before and after the test filters.Because the particle concentration was expected to be higher than the upper limit of the APS, a dilutor (Model 3302A, TSI, USA) was applied to dilute the aerosol 100 times before it entered the APS.In addition, the saturation was measured by weighing the filters before and after the experiment with an electronic balance (HR-120, AND, Japan).

Filter Characterization
Fibrous filters are widely used in oil mist filtration.This study used medium-high efficiency glass fiber filters; their properties are shown in Table 1.
In Table 1, the fiber diameter was statistically determined from numerous fiber images taken with a Scanning Electron Microscope (SEM).The packing density can be calculated by the following formula (Mullins et al., 2014): where m f is the fiber mass, kg; V is the filter volume, m 3 ; ρ f is the fiber density, kg m -3 .The thickness and the basic mass were provided by the manufacturer.

The Oil Mist
The oil mists in these experiments were generated by evaporation and condensation of the DEHS on the sodium chloride cores.The particle size and viscosity were changed by varying the evaporation temperatures.The higher the temperature was, the more vapor was evaporated, and the more oil condensed on the solid core, which produced oil mists with larger particles and lower viscosities.This study represented oil content by the volumetric ratio of sodium chloride to DEHS.To determine the volumetric ratio of sodium chloride to DEHS, a special case was constructed in which no oil was evaporated.In this situation, the generated condensation core consisted only of sodium chloride and the diameter of the condensation core was measured by an Aerosol Generator and Monitor system (Mode 1500, MSP corp., USA).Because the diameter of the condensation core was constant, the diameter of the coated oil could be calculated by subtracting the diameter of the condensation core from the diameter of the oil mist particle, and thus the volumetric ratios were obtained.Additionally, in order to investigate the variance of saturation with an increasing ratio of solid components, a saturation value for pure liquid particles was needed as a basic value.We obtained that value by running the generator under a high temperature of 210°C, which resulted in the generation of particles with a considerably low ratio (0.5‰) of solids.We assumed the particles with such a low ratio of solids as pure liquid particles.Besides this special case, this study run other five cases with different evaporation temperatures listed in Table 2.
As can be seen in Table 2, the particles were determined to be monodisperse aerosol with δ < 1.15.Moreover, as the temperature increased, the CMD increased and the volumetric ratio decreased.

Experimental Proceedings
Our investigation studied filter performance over all stages of an entire filtration process with different evaporation temperatures.The following filtration procedure was performed identically for each temperature setting.
Before the commencement of the experiment, the filter, the connecting tube, and the vessel were weighed; these weights were recorded as the original values.The upstream aerosol was diluted five times with cleaned compressed air and then measured five times by the APS with the dilutor for 3 min.It was found that the upstream particle distributions were constant, so the APS measurements upstream of the filter were only taken before and after the experiment.Immediately after the generation, the valve for compressed air was closed and the valve for the APS was switched on to measure the downstream particle distribution.The particle distribution was monitored at 4 min intervals and the pressure drop was recorded every 1 min.The measurements were stopped when the time for the particle distribution and the pressure drop was at least twice the time that the filtration processes took to reach the quasi-equilibrium state (the drainage rate had been constant).But the experiments were continued for an additional period of time, equal to twice the time the system required to reach the quasiequilibrium state to allow observation of any re-entrainment that might occur.The face velocity of the filter was maintained at 10.1 cm s -1 during the experimental process.At the conclusion of the experiment, the filter was weighed again, and the real saturation value was obtained by dividing the difference of the weight by the assumed maximum saturation mass (Mead-Hunter et al., 2013): where m c is the weight change of the filter, kg; m max is the maximum oil mist holding capacity of the filter, kg; ρ oil is the oil mist density, kg m -3 .To examine the mass balance, the weight of drained liquid was measured by weighing the tube and the vessel.The experiment was repeated 3 times.
In addition, this study applied SEM to identify the particle morphologies at different stages of filtration.Three experiments were conducted to run the process to the three different stages, and the filter medium was immediately removed for scanning when the expected condition was reached.

Theoretical Model of Filter Efficiency
Filter efficiency is an important parameter for evaluation of filter performance.For the oil mist filtration, most filters operate at quasi-equilibrium state (Mead-Hunter et al., 2013), so we need to build an efficiency model for this state.Filter efficiency models include single fiber efficiency and overall filter efficiency.For single fiber efficiency, Mead-Hunter et al. (2012) showed that the capture efficiencies for oil mists can be calculated according to traditional single fiber efficiency equations, but for the overall filter efficiency, a new model should be developed.
To derive the overall filter efficiency, we need to understand the single fiber efficiency models.The single fiber efficiency theory is base on the basic capture mechanism of interception, impaction and diffusion.The single fiber efficiency for interception, E int , is (Raynor and Leith, 2000): where R is the ratio of particle diameter to the fiber diameter (d p /d f ); Ku is Kuwabara hydrodynamic factor, and can be calculated by the following expression: The single fiber efficiency for impaction, E imp , is (Stechkina et al., 1969): where J can be defined as (R < 0.4): J = (29.6 -28α 0.62 )R 2 -27.5R 2.8 (6) when R > 0.4, J = 2.The Stk in Eq. ( 6) is the Stokes number and can be defined as: where ρ p is the particle density, kg m -3 ; u ′ is the interstitial velocity, m s -1 ; µ is the dynamic viscosity, N•s m -2 ; C c is the Cunningham correction factor, which is described as: where λ is the free path for air at 101 kPa and 293 K (66 nm).
The single fiber efficiency for diffusion, E diff , is (Hinds, 1999): where Pe is the Peclet number: where D is the particle diffusion coefficient, (m 2 s -1 ): where k is the Boltzmann's constant (1.38 × 10 -23 J K -1 ), and T is the absolute temperature, 293K.
The combined single fiber efficiency, E f , is then determined from: Finally, to determine the overall capture efficiency, the equation for oil mist can be modified based on the pure liquid filtration model (Payet et al., 1992).Because a difference exists in the saturation formula (Mead-Hunter et al., 2012), we improved the model.
According to the results of Gilet et al. (2010), the critical volume of a pure liquid pool before it drops can be calculated from the force balance: where C v is a proportionality factor that may depend on surface tension among other factors, and can be calculated as: where c v is a coefficient and is taken as 1, and λ is the capillary number (m).In Eq. ( 13), χ can be approximately taken as 15 (De Gennes, 1985), X/W is the length-width ratio of the liquid pool (because liquids tend to be spherical, this ratio was 0.5), v is the drainage velocity (m s -1 ), ρ is the density of the particle (kg m -3 ), g is the acceleration of gravity (m s -2 ).Because Kampa et al. (2014) have found that the state of liquids within a filter matrix span the whole thickness of the filter with quasicontinuous channels between them, we assumed that all the fibers through the thickness of the filter operated as a unified layer, with all liquid pools distributed at intersections when the filtration reached its quasiequilibrium state.Also, for simplification, we assumed the fibrous filter was constructed only with horizontal and vertical fibers.
For the oil mists, the solid core could increase the viscosity of the mists and thus change the saturation.We assumed the increase of the viscosity increased the collective volume of the liquid bridges at the intersections but the number of the liquid bridges at the intersections was constant.Based on these assumptions and Eq. ( 13), we can see that the saturation only depends on the viscosity and drainage velocity.At quasiequilibrium state, the oil mists on the fiber were at the initial drainage velocity.Because the ratio variation of the solid core in the oil mist didn't influent the initial velocity, we assumed the velocity value was the same for oil mists with different ratio of solid core (Mead-Hunter et al., 2012).Thus, the efficiency model for oil mist is: where S e is the saturation of pure liquid, Z is the filter thickness, µ is the dynamic viscosity of the oil mist, µ ′ is the viscosity of the pure liquid, and the relationship between these two viscosities is (Murshed et al., 2008): where ϕ is the particle volume fraction.

Filter Pressure Drop and Efficiency of Oil Mist
The filter performance can be evaluated from the pressure drop and efficiency.Fig. 2 shows the changes in pressure drop and efficiency for the entire clogging process; Fig. 3 shows the corresponding particle morphologies at the microscopic scale.The case shown here used an evaporation temperature of 150°C (the particle size could be seen in Table 2); other cases had similar results and are not shown here.
Fig. 2 reveals that the three stages of the filtration were evident from the change rates of the curves: • The first stage was the initial stage, in which the pressure drop increased slowly and the efficiency dropped at a slow rate.Correspondingly, Fig. 3(a) shows that the captured particles induced the formation of droplet chains along the fibers.These collected droplets were not sufficient to interfere with the airflow, which explained the small variance of pressure and efficiency at this stage.• The second stage was the transitional stage.After a short period of slow changes, the pressure showed a sudden exponential growth and the efficiency experienced a significant fluctuation.A microscopic interpretation is that the droplets that were collected formed thin films around the fibers, but those films were almost immediately broken up through Plateau-Rayleigh instability, so the liquids were reallocated and the droplets coalesced to form liquid bridges at the intersections of the fibers, as shown in Fig. 3(b) (Mead-Hunter et al., 2014).Because the liquid bridges significantly increased in flow resistance, the pressure drop increased rapidly.Moreover, the interstitial velocity was increased during this stage with the reduction of free sections to the air flow, which in turn was expected to increase the filter efficiency because of impaction.However, it should be noted that there must have been a point at which the efficiency reached its lowest value; we assumed it occurred when the films were formed around the fibers.When the films broke up and the reallocation began, the filter efficiency started to increase.• The final stage was the quasiequilibrium stage, in which pressure drop and efficiency were constant.The oil mists were reallocated within the filter and the filter became saturated (Fig. 3(c)).Aerosol began to drain from the surface of the filter at the same rate at which it was captured.In addition, we observed that re-entrainment of the collected particles collected was not notable.

Pressure Drop for Oil Mist of Different Oil Contents
The changes of pressure drop could vary with different loading particles contained in different oils.Fig. 4 plots the real-time pressure drops under five different evaporation temperatures with particles of 0.583-1.290µm in diameter.All five cases had the same filter velocity and the particle concentrations were similar.
It can be seen from Fig. 4 that although the pressure drop curves had the same shape, the times required for the filters to reach the saturation points (approximately 5 h-20 min) and the pressures of the quasi-equilibrium states (6833 Pa-6494 Pa) decreased with the increase of the oil content (volumetric ratio).A possible reason for the shorter time is that particles with larger portions of oil have more opportunities to encounter each other, so they more easily coalesced at the intersections of fibers.Moreover, particles with relatively large ratios of oil could make up mists with relatively low viscosities (Krieger and Dougherty, 1959;Lee et al., 2008); with a mist of low viscosity, a relatively low volume of oil mist could be captured and thus the time required to reach quasiequilibrium could be shorter and the pressure drop could be lower.In general, the pressure drop curves indicate that the higher the oil content was, the more rapidly the filter reached its stable state.

Particle Efficiency for Oil Mist of Different Oil Content
This study also examined the variations of the filter efficiency for the five cases and found that the shapes of the curves were similar to the efficiency curve in Fig. 2 and that the time for the filter to be saturated coincided with the time for the pressure drop to reach saturation.Yet, differences existed in the ratio of the quasiequilibrium efficiency to the initial efficiency, as shown in Fig. 5.
Fig. 5 reveals that the efficiency ratio became higher when the oil content increased.For oil mist filtration, particle diameter and saturation are two important parameters that determine the filter efficiency.If the saturation is constant,  the efficiency increases for mists with larger particles; the dominant capture mechanism for these particles is impaction, because the retained droplets increase the flow resistance, leading to an increase in interstitial velocity, whereas for smaller particles governed by diffusion, the filter efficiency could decrease over time.However, if the saturation changes, larger particles do not necessarily cause higher filter efficiency, because the total quantity of captured droplets might decrease.For our cases, the changes of oil content in the particles altered both particle diameters and saturations; the results suggest that the particle diameter was the major influencing factor.It should be noted that the particle diameter was tested in a relatively narrow range from 0.583 to 1.290 nm.To generalize the influence of the oil content on efficiency, we used a mathematical model to explain it in a broader range.We first validated the model using the experimental efficiencies which were measured when the filter reached saturated state, as shown in Fig. 6.Note that the saturation value for pure liquid particles was 0.57 as specified in Eq. ( 15).Fig. 6 illustrates that the results from the theoretical model and the experiment agreed with each other.However, there was a systematic deviation.For the particles smaller than around 0.7 µm, the results from calculation were smaller; for the particles larger than around 0.7 µm, the theoretical results were larger.We assume that reason could be the PALAS 3000 generator generated monodisperse particle rather than mono-sized particle.For example, there were some smaller particles mixed in the particles that the peak size of these particles was 0.898 µm.As the efficiency for the smaller particles was lower than that of the particles of 0.898 µm in diameter, the experimental efficiency would be lower than the calculation efficiency at exactly 0.898 µm.The reason for the lower experimental efficiency of particles of 1.110 and 1.290 µm was the same as the particles of 0.898 µm.Similarly, for the particles of 0.583 and 0.673 µm, the experimental efficiencies were higher was because of the existing of larger particles.But because deviations were small, we assumed our model was useful for predicting the efficiency of oil mists.
Using this model, we further evaluated the influence of the oil content on the filter efficiency.In order to reveal how the filter efficiency can be affected by the oil content, we used Figs.7 and 8 to show the change of the filter efficiency with different particle sizes and filter saturation values, and to show the changes in efficiency with the same two factors.Fig. 7 illustrates that the higher the saturation was, the lower the filter efficiency was.When the saturation increased over 0.5, the decrease of the filter efficiency for particles of the same size over the whole particle size range become notable.This result indicates that a critical value for saturation existed; above that value, saturation played an important role in influencing the filter efficiency.Moreover, with increasing saturation, the point of rapid decrease in efficiency moved forward from the size range where the efficiency was low (80 nm) to the size range where the efficiency was high (30 nm and 500 nm) (Fig. 8).Because a higher saturation could have much lower filter efficiency, these results indicated that the change of oil content could most affect particles in the size ranges near 30 nm and 500 nm.For particles larger than 600 nm, the filter efficiency was not affected much, which also explained our previous experimental results.In general, all the results indicated that when the saturation was increased above 0.5 by decreasing the oil content, the filter efficiency was affected more notably, especially for the particles whose sizes were near 30 nm and 500 nm.

CONCLUSIONS
This study investigated filter performance with oil mist over an entire filtration process.We developed a model for mist filtration and studied the influence factors.Results showed that the mist filtration tended to reach a quasiequilibrium state with a constant pressure and filter efficiency after a relatively short period of fluctuation.The clogging process tended to be accelerated if the amount of oil coated on the solid particle cores increased.Also, the pressure decreased and filter efficiency increased with increased oil content.The model explained the relationship between the oil content and the filter efficiency.Two of the major influencing factors were particle size and filter saturation.Calculation results indicated that decreasing filter efficiency became notable when the saturation was higher than 0.5, especially for particles with sizes near 30 nm and 500 nm.

Fig. 4 .
Fig. 4. Changes of pressure drop for different oil content levels (represented by the volumetric ratio of solid core to the oil).

Fig. 5 .
Fig. 5. Ratio of initial and final filter efficiency of different oil content levels (represented by the volumetric ratio of solid core to the oil).

Fig. 6 .
Fig. 6.Comparison of the calculated and experimental filter efficiency.

Fig. 7 .
Fig. 7. Influences of particle size and saturation on the filter efficiency (S is the saturation of oil mist).

Fig. 8 .
Fig. 8. Variance of filter efficiency with change of saturation (S is the saturation of oil mist).

Table 1 .
Characteristics of the test filter.

Table 2 .
Particle number distributions and volumetric ratios of the oil-coated particles (NaCl to DEHS).