Artificial polydopamine interface for high ‐ performance ambient particulate matter removal at large velocity

Ambient particulate matter (PM) has been identified as the fourth ‐ ranking risk factor for mortality globally, and efficient ventilation filtration technologies are urgently needed. In most previous trials, however, high filtration efficiency was achieved either at a low face air velocity or at a large pressure drop cost. Here, nine coarse filters with in situ polydopamine (PDA) coatings were reported, which significantly improved the efficiency ‐ pressure drop ‐ energy consumption performance. By optimizing the filter substrate and synergistically modulating the electric fields, the artificial PDA coarse filter showed a high filtration efficiency of 96.9% for 0.3 – 0.5 μ m particles, and a low pressure drop of 9.2 Pa at 1 m/s air velocity. At an extremely large air velocity of 4 m/s, the filtration efficiency remained as high as 94.3% for 1 – 3 μ m particles. This work offers the engineering application opportunity for high ‐ air ‐ velocity filtration, paving the way to a safe, healthy, and energy ‐ saving environment.


| INTRODUCTION
Ambient particulate matter (PM) contributes to the global burden of disease. [1] In 2019, more than 6.44 million deaths were estimated to be caused by PM pollution, which was identified as the fourth-ranking risk factor for mortality globally. [2] In addition, many bacteria and viruses, such as SARS-CoV-2, have been confirmed to transport through aerosols and droplets produced by human sneezing, coughing and breathing. [3,4] As most people spend over 90% of their time indoors, [5] efficient indoor PM removal strategies for ventilation systems have become essential. Among them, the most used one is fibrous filtration. However, there is an intrinsic conflict between filters' high filtration efficiency, low pressure drop, and long service life (large dust-holding capacity while maintaining acceptable filtration efficiency and pressure drop). For example, a commercial filter with initial filtration efficiency of~88% for 0.3 μm particles has an initial pressure drop of 11.3 Pa at 0.1 m/s face air velocity. After loading 9.5 g/m 2 PM on its surface, the pressure drop of the filter remarkably increased to 250 Pa. [6] A large pressure drop not only leads to noise problems but also brings large fan energy consumption and maintenance costs. [7] To avoid the above, electrostatic force is armed with fibrous filters to promote filtration efficiency and allow for lower pressure drop. For decades, considerable efforts have been made to develop electret fibers by charging the fibers via electrospinning, [8][9][10] triboelectrification, [11,12] corona discharge, [13,14] , and thermal charging. [15,16] However, the charge on the fibers may be shielded or neutralized by the collected particles or the pass-by air moisture, thus reducing the filtration efficiency. [17,18] Continuous charging PM and fibers seems a good solution to obtain high efficiency, low pressure drop and long service life for air filtration. PM can be charged by ionizers [19,20] or corona discharge, [21,22] while the filters can be charged by contact [23,24] or polarization. [25,26] Since most filters in these studies rely mainly on mechanical forces to capture PM, electrostatic forces were not fully utilized and the pressure drops were relatively high. A promising method that makes efficient use of electrostatic force is the two-stage electrostatically assisted air (EAA) coarse filtration, where PM is charged by corona discharge and a coarse filter with low pressure drop is charged by a polarizing electric field. [27] Conventional filters with and without different surface modifications were studied, [28][29][30] and a polydopamine (PDA) coated polyethylene terephthalate (PET) reached the highest filtration efficiency (99.48% for 0.3 μm particles) with a low pressure drop of 9.5 Pa at 0.4 m/s. The filters maintained steady performance for up to 30 days and held massive PM (173.9 g/m 2 ) on the filters. [30] However, in heating, ventilation, air-conditioning and cooling (HVAC) systems, PM filtration is required to work at a high face air velocity, for example, 1 to 4 m/s. At a high air velocity (3.7 m/s), the filtration efficiency of EAA PDA coated PET decreased to 76.91% and the pressure drop increased to 215 Pa. [30] Moreover, the study did not consider the power consumption of supplies used for PM charging and filter polarizing, which may overestimate the performance-cost ratio of electrostatic filtration.
This work aims to improve the EAA filtration performance by self-assembled surface modification with PDA on a series of air coarse filters. The incorporation of PDA clusters enabled the fibers to show promising rough surfaces with preferable dielectric properties, which demonstrated attractive attributes of high filtration efficiency and low pressure drop at a high face air velocity (1-4 m/s). The important influence of the filter substrate on filtration efficiency enhancement and pressure drop change was examined in detail, and an optimal substrate among nine conventional air coarse filters was obtained. The particle charging and filter polarizing voltages (U c and U p ) were synergistically controlled to obtain an EAA PDA coated filter with small power consumption and a remarkably improved filtration efficiency. The advantages of this work in high filtration efficiency, low pressure drop and low power consumption at high air velocities were demonstrated by comparison with published studies and commercial air coarse filters.

| Fabricate nano-micro-milli fibrous structures with the polydopamine interface
Nine commercially available air coarse filters for HVAC ventilation systems (Supporting Information: Figure S1a, upper) were chosen as substrates for their low pressure drop and large dust containing capacity. This is because, unlike conventional high-efficiency nanofibrous filters with the thin thickness (<10 2 μm) and high dense, [31][32][33] coarse filters usually havẽ 10 1 mm thickness (Table 1) and spongy structure thanks to their robust >30 μm fibers (Supporting Information: Figure S1b-j). Sufficient gaps between the fibers (>200 μm, as shown in Supporting Information: Figure S2) allow air to pass easily through the filters after coating. Most of those commercial coarse filters are made of PET for their low costs, so 8 PET coarse filters were chosen as the substrates in this study. Besides, one PA coarse filter usually for industrial filtration with a relatively high cost was chosen for a comprehensive comparison. PDA is selected as the coating material for its preferable dielectric property, [30] versatile adhesion, [34] , and environmental-friendly synthesis process. [35] By simply dipping coarse filters into nontoxic dopamine solutions, a surface-adherent PDA interface can be formed onto the fiber surfaces via autopolymerization with a slight amount (<3.9 wt%) of the fibers, painting the substrates brownish gray (Figure 1a,b). Figure 1 and Supporting Information: Figures S1 and S2 showed images of the bare and the PDA coated fibers, demonstrating the PDA nanoclusters on the substrate surfaces. As Filter #3 was an activated carbon (AC) coated filter before PDA coating, it was suspected that the self-assembled PDA polymerization process might wash off some AC, resulting in a reduced weight (3.2 wt%) after PDA coating. In summary, the PDA coatings built <1 μm thick nanostructure on coarse fiber, which was one magnitude smaller than the fiber diameter and two orders of magnitude smaller than the fiber gap, roughening the fiber surface without blocking the airflow way (Figure 1a,b). Therefore, the high dielectric constant PDA interface was successfully incorporated on the coarse filters.   Abbreviations: α, solidity calculated according to Supporting Information: Method S1; ε r , relative dielectric constant of the substrates (or coating materials) from references [30,[36][37][38] ; L, thickness; PA, aromatic polyamide; W, weight per unit area.

| Influence of polydopamine interfaces on filtration performance
The filter samples were installed in an EAA filtration module, of which the structure and the working principle have been described in the previous studies. [30] In brief, as shown in Figure 2a, two direct-current power suppliers (73030P, Boer Co., Ltd) worked for PM precharging and filter polarizing, respectively. When supplied with high U c , the tungsten needle formed an extremely uneven electric field around it to perform a corona discharge, producing large amounts of ions attached to and charging the PM with q. [39] When supplied with high U p , the upstream screen electrode formed an electric field (E) with the downstream grounded screen electrode. The filter installed between the electrodes was induced by E to generate untransferable charges on their surfaces. [40] Owing to the strengthened electric force as shown in Figure 2b,c, the charged particles are easily captured when they pass by the polarized fibers. In EAA filtration, the radial electrostatic force between a charged particle and a neutral and homogeneous dielectric cylindrical fiber in an electric field can be described by [41] : where q (C) is the charge on the PM; E (V/m) is the electric field formed by the parallel electrodes through the filter; d f (μm) is the fiber diameter; r (μm) is the distance between the centers of the fiber and the PM. As most coarse filter substrates were made of polymer with relatively low ε r , when they were coated with high ε r PDA and got thick in d f , F E got stronger and therefore electrostatic filtration efficiency enhanced. As shown in Figure 3a, all EAA filters showed enhanced filtration efficiencies for PM 0.3-0.5 after PDA coating. A large amount of NaCl particles accumulated on the fiber surfaces in dendrites when driven by electrostatic attraction (Figure 3d). A practically significant finding was that the efficiency enhancement depended on filter substrates. It seemed that the higher the filtration efficiency of the bare substrate, the less enhancement in filtration efficiency would be after PDA coating, except for Filter #3 ( Figure 3e). As shown in Table 1, Filter #3, an AC coated PET filter, did not enhance the surface ε r after PDA coating but lost some high ε r AC cakings, resulting in a limited filtration efficiency enhancement after PDA coating. It seems coarse filters with lower mechanical efficiency have greater potential for electrostatic efficiency improvements, which agrees with Joe's findings. [42] Therefore, though much progress has been made in recent years towards finer nanofibers, using micro-sized coarse fibers to maximize their electrostatic filtration efficiency is a promising approach.
Another extraordinary finding was that coating PDA would maintain (Filters #1-#3) or even reduce the pressure drops (Filters #4-#9) of the substrate filters. As shown in Figure 3b, the pressure drop of Filter #8 decreased most after the PDA coating, from 25.6 to 11.9 Pa at 1 m/s face air velocity. The high probability of this phenomenon was verified with three additional sets of bare and coated Filters #1 and #8, which had similar weights (Table 1) and fiber diameters (Supporting Information: Figure S4). Pressure drops of all Filters #1 were increased and all Filters #8 were decreased after PDA coating, though all of them showed nearly no gain in weight (Supporting Information: Figure S3). According to Davies' empirical correlation, [43] the pressure drop is decided by the filter solidity, thickness and fiber diameter (Supporting Information: Method S2). However, calculations showed that the pressure drop of Filter #1 would be decreased after the PDA loading, while that of Filter #8 would be increased, both of which were contrary to the experimental results (Supporting Information: F I G U R E 2 Schematic illustration for EAA coarse filtration. (a) Schematics of experimental apparatus for filtration performance evaluation. (b, c) Schematics of the electrostatic interaction between the PM and the fibers. (b) When both the PM and the fibers are uncharged, the electrostatic force between them is so weak to capture PM. (c) When the PM is charged with q and the fibers are polarized by E, the electrostatic force between them is strengthened to capture PM even far from fiber surfaces. EEA, electrostatically assisted air; PM, particulate matter. Table S1). Such differences might be attributed to the fact that Davies' correlation did not consider the influence of the morphology of a single fiber and the filter architecture constructed of multiple fibers. The nano protrusionmodified rough fibers would generate a more streamlined geometry for the airflow, resulting in a lower pressure drop than the smooth substrate fibers with circular cross section. [44] Similarly, the fiber roughened by PDA coatings (Supporting Information: Figure S1b during the PDA polymerization process. Nevertheless, a simple rule for engineering was that the coarse filter with higher pressure drop reduced more after PDA coating (Figure 3f). For medium-grade filter whose pressure drop achieved 33.0 Pa at 0.2 m/s air velocity, the pressure drop increased significantly to 161.5 Pa at 0.18 m/s after PDA coating. Therefore, the PDA surface modification might only be applicable for performance enhanced coarse filters.
Generally, a high filtration efficiency is traded off by large pressure drop, and therefore leads to the high energy consumption of the driving fan. Accounting for both filtration efficiency and pressure drop, the quality factor (QF) is used to evaluate the performance of EAA filtration efficiencies of Filters #1-#9. As shown in Figure 3c, PDA coated Filter #6 achieved the highest QF for PM 0.3-0.5 , indicating it was a preferable filter material, which was tested for detailed performance under different working conditions in the following sections.

| Filtration performance enhanced by electrostatic effect
The particle charging voltage and the filter polarizing voltage synergistically enhance the PM filtration efficiencies. As shown in Figure 4a, the mechanical filtration efficiency (U c = U p = 0) of coarse Filter #6 for PM 0.3-0.5 was 10.6%, which is consistent with its low pressure drop (9.2 Pa at 1 m/s). When lifting U c to 6 kV, the corona discharging current was increased to a detectable 1 μA (Supporting Information: Figure S7), and the filtration efficiency was significantly increased to 78.4%. When further lifting U c to 9 kV, the discharging current was increased nearly exponentially to 8 μA, and the filtration efficiency was increased further to 93.7%. By lifting U p to 20 kV, the filtration efficiency could be further enhanced to 97.5%. This result confirmed the impressive ability of synergistic particle charging and filter polarizing to enhance the electrostatic filtration effect for coarse filters. As shown in Figure 4b, the QF for PM 0.3-0.5 was increased from 0.012 to 0.300 Pa −1 when lifting U c from 0 to 9 kV, and was increased to 0.401 Pa −1 when further lifting U p from 0 to 20 kV.
A larger value of QF indicates a larger filtration efficiency or a lower pressure drop, which means the filter reaches high performance with low operation cost. However, QF does not consider the power consumption of suppliers, which should be included to evaluate the operation cost for electrostatic filtration. As shown in Figure 4a,c, the filtration efficiency was slightly enhanced from 96.9% to 97.5% by lifting U c from 8 to 9 kV (U p = 20 kV), while the power consumption almost doubled (from 16.3 to 32.1 W/m 2 ). To avoid overestimating the performance-cost ratio of the electrostatic filtration, the electrical power consumption is included in the comprehensive quality factor (CQF) by assuming that the extra power consumption for efficiency improvement is equivalent to an extra equivalent pressure drop. [45] As shown in Figure 4d, when U c got higher than 6 kV, continuing lifting U c would no longer improve CQF. It should be noted that the optimal working voltages (U c and U p ) should be selected with regard both to CQF and to the actual needs (e.g., specific filtration efficiency requirements or energy consumption restrictions). Although U c = 6 kV and U p = 20 kV made the highest CQF (0.210 Pa −1 ), U c = 8 kV, and U p = 20 kV could be selected as the optimal working condition for its filtration efficiency higher than 95% (96.9%) and the high-enough CQF (0.167 Pa −1 ).
Moreover, the filtration efficiency enhanced by the electrostatic effect was stably high during a 100-h test with average values of 96.4%, 96.7%, and 97.5% for indoor ambient PM 0.3-0.5 , PM 0.5-1 , and PM 1-3 (Figure 4e). The pressure drop increased slightly from 8.6 to 11.1 Pa at 1 m/s face air velocity (Figure 4f), indicating the potential application of the filter in high-velocity and long-term air filtration.

| Multiparameter performance for high-velocity air filtration
For application in HVAC systems, PM filtration is required to work at high face air velocities, for example, 1 to 4 m/s. However, there is an intrinsic conflict that high air velocity would cause undesired large pressure drop and low electrostatic filtration efficiency. Here, a preferable material (PDA coated Filter #6) working at optimal charging and polarizing voltages (U c = 8 kV, U p = 20 kV) was used to examine its performance at 1-4 m/s face air velocity. As predicted, the filtration efficiency decreased, and the pressure drop increased as the air velocity rose (Figure 5a,b). At high air velocities, the residence time of PM in the corona charging and the filter media is substantially decreased, resulting in a filtration efficiency decrease. Particularly, when the face air velocity rose from 1 to 4 m/s, the PM residence time between the high-voltage pin electrode and the grounding ring electrode decreased from 8 to 2 ms, resulting in a considerable decrease in the PM charging efficiency. However, as shown in Figure 5a, PDA coated Filter #6 still showed a significantly higher filtration efficiency for PM 0.3-0.5 (96.9%-80.6%) at 1-4 m/s compared with the bare substrate (95.6%-75.9%). For larger PM including PM 0.5-1 and PM 1-3 , the PDA coated Filter #6 could maintain higher filtration efficiency of 90.7% and 93.7%, respectively (Supporting Information: Figure S8).
Besides, as shown in Supporting Information: Method S3 and Figure S9, the Reynolds number reached over 6.4 (>1) at 4 m/s face air velocity, indicating a trans-turbulent flow. Therefore, other than those electrospun filters tested at relatively low air velocities, the relationship between the EAA filter pressure drop and the air velocity (1-4 m/s) is no longer linear, and a squared term is introduced according to the Darcy-Forchheimer model: where Δp (Pa) is the pressure drop of the filter; µ (Pa·s) is the air dynamic viscosity; v air (m/s) is the face air velocity; A few studies reported the electrostatic filtration performance at high air velocities for PM below 0.5 µm, which were compared with this study in Figure 5c,d. The detailed information was provided in Supporting Information: Table S2. It was shown that the EAA PDA coated filters in this study had lower pressure drop than filters in the literature when achieving similar filtration efficiency as theirs. In particular, compared to electrospun fibrous filters (Refs. 4 [46] and 5 [47] in Figure 5c), the pressure drop of filters in this study was reduced by 1 to 2 orders of magnitude. Compared to other EAA coarse filters (Refs. 1-3 [27,30,45] in Figure 5c), the PDA coated filters in this work allowed for a lower U c , which resulted in lower extra power consumption. As shown in Figure 5d, the EAA PDA coated filters in this work showed a remarkably higher (>2.1 times) CQF than other EAA coarse filters. At higher air velocities (e.g., 2 m/s), the advantage of this study remains significant. For example, an electrospun polyethylene oxide filter with 34 Pa pressure drop showed 51% filtration efficiency, [46] while the PDA coated Filter #7 in this work showed a close pressure drop (37.9 Pa) and remarkably higher filtration efficiency of 91.9%. Therefore, PDA coated filters with electrostatic assistance of particle charging and filter polarizing are expected to facilitate the wide application of EAA coarse filters in HVAC systems, where the face air velocity is high. Besides, typical PM concentrations and sources influenced the filtration efficiency in 2% (Supporting Information: Figure S10), indicating that the performance of EAA  Figure S5a. Comparison of (c) filtration efficiency, pressure drop, QF and (d) CQF of filters in this study with filters in the literature. [27,30,[45][46][47] Detailed information was provided in Supporting Information: Table S2. CQF, comprehensive quality factor; PM, particulate matter; QF, quality factor. | 253 filtration would be applicable in various areas for a safe, healthy, and energy-saving environment.
As an example of a complex task to engineer, an air filter often satisfying several contrarian parameters, such as high filtration efficiency and low pressure drop at large air velocities, a multiparameter performance assessment was carried out using radar plots ( Figure 6). Besides filtration efficiency (%), pressure drop (Pa) and air velocity (m/s), the intrinsic parameters of filters were chosen: filter thickness (mm), porosity and fiber diameter (µm). Thicker filters are expected to have greater dust containing capacity, therefore serving longer and reducing cost. Filters with higher porosity are expected to have lower pressure drop and save weight and cost. Coarse filters with larger fiber diameters are mechanically stronger and cost less. Therefore, an ideal filter ( Figure 6a) is expected to perform~100% filtration efficiency and~0 Pa pressure drop at a large air velocity (e.g., 1 m/s), and to have~1 porosity, adequate thickness (~10 1 mm) and fiber diameter (~10 1 µm) as well. By optimizing the filter substrate, in situ coating of PDA, and synergistically modulating the electric fields, the artificial PDA coarse filter in this study showed exciting multiparameter performance close to the ideal model (Figure 6b,c). However, for most electrospun filters and commercial filters, though high filtration efficiency and low pressure drop could be achieved by charging (corona or triboelectrification) or sacrificing porosity, the air velocities were lower than 0.2 m/s and the filter thicknesses were less than 4 mm (Figure 6d-i), which limited their broader engineering application for highvelocity and long-term air filtration.
In summary, this study has described the fabrication of a series of air coarse filters exhibiting high filtration efficiency and low pressure drop at extremely large face air velocities by self-assembled surface modification of PDA. The incorporation of PDA interfaces enabled the microfibers to show promising rough surfaces with high ε r , which could be obtained via a simple dip-self-assembled-coating process under a mild reaction condition. It was found that coating PDA increased the filtration efficiency of all nine conventional air coarse filters with electrostatic assistance of particle precharging and filter polarizing. After PDA loading, the substrate material significantly affects the filtration efficiency improvement (from 0.2% to 14.2%). Greater efficiency enhancement could be achieved by coating PDA on smooth fibers with lower initial filtration efficiency. An extraordinary finding was that coating PDA would maintain or even reduce the pressure drop (up to 13.7 Pa at 1 m/s air velocity) of the substrate filters, the underlying physical nature of which remained unclear because of the complex influence of d f and morphology of every single fiber, and the structure of the whole filter during the PDA polymerization process. Nevertheless, a simple rule for engineering was that the coarse filter with higher pressure drop reduced more after PDA coating.
Electrostatic assisted coarse filters are a promising approach for their significant efficiency enhancement and low pressure drop maintaining. With the synergistic effect of particle precharging (U c = 8 kV) and filter polarizing (U p = 20 kV), the as-prepared PDA coated Filter #6 exhibited remarkably improved filtration efficiency for PM 0.3-0.5 from 10.6% (U c = U p = 0) to 96.9% at 1 m/s air velocity. More importantly, at a large face air velocity of 4 m/s, the filtration efficiency of coated Filter #6 still maintained up to 80.6%, 85.1%, and 94.3% for PM 0.3-0.5 , PM 0.5-1 , and PM 1-3 , respectively. And the pressure drop of coated Filter #6 was maintained at 108.6 Pa, 25% lower than that of the bare filter (144.2 Pa). Overall, PDA coated filters with electrostatic assistance of particle pre-charging and filter polarizing offers a practical guide to the wide application in high-air-velocity ventilating systems (e.g., ventilation in public buildings and vehicles, air purifications in clean rooms and natural air cooling in data centers) for a safe, healthy and energy-saving environment.

| Preparation and characterization of filter samples
Commercial fibrous coarse filters were cut into slices in diameter of 50 mm as substrates (detailed characteristics in Table 1). Each slice was fully soaked in 60 ml of 10 mM Tris-buffer aqueous solution (Sigma-Aldrich) with stirring for 30 min (200 rpm, 25°C). According to a previous study, [30] an optimal amount (140 mg) of dopamine hydrochloride (Sigma-Aldrich) was added into the solution and stirred for 24 h (200 rpm, 25°C) for selfassembled polymerization. After being washed with water (4 times) and ethanol (1 time), and being dried in an oven at 60°C for 24 h, PDA coated filters were obtained. The surface morphologies of the filters were analyzed by optical microscopy (BX53M, Olympus Co), scanning electron microscopy (SEM, JSM-IT500A, JEOL) and a field-emission scanning electron microscopy (FE-SEM, Gemini 300, Zeiss) coupled with energy dispersive X-ray spectra (EDS). The fiber diameters were measured using ImageJ software based on SEM images. The weight of the filters was obtained by an analytical balance (BSA124S, Sartorius).

| Evaluation of filtration performance
To evaluate the effect of the substrate filters, PDA coatings, supplied voltages and air velocities on the filtration performance, tests were conducted in an acrylic air duct (inner diameter: 50 mm) as shown in Figure 2a.
When not specifically stated, we used NaCl particles as the feeding PM. The ambient air with PM removed by a HEPA filter was driven into the experimental air duct via a duct fan. NaCl particles were generated by a nebulizer (Huifen 3321, China, with 0.9 wt% NaCl solution), dried by a diffusion drier and removed charge by a neutralizing tube (SIMST190250, TSI Inc, length: 2 m). When using indoor ambient particles as feeding PM, the HEPA filter at the inlet of the air duct in Figure 2a was removed and the gas circuit for NaCl generation was turned off. The number concentrations for PM with the size of 0.3-10 μm were measured by an optical particle counter (Aerotrak 9306, TSI Inc), and the single-pass filtration efficiency, η(d P ) was calculated by: where d P (μm) is PM diameter; C up and C down (pcs/L) are the number concentrations of particles in the airflow before and after the EAA filtration module, respectively. The counting of particles was performed every 1 min during an 8 min measurement for alternately C up and C down . A digital differential gauge (DP-CALC 5825, TSI Inc) with a resolution of 0.1 Pa was used to measure the pressure drop of the filters. An air velocity meter (VELOCICALC 9535-A, TSI Inc) with a resolution of 0.01 m/s was used to measure the face air velocity.
The measurements of pressure drop and face air velocity were performed every 10 s for 5 times, respectively. The air temperature and relative humidity were not controlled but measured by a recorder (TH20R-EX-H, Huahanwei) at the air duct inlet. The supplying voltages and the loop currents were recorded by corresponding power supplies. The power consumption of the module, P (W/m 2 ), is then calculated by: where the subscripts c and p stand for charging and polarizing, respectively; U (kV) is the supply voltage; I (μA) is the loop current; A is the cross-sectional area, π × 0.025 2 m 2 . QF(d P ) considers filtration efficiency and pressure drop of the filter, which is calculated by [52] : CQF(d P ) considers additional power consumption of the EAA filtration module, which is calculated by [45] : where η fan is the efficiency of the fan in an HVAC system, 0.71.