Laboratory study of the collection efficiency of submicron 1 aerosol particles by cloud droplets. 2 Part II - Influence of electric charges.

12 A new In-Cloud Aerosol Scavenging Experiment (In-CASE) has been developed to measure the 13 collection efficiency (CE) of submicron aerosol particles by cloud droplets. Droplets fall at their 14 terminal velocity through a one-meter-high chamber in a laminar flow containing aerosol particles. 15 At the bottom of the In-CASE’s chamber, the droplet train is separated from the aerosol particles 16 flow and the droplets are collected in an impaction cup whereas aerosol particles are deposited on 17 a High Efficiency Particulate Air (HEPA) filter. The collected droplets and the filter are then analysed 18 by fluorescence spectrometry since the aerosol particles are atomised from a sodium fluorescein salt 19 solution (𝐶 20 𝐻 10 𝑁𝑎 2 𝑂 5 ) . In-CASE fully controls all the parameters which affect the CE - the droplets 20 and aerosol particles size distributions are monodispersed, the electric charges of droplets and 21 aerosol particles are known and set, while the relative humidity is indirectly controlled via the 22 chamber’s temperature. This paper details the In-CASE setup and the dataset of 70 measurements 23 obtained to study the impact of the electric charges on CE. For this purpose, droplets and particles 24 charges are controlled through two charging systems developed in this work - both chargers are 25 detailed below. The droplet charge varies from -3.0x10 4 ± 1.4x10 3 to +9.6x10 4 ± 4.3x10 3 elementary 26 charges while the particle charge ranges from zero to -90 ± 9 elementary charges depending on the 27 particle radius. A droplet radius of 48.5 ± 1.1 μm has been considered for four particle dry radii 28 between 100 and 250 nm while the relative humidity level during experiments is 95.1 ± 0.2 %. The 29 measurements are then compared to theoretical models from literature – showing good agreements.


INTRODUCTION 31
Aerosol particles (APs) are a fundamental part of the atmosphere since they act on climate and more 32 locally on meteorology (Twomey, 1974). They are also a key topic in human health where APs are 33 known to increase the mortality (Dockery et al., 1992). For these reasons, the processes involved in 34 the removing of the atmospheric AP have been investigated extensively over the last decades, 35 through theoretical works (Slinn and Hales, 1971;Beard, 1974;Slinn, 1974;Young, 1674; Grover and 36 Beard, 1975;Grover et al., 1977;Slinn, 1977;Davenport et al., 1978;Wang et al., 1978;Flossmann,

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When a droplet with a charge approaches an AP of charge , the partial influence of the AP 83 electrostatic field on the droplet leads to the re-orientation of the water dipoles. As a result, a 84 surface charge distribution on the droplet is created and supposed to be comparable to the one of a 85 conductive sphere. In an electrostatic equivalent problem, the droplet can be replaced by two-point 86 charges (Jackson, 1999). One modelling the charge distribution, inside the droplet and near its 87 surface, another for the residual droplet charge located at the droplet surface. Finally, the analytical 88 expression of the electrostatic forces is the addition of two Coulomb forces between the AP and the

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Several laboratory studies investigated the influence of the electric charges on the CE (Beard, 1974; 99 Wang and Pruppacher, 1977;Lai et al., 1978; Barlow   108 measurements in the literature as Barlow and Latham (1983) concluded after highlighting a discrepancy of few orders of magnitude between all these authors. Nevertheless, Wang and 110  and Wang et al. (1983) succeeded in controlling the charges and the sizes (as well 111 as the relative humidity for Wang and Pruppacher (1977) but they considered only unlike signs 112 between both droplets and APs. In their study, Lemaitre et al. (2020) did not observed any influence 113 of electric charges on CE since for the low relative humidity level and the large droplet radius 114 considered, the diffusiophoretis and thermophoresis dominated the AP collection.

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Thus, only the Coulomb inverse square term in the analytical expression of the electrostatic forces 116 can be documented whereas the contribution of the short-range attractive term has not been 117 experimentally verified until now.

126
Thus, a novel experiment has been designed to study the influence of electric charges on the CE 127 which is presented in this paper. Note that this experiment was also used to study the influence of 128 relative humidity which is the object of the companion paper: Part I (Dépée et al., 2020).

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The first part of the paper describes the experimental setup. Afterwards, the method to evaluate  whereas the overflow ends in an exhaust (black, Figure 2

225
The charging relationships of the charger used during all experiments are presented in Figure 4. They

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A method to evaluate the droplet charge was developed in this study and is detailed in Appendix B.

259
In Figure

299
The collection efficiency ( ) is calculated from the equation (1): Where , is the AP mass collected by all droplets which is directly measured by fluorescence With -the droplet radius, -the droplet generation frequency, ∆ -the experiment duration (from

314
In equation (2)  to the HEPA filter and the humidifier (Figure 2). The measured penetrations are presented in Table 3.

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It is observed the penetration decreases when the AP charges ( ) increases and the AP radius ( ) 328 decreases since the electrical mobility of APs is larger. During experiments, the AP number 329 concentration was ranged from 3.10 4 cm -3 (for =100 nm and = −10 ± 1 | |) to 2.10 3 cm -3 (for =250 330 nm and = −90 ± 9 | |). As a reminder, the pipes are anti-static and connected to the ground (as 331 well as the collision chamber) so there is no charge accumulation due to AP deposition during 332 experiments. Thus, the penetrations presented in Table 3 are assumed to be constant over time.

333
Note that the AP deposition was neglected in Part I (  The relative CE uncertainty ( ) is calculated following Lira (2003) and presented in equation (5): Where the relative uncertainties are related to the droplet radius ( ≈1%), the effective height of 349 interaction between droplets and APs (

352
The relative uncertainty , is evaluated through the equation (6) : Where is the relative uncertainty of the dilution performed during the spectrometry analysis, 355 assumed to be equal to 1 %, and is the relative uncertainty of the fluorimeter which can 356 be up to 30 % when the measured AP mass is close to the detection limit. The relative uncertainty of 388 @ * ( ) = @ ( ) + ( Where @ is the fluid velocity at the AP location, the AP relaxation time and the AP mass.

389
The expression of the buoyancy force ( ) is detailed in equation system (B.1), and ℎ in the is defined in equation (10) :

393
With 0 -the permittivity of the free space, -the unit vector in the radial direction from the 394 droplet centre to the AP centre, * -the distance between the AP and droplet centres, normalised 395 by the droplet radius .

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Note that the same influence of the charge product on the CE is observed for the other three wet AP

460
In Figure 8, the CE measurements (circle) for a neutral droplet ( = 0 ± 600 |e|) are presented for 461 the 4 wet AP radii -referred by the color code -with the respective theoretical CE values (triangle).

462
The dashed line represents the theoretical CE value without electrostatic forces.

503
This latter is assumed to be equal to | ,∞ − ,∞ | where ,∞ is the AP settling velocity.

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Since this prediction models the contribution of the attractive Coulomb forces on the CE, only the CE 506 measurements with a negative charge product for the 4 AP radii are compared. In Figure 9, the

544
A good accordance between the model and the CE measurements are shown. Indeed, it appears that 545 there are as many data points above the "Model=Measurement" line as below, meaning that the 546 model overestimates as much as underestimates the observations. Thus, it can be assumed that there 547 is no missing or unnecessary microphysics effects in the CE modelling. Moreover, the mean difference 548 between the modelled CEs and the 70 measured CEs is 66 %. This is a reasonable value for a 549 microphysics parameter such as the collection efficiency which varies on several orders of magnitude, 550 especially since the value was calculated disregarding the different uncertainties (error bars in 551 Figure 10) and was as a result over-evaluated.

552
Nevertheless, 6 data points seem inconsistent with discrepancies between model and measurements 553 from 150 to 1000 %, occurring for the smallest CE values in Figure 10 (lower left). Note that the 554 discrepancies should be even worse since the modelled CEs, set to 10 -5 , are actually much lower. By 555 examining these data points, it appears that the measured AP masses in the droplet impaction cup -

556
, in equation (1) -are very close to the detection limit of the spectrometer used. Moreover, for the experimental conditions, the model predicts AP masses in the droplets lower than the detection 558 limit since the Coulomb inverse square term in equation (10) was very repulsive. So, the assumption 559 can be made that a pollution occurred during the various steps of the protocol (end of experiment, 560 disassembly of the chamber's bottom to reach the droplet impaction cup, change of room for the 561 analysis, etc.). Note that the detection limit of the spectrometer is 10 -15 kg (for the nominal analysis 562 volume considered), which only represents ten APs with a dry radius of 250 nm deposited on the 563 droplet impaction cup. Thus, it exists an important uncertainty in these CE measurements related to 564 a possible contamination. This is difficult to quantify but the low uncertainties of the CE 565 measurements below 10 -4 were increased in Figure 10. To reduce this potential pollution, it would 566 be necessary to work in a cleanroom or increase the experiment duration to avoid detection problem.

567
However, for these data points the experiment duration was almost 6 hours and, beyond this 568 duration, stability problems of the piezoelectric droplet generator were frequent.

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In the new measured CE dataset, the APs and droplets are accurately charged through custom-made 616 droplet and AP chargers detailed above. Since both charge polarities are found in clouds (Takahashi, 617 1973), the droplets were negatively as well as positively charged during experiments. Moreover, 618 several amounts of elementary charges on the droplet were considered to represent a neutral droplet 619 but also the weakly and strongly charged droplets respectively found in stratiform and convective 620 clouds (Takahashi, 1973

639
The CE measurements with opposite signs on the droplet and AP were compared to the prediction of    Flossmann, 1985) to examine the influence of the electric charges on the total wet AP removal in the 663 atmosphere. It could strongly affect the atmospheric AP removal since cloud droplets are known to 664 be charged (Takahashi, 1973) as well as the atmospheric AP, even more when APs are radioactive.    paper, droplets are generated at a velocity larger than their terminal velocity. It has been found that 793 a distance between the droplet generator and the capacitor of 15 cm was large enough to allow 794 droplets to reach their terminal velocity. In the setup in Figure B.1, this requirement prevails.

796
An experiment was performed to ensure that reversing the Beard (1976) model was a suitable method 797 to evaluated the droplet radius. For this purpose, the same droplet train was recorded in optical 798 shadowgraphy with a camera zoom at the lowest and at the greatest to respectively apply the Beard 799 (1976) model inversion and the circle Hough transform. In all tests, it was found a discrepancy of less 800 than 2 % between the two methods, giving overvaluations as well as undervaluations when comparing 801 one to the other.

802
Also, the disturbance of the electric field at the capacitor ( ) on the vertical droplet velocity was 803 studied. was then turned on and off to investigate the change in vertical droplet velocity. It was 804 found that during tests, reduced the vertical velocity up to 1.3 %. This situation was for a droplet 805 charge ( ) and a capacitor potential ( ) both negative. Some other tests also showed that the 806 droplet vertical velocity was increased up to 0.3 %, for a droplet charge and a capacitor potential of 807 unlike sign. Since these two extreme cases respectively represent an undervaluation of less than 808 0.7 % and an overestimation of less than 0.2 % of the droplet radius -this effect was neglected.

809
Finally, two other validations can be formulated by examining Figure 6. First, several capacitor