Laboratory study of the collection efficiency of submicron 1 aerosol particles by cloud droplets . 2 Part I-Influence of relative humidity 3

12 A new In-Cloud Aerosol Scavenging Experiment (In-CASE) has been conceived to measure the 13 collection efficiency (CE) of submicron aerosol particles by cloud droplets. In this setup, droplets fall 14 at their terminal velocity through a one-meter-high chamber in a laminar flow containing aerosol 15 particles. At the bottom of the In-CASE’s chamber, the droplet train is separated from the aerosol 16 particle flow 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 (C20H10Na2O5 ). 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 controlled, while the relative humidity is indirectly set via the chamber’s 22 temperature. This novel In-CASE setup is presented here as well as the first measurements obtained 23 to study the impact of relative humidity on CE. For this purpose, droplets and particles are electrically 24 neutralised. A droplet radius of 49.6 ± 1.3 μm has been considered for six particle dry radii between 25 50 and 250 nm and three relative humidity levels of 71.1 ± 1.3, 82.4 ± 1.4 and 93.5 ± 0.9 %. These 26 new CE measurements have been compared to the Wang et al. (1978) and the extended model of 27 Dépée et al. (2019) where thermophoresis and diffusiophoresis are implemented. Both models 28 adequately describe the relative humidity influence on the measured CE. 29


INTRODUCTION
Far away from the source, the main mechanism involved in the AP scavenging originates from the radii ( ) -see Figure 1, C. Note that the electrostatic forces can have a significant influence on the

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There are also thermophoretic and diffusiophoretic effects which can influence the CE. In clouds, 74 they shall favour the CE increase when evaporation occurs and decrease CE during condensation (due 75 to a thermal equilibrium between the droplet and the air). Thermophoresis exists when a thermal 76 gradient prevails between the air and the droplet. When the relative humidity is below 100 %, the 77 evaporating droplet's surface temperature ( , ) is colder than the bulk air temperature ( ). The 78 average kinetic energy of air molecules is then decreasing when approaching the droplet's surface.

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An AP is thus attracted by a thermophoretic force near the evaporating droplet (see Figure 1, F)

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The relative humidity in the collision chamber is set through the temperature, this latter being 152 controlled via a cooling system. In the next sections, the droplets and AP characterisation as well as 153 the In-CASE's chamber are detailed.

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156 Figure 2 In-CASE setup to study the influence of relative humidity.
when the concentration is three times larger. Since the geometric standard deviation ( ) is above 169   presented in this current paper.

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The droplet generator is placed at the top of the In-CASE's collision chamber, within an injection 205 head (see Figure 6). Few times during an experiment, droplet pictures are recorded by optical 206 shadowgraphy through two facing portholes in the injection head (see Figure 6). A circle Hough 207 transform is then applied to evaluate the droplet radii in the recorded pictures. An example is given 208 in Figure 4   219 220

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It is well-know that the piezoelectric droplet generator produces highly electrically charged droplets.

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With a similar device, Ardon-Dryer et al. (2015) measured up to 10 4 elementary charges on the 224 generated droplets. Since this paper focused only on the relative humidity influence, the droplets,

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as well as APs, must be neutralised.

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To do so, an electrostatic inductor was built following Reischl et al. (1977). Two parallel metal plate 227 are placed at the droplet generator's nozzle -this is the electrostatic inductor shown in Figure 5 228 (labelled 1, left). One plate is connected to a potential ( ) while the other is connected to the 229 neutral potential -as presented in Figure 5 -in order to induce an electric field (~10 2 -10 3 V/m).

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Sodium chloride is added to the pure water that feeds the piezoelectric injector. According to the 231 generated electric field polarity, the system can selectively attract negative or positive ions toward

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To evaluate the droplet charge and then, neutralise the droplets, an ex situ experiment has been 239 conducted where the droplet train passed through a capacitor (labelled 2, Figure 5, left). One 240 capacitor's plate is connected to the neutral whereas the other is connected to a high potential ( )

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-inducing an electric field (~10 5 -10 6 V/m). A Faraday cage surrounding the capacitor and a plate 242 maintained at a neutral potential are set in order to prevent the electric field at the capacitor ( ) 243 from disturbing the electric field at the inductor ( ) which could change the droplet charge.

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Finally, the potential which electrically neutralises the droplet is found by selecting for the 245 value which minimises the droplet train deflection.
246 Actually, this system can also be used to precisely evaluated the electric charges on the droplets (for

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Note that, the droplet charge induced by the piezoelectric injector has been calculated to inductor, set in the injection head (see Figure 6).

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The In-CASE chamber (see Figure 2) is subdivided into three stages -the injection head, the collision 262 chamber and the In-CASE chamber's bottom part. These three parts will be detailed in the next 263 subsections.

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The injection head is composed of two parts -the droplets and the APs injection. The upper part is 268 used to inject the droplets while the APs are inserted in the second part about 10 cm below. This 269 distance is required to measure the droplet size through the two facing portholes (see section 1.3.1)

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but also to let droplets decelerate and reach their terminal velocity.

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The droplet train is injected through a 3D printing set at the top of the droplet injector (see Figure 6).

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This 3D printing has been constructed to precisely place the droplet generator and the electrostatic 273 inductor together (see Figure 5, right). Indeed, the electrostatic inductor has to keep the same 274 position relative to the droplet generator to prevent changes in the electric field which in turn,

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can disturb the droplet charge and stop the neutralisation.

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The APs are inserted from the sides of the entire circumference through a kind of flat torus. This

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The collision chamber is a one-meter stainless steel cylinder with an inner diameter of 5 cm (see

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The temperature and the relative humidity discrepancies between top and bottom were respectively

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Note that the AP flow before the injection head is also thermally set to inject APs with the same 308 temperature as in the collision chamber.

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The change in droplet radius due to vaporisation in the collision chamber is calculated according to

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Consequently, the CE measured are applied for size of respectively 58.0, 63.5 and 78.5 nm AP radii.

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Note that the AP density is not the one of sodium fluorescein salt ( = 1580 kg.m -3 ) since

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APs contain water. Indeed, the water density ( ) should be considered in the AP density ( ) 336 calculation. At a given relative humidity ( ), the AP density inside the chamber is then deduced by 337 the equation (1): (1) Since the relative humidity after the dryer (see Figure 2) ranges from 10 to 20 %, the AP growth factor 341 342 The CE is calculated from the AP mass collected by the droplets during an experiment and the average 348 AP mass concentration in the collision chamber. To obtain these quantities, the droplet train must 349 be separated from the interstitial APs (which were not collected).

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1.4.3.1 APs and droplets separation 352 353 The system developed to separate the droplet train from the AP flow is presented in Figure 9.  The droplets and APs separation were verified with two tests. First, In-CASE was run under usual 379 experimental conditions except no droplets were generated. After five hours of experiment, a 380 spectrometry analysis was performed in the droplet impaction cup and no fluorescein was detected.

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Thus, no AP had settled on the droplet impaction cup during the experiment.

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The second test was to ensure that droplets were collected by the impaction cup. Then, In-CASE was Where the AP mass collected by all droplets ( , ) is directly measured by spectrometry analysis in 408 the droplet impaction cup (see Figure 9) while the mass of available APs in the volume swept by the     Table 1 shows this parameter for every AP flowrate 446 used during the experiment and for a given selected AP radius. The double charged AP radius with 447 the same electrical mobility as the selected AP radius (single charged) is also indicated -when this 448 latter size is large enough compared to the cut-off radius, it is assumed that there is no contribution 449 of the multiple charged APs in the CE measurement. This is the case for a selected AP radius of 200 450 or 250 nm where the AP size distribution at the DMA outlet can be considered purely monodispersed.

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However, for a selected AP radius of 50 or 150 nm, according to

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The first AP radius uncertainty is related to the AP selection by the DMA. Nevertheless, this 464 uncertainty has been neglected since the spectral bandwidth of the DMA is quite small compared to 465 the AP radius uncertainty addressed below.

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Indeed, the only significant AP radius uncertainty results from the effective AP radius inside the In-

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Since the method of CE evaluation differs in the presence of multiple charged APs, the uncertainty 483 calculation is also different depending on the situations. The method is described in the Appendix B. 488 Where is the number of injected droplets during the experiment. The relative CE uncertainty ( )

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is then evaluated according to Lira (2003) and summarised by the equation (8): In all experiments, the droplet charge is 0 ± 600 elementary charges with a radius of about 50 μm.

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Since the AP charge distribution is similar to a Boltzmann distribution, an AP charge of more than

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The experimental conditions presented in Figure 9 are summarised in Table 2. The wet AP radii are 568 evaluated with the mean experimental conditions as well as the AP density ( ) which is calculated 569 with (1). The CE measurements are summarised in Table 3.

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Regarding the experimental results, it can be noted that the influence of the relative humidity via 572 the thermophoresis and diffusiophoresis contribution on the CE is of first order. For the larger AP 573 radii studied, the CE increases by a factor of 4 when the relative humidity passes from 93.5 to 71.1 %

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-filling up the Greenfield gap as the models predicts. A slight decline of the contribution of these 575 two phoretic effects is observed when the AP radius decreases -the previous factor of 4 reducing to 576 a factor of 3 for the smaller AP radii and for the same relative humidity range (from 93.5 to 71.1 %).
the contribution of the Brownian motion on the CE increases and starts dominating the thermophoretic and the diffusiophoretic forces. Consequently, the influence of the relative humidity 580 on the CE is negligible for nanometric AP radii.

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Moreover, the impact of the AP size is lower than the influence of the relative humidity for the 582 experimental conditions considered. Indeed, between the larger and the smaller AP radii, the CE is

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This observation is in line with the modelling of the CE when a threshold is more and more visible as 587 the relative humidity decreases, for the submicron AP radii studied.

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Finally, for the AP sizes and the droplet radius studied, both models describe relatively well the     Table 3 while lines are the CE modelling resulting from the 610 experimental conditions found in Table 2.   varying the ratio of the multiple charged APs (by changing the AP size distribution mode in Figure 3).

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The matrix system is then described through the equation (16): Where the one-dimension matrix of the collected mass ( ) for the set of experiment is 741 noted as the equation (17):

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The two-dimension matrix of the available AP masses in the volume swept by the droplet ( )