Modifying natural droplet systems by charge injection

Modifying droplet behavior has wide applications, from removing pathogens to increasing rainfall. In an environmental experiment, negative charge release is demonstrated to inﬂuence a natural fog. During charge emission, the average mass concentration of 1 μ m droplets increased by 95.3%. For smaller droplets, concentrations during charge emission exceeded those without charge emission at the 99% conﬁdence level. This is consistent with charge both facilitating formation of small droplets and inhibiting their evaporation. Physics-based droplet modiﬁcation has immediate relevance to weather modiﬁcation and, conceivably, pathogen control, without the introduction of additional chemical materials.


I. INTRODUCTION
Droplet systems are ubiquitous in nature, such as in clouds, or exhalations which transmit disease.In weather modification, attempts are made by chemical means to encourage small droplet growth in clouds to produce rain.Alternatives consuming less resource without generating residues are, however, desirable.One physics-based approach is to introduce charge.Charge affects droplet stability [1], interdroplet forces [2][3][4], and collision efficiencies [5][6][7], changing the droplet size distribution.Further, charge modifies aerosol deposition, allowing targeted material delivery or decontamination [8,9].New methods to disrupt droplet systems carrying pathogens such as COVID-19 may also have contemporary relevance [10], if a therapeutic benefit can be demonstrated.
Observations of ionization affecting water clouds [11,12] motivate experiments to investigate charge effects on natural drop systems.Although non-thunderstorm-cloud droplets are commonly charged [13], direct experimentation is difficult.Surface fogs offer a more practical alternative, having droplet sizes (1-10 μm diameter) similar to some clouds [14,15] and exhaled drops [16].Observations of charge release into fog are described here.Relevant theory on the stability of charged droplets is given first, followed by experimental implementation.Results are then summarized and discussed.

II. THEORY A. Formation of charged droplets
Droplets form on small aerosol particles, influenced by vapor supersaturation and charge [1,17].The change in free * Present address: MetOffice, Fitzroy Road, Exeter, UK. energy G when a water droplet of radius a forms on a cloud condensation nucleus of radius a 0 is

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with M r , ρ w , and γ the relative molecular mass, density, and surface tension of liquid water, respectively; N A is Avogadro's number; k B Boltzmann's constant; T a the droplet temperature; S the local water vapor saturation ratio; and je the charge carried (for j the number of elementary charges, e, carried) and ε 0 is the permittivity of free space.The saturation ratio required for droplet formation is found from the turning point of Eq. ( 1), as In Eq. ( 2), f T is the Thomson factor for surface tension; f R is the Rayleigh factor for electrical forces; and the final term represents the effect of dissolved salt, with b = 3i V M r m 4πρ w M s , i V the Van't Hoff factor, M s the relative molecular mass of the salt, and m the dissolved mass of salt.The Thomson and Rayleigh terms are given by and respectively where R v is the gas constant for water vapor, [17,18].Figure 1(a) shows how increasing charge affects the water droplet formation, by decreasing the critical supersaturation and increasing the critical size.

B. Evaporation of charged droplets
Droplets evaporate according to the local vapor concentration.The variation in a droplet's radius a with time t as it evaporates is given by for vapor diffusivity D v , and f V , a ventilation coefficient [15].The difference term on the right-hand side (RHS) describes vapor transfer between the ambient environment (temperature T ∞ and vapor pressure e ∞ ) and a droplet with surface vapor pressure e s .As the droplet shrinks, the Rayleigh factor f R and Thomson factor f T become increasingly important, with the charge effects arising through f R .When f R = f T , a droplet of radius a is at the Rayleigh limit if the number of elementary charges carried is Alternatively, the Rayleigh radius can be calculated from (6) given a droplet charge [17].If j R is exceeded, or the droplet evaporates to become smaller than the Rayleigh radius, it will become unstable due to imbalance between electrical and surface forces [19].
Further, during evaporation, a droplet cools, with an instantaneous temperature given by Eqs. ( 13)-( 23) of [15] as Here, k g is the thermal conductivity of the surrounding gas and L the latent heat of vaporization.
Equation ( 5), with Eqs. ( 3), (4), and ( 7), can describe evaporation of a droplet from an initial size.Figure 1(b) shows an illustrative numerical solution for near-saturation conditions, such as in fog, using an adaptive, fourth-order Runge-Kutta method [20].The evaporation time lengthens with increasing initial droplet charge, until the droplet reaches the Rayleigh radius when the calculation is stopped.Less charge is required to slow the evaporation if the relative humidity becomes extremely close to 100%, with a correspondingly smaller Rayleigh radius.

C. Growth by collision
Drops can grow through gravitational collisions and coalescence, although this is not expected to be important in fog due to the droplets' small collision cross sections.Nevertheless, for charged droplets, the collision efficiency E coll increases due to electric image forces which are large and attractive at small separations, regardless of their relative polarities.For neutral drops of radii R = 2 μm and r = 1 μm, E coll = 0.03.This approximately doubles if both drops carry -2e (elementary charges), reaching E coll = 0.08 for -5e on both drops [7].Turbulence is an additional aspect of some droplet interactions [21,22], and a fully turbulent simulation [23] indicates that the electrical effects can propagate from small droplets through to raindrops.

D. Droplet charging timescale
Establishing likely charging timescales for fogs informs the design of experiments.Charge in air is partitioned between "small ions"-molecules clustered around a core elementary ion-and aerosol or droplets, between which charge is exchanged, typically by diffusion.Atmospheric small ions produced at a volumetric rate q, with number concentrations n + and n − for positive and negative ions, respectively, are governed by the ion balance equation, The RHS loss terms are due to ion-ion recombination and ion-droplet attachment, with coefficients α and β, respectively.β depends on droplet size and charge [24]; hence the attachment term integrates across the droplet size spectrum, for Z (a) the number concentration of droplets with radius a, with summation across all possible charges j.Simplifying to equal ion concentrations n, droplets of uniform size and concentration Z, with ion loss by attachment dominating over recombination (nβZ αn 2 ), Eq. ( 8) becomes Assuming the neutral limit ( j → 0), an estimate for the attachment coefficient is For 1 μm radius droplets in a fog [14] at 278 K, with μ = 1.2 × 10 -4 V m 2 s -1 [25], β 0 = 3.6 × 10 -11 m 3 s -1 ; hence with Z = 100 droplets cm -3 the ion attachment timescale 1 is 280 s.

E. Natural droplet experiment
The droplet population during charge release was examined using natural fog, in an experiment at the University of Reading's site at Sonning Farm near the River Thames (51.481 55°N, 0.897 154°W), 5 km from the campus (51.441 36°N, 0.938 07°W).Weather data showed that nearsurface fogs were infrequent; hence a bespoke unattended apparatus was designed.
The fog droplet size distribution was monitored with a light optical aerosol counter (LOAC) [26], operated alongside an electric field mill, sonic anemometer, and an array of four corona emitters to inject negative charge (-0.5 nA each) into the fog (see Fig. S1 in the Supplemental Material [27]).The emitters were switched on and off every 10 min, following the timescale estimated from Eq. (10).

III. RESULTS
During spring 2020 only 3 days (of 38 operating) had thin fog, with the foggy night of 15-16 March 2020 (see Fig. S2 [27]) analyzed further.Figure 2 summarizes the experimental data, after a correction was applied for LOAC's internal real-time clock drift (see Fig. S3 [27]).In Fig. 2(a), the series of LOAC droplet size spectra is shown, illustrating the transient bursts of droplets associated with fog.From this, a threshold fog droplet concentration was derived (see also Fig. S4 [27]).Figure 2(b) shows the atmospheric electric field determined at the apparatus (n.b., plotted, by convention, as the potential gradient (PG), where for E z , the vertical electric field, PG = -E z ), and the mean horizontal wind speed U.The PG increases during the more persistent fog, with wind speeds light throughout.The spline-detrended PG is shown in Fig. 2(c), on which the corona emission cycle has been overplotted.
In Fig. 3, the detrended PGs of Fig. 2(c) before [Fig.3(a)] and during [Fig.3(b)] the fog are compared.Before the fog formed on 15 March, the PG distributions with emitters on and off were similar, suggesting the emitted ions were being effectively dispersed away from the experimental volume.During the fog, the detrended PG distribution shifted negatively with the emitters on [Fig.3(b)], changing from a mean of 0.5 V m -1 with the emitters off to -0.5 V m -1 with the emitters on (see also Table I).This relative PG change of ∼1% at the field mill indicates that the emitters were functioning, acting to increase negative charge in the region from which the droplets were being sampled.Nearer the emitters, the charge asymmetry is likely to be larger.
Cycling the emitters on and off allows fog droplet data to be compared, with and without additional negative ions.Droplet number concentrations in each case are compared in Fig. 4. Due to the LOAC timing correction uncertainty of ±2 min, only values from the inner 5 min of the emitters on and off periods are used, although results are similar for the inner 4 or 6 min.In Fig. 4(a), median fog droplet number concentrations during emitters on and off are shown; an increase is apparent for the smaller droplet sizes.Figure 4(b) compares the spread (as interquartile range) of the droplet concentrations for emitters on and emitters off by size, showing that the number concentration difference in Fig. 4(a) is also associated with increased variability during emitters on.A least squares line to the Fig. 4(b) points has a gradient of 0.86 ± 0.05 (±1 SE), significantly different from the 1:1 line around which the points would be expected to cluster if the emitter on and emitter off situations were the same.Further, statistical tests (see Fig. S5 [27]) show significant differences in droplet concentrations between the emitter on and off conditions, for the size bins between 0.3 and 1.1 μm.
Mass concentration is more physically relevant than number concentration as it reflects the distribution of liquid water.Figure 4(c) shows median mass concentrations by droplet size.The 99% confidence range on the median mass concentration during emitters off is found by bootstrapping (i.e., repeatedly computing medians from combining different subsets of the available values, and taking the inner 99%).Figure 4(c) shows that the increased mass concentration of smaller droplets up to 1.1 μm during charge emission lies beyond the range of the variability occurring naturally without charge emission (see also Fig. S5 [27]): the 1.1 μm droplets' mass concentration increases by 95.3%.Mean mass concentrations for the small sizes steadily increase during emitters on and decrease during emitters off (Fig. S6 [27]).For larger droplets ( 1 μm), no significant change occurs, consistent with the Coulomb barrier inhibiting collisions [23], which is an additional contribution to stabilizing the droplet distribution.

IV. DISCUSSION
This experiment shows introduction of negative ions into an unbounded natural fog is associated with more abundant 1 μm diameter droplets.Instrument effects need to be considered as a possible cause, as droplet collection and sampling might be influenced by drop charging.A previous generation instrument to LOAC, STAC, was examined for this, and showed no difference in laboratory test measurements with and without prior charged particle removal using an electrostatic trap [28].Further, in the Sonning experiment, charging might be expected to deposit charged droplets in the plastic inlet or laser chamber of the LOAC, reducing the measured concentrations.The opposite effect, of an increase in concentration, is observed.
Charge can facilitate initial droplet formation by reducing the required critical supersaturation, and stabilize small droplets against evaporation.Both processes will act to increase the abundance of small droplets, as observed.The droplet charge and local humidity are therefore critical in determining what occurs.
In our laboratory experiments using acoustically levitated droplets, a single ionizer of the same model was able to generate Rayleigh disintegrations in droplets of ∼100 μm size [29].Such an "electrospray" approach to charging can yield charge levels up to a few times less than the Rayleigh limit [28,30].In the fog experiment, the four emitters provided -2 nA, or 1.4 × 10 10 negative ions s -1 .For a cylindrical region of unit area in the 3 m between emitters and detector, the additional negative ion generation would be about 5 × 10 9 ions m -3 s -1 , assuming uniform ion distribution with no wind removal or vertical electrical migration, which is typically smaller than turbulent dispersion scales (Table I).In calm, foggy conditions the artificial negative ion generation will therefore exceed the natural ion production rate [31,25] by ∼500.Equally partitioned across 100 droplets cm -3 , this volumetric charge generation rate is equivalent to ∼3000 e min -1 per droplet.(The measurements of Fig. 4 were determined 5 min after the emitters were switched on and Fig. 3   increased negative charge in the experimental volume).An abundance of negatively charged droplets, with lengthened evaporation times, or charged aerosols on which droplets can more readily form, is therefore likely.

V. CONCLUSION
Introducing ions influences natural droplet behavior, with an increase in droplet mass concentrations for micron size droplets observed after negative charge was emitted.This illustrates a possible route for weather modification, based on droplet physics rather than chemical materials, and supports a physical link between ionization and cloud behavior.It also suggests a method to be investigated further to displace aerosol mass, for example, of pathogens, towards larger sizes, ultimately facilitating gravitational removal.
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FIG. 2 .
FIG. 2. Experiment time series from 20 UTC on 15 March to 06 UTC on 16 March.(a) Droplet concentrations for all size bins recorded by the LOAC.The fog threshold chosen (0.3-0.4 μm droplet concentrations in their upper quartile) is also shown, as a dashed horizontal line.(b) Potential gradient (PG) (with smoothing spline) and horizontal wind speed U at 3 m.(c) Spline-detrended PG, with emitter cycling overplotted.(U and PG were sampled at 1 s and LOAC at 1 min).

FIG. 3 .
FIG. 3. Histograms of detrended potential gradient (PG) with (blue/gray bars) and without (brown solid bars) negative ion emission, during (a) 15 March up to 20 UTC and (b) for the periods with droplets exceeding the fog threshold of Fig. 2.

FIG. 4 .
FIG. 4. Comparisons of droplet size distributions from LOAC scans during fog conditions, with emitters on and off.(a) Median droplet number concentration by diameter, colored by bin size.(b) Interquartile ranges (IQR) of the droplet concentrations by size during the emitter on and off periods, plotted against each other [colors show bin sizes, as for (a)].(c) Median mass concentration by size bin, with 99% confidence interval (CI) on the median.(Concentrations are medians from the inner 5 min of the emitters on and off times: confidence ranges for the emitters off condition medians found by bootstrapping).

TABLE I .
Summary data before and during fog circumstances.