the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 26 Jan 2026
Numerical study of the collection of aerosol particles by falling deformable drops
Abstract. The free fall of a drop through gas loaded with solid particles gives rise to multiple physical interactions, which remain poorly documented, esp. when the drop is no longer spherical. In particular, no model predicts the particle collection efficiency for drops undergoing deformations or oscillations. This study aims to contribute to this effort by investigating numerically the dynamics of water drops freely falling in air laden with dispersed solid particles, for drop Reynolds and Weber number such that drops present deformations/oscillations or not (e.g., Re = 30, 70, 500 and 876). An Eulerian-Lagrangian framework is adopted. The drop internal and external flows are simulated with Direct Numerical Simulation (DNS), and the dynamics of the liquid/gas interface are tracked using a combination of the Volume of Fluid (VOF) and Level Set methods, this approach predicts the interface dynamics in line with experimental data. The trajectories of solid particles are simulated using Lagrangian tracking and taking into account drag, gravity, and Brownian motion. For spherical drops with Reynolds numbers below 200, our methodology replicates previous results. In the presence of oscillations/deformations, the flow parameters of the two continuous phases are correctly predicted. The particle collection efficiency also follows the experimental trend, but the values differ significantly from measurements found in the literature. We therefore propose certain areas of improvement with the goal of obtaining better fits to the available experimental data.
- Preprint
(2326 KB) - Metadata XML
- BibTeX
- EndNote
Status: open (until 10 May 2026)
-
RC1: 'Comment on ar-2026-1', Anonymous Referee #1, 17 Feb 2026
reply
-
AC1: 'Reply on RC1', Emmanuel Belut, 09 Apr 2026
reply
General Authors answer: We would like to thank the anonymous reviewer (Reviewer #1) for taking the time to carefully examine our paper. We have moved parts from the 'Discussion and Conclusions' section to the 'Results' section, as suggested. Three paragraphs were moved from the former 'Discussion and Conclusions' section to the 'Results' section, where they belong. The former ‘Discussion and Conclusions’ section is now just the Conclusion section. A few sentences in the conclusion had to be modified slightly to ensure it could stand alone. Modifications are highlighted in the document (bold blue). Some typos and minor syntax errors have also been corrected in the text and appear in bold blue in the revised version of the document.
Minor issues:
Introduction: I suggest providing a supporting discussion why the 1 and the 2 mm drop sizes have been chosen.Authors answer: In the case of deformable drops, this paper considered drops of 1.39 mm and 2 mm in freefall in ground-based atmospheric conditions (Reynolds numbers of 500 and 876, respectively). These drop sizes were chosen to enable comparison with existing literature data on capture efficiency (Lai et al., 1978; Querel et al., 2014) and drop dynamics (terminal velocity, mean axis ratio, and oscillation frequency: Beard, 1976; Szakall et al., 2010). Obviously, in the future, results would benefit from being enriched with larger drop results (up to 4-6 mm).
- We propose to add the following justification to the introduction of the paper :
Initial text L47: “Secondly, simulations are performed for flow regimes with drop oscillation and deformation (drop Reynolds of $500$ and $876$), for which -- to our knowledge -- no simulation results of aerosol particle collection efficiency are available in the literature. For these regimes, the simulation results for the continuous phases are validated (…) “
New text proposal :"Secondly, simulations are performed for flow regimes with drop oscillation and deformation, for which -- to our knowledge -- no simulation results of aerosol particle collection efficiency are available in the literature. We chose the case of 1.39 mm and 2 mm diameter water drops falling freely in ground-based atmospheric conditions (drop Reynolds numbers of $500$ and $876$),for which experimental validation data is available. For these situations, the simulation results for the continuous phases are hence validated (…)"
Line 194: Did the authors observe multiple oscillation modes, or only the axisymmetric one? Is that at all possible to observe the different oscillation modes in the numerical model?
Authors answer: It is a limitation, but in this work, we did not analyze in detail the oscillations modes of the drop, since the primary objective focused on aerosol capture efficiencies. However, we would firstly like to thank the reviewer for suggesting this idea, which we had not previously considered. It offers the potential for more advanced physical validation of droplet dynamics and has very real applications in atmospheric science. Clearly, the simulation data enables all oscillation modes to be observed and quantified, provided that the simulated physical time is long enough to capture several periods of the slowest oscillation mode once the drop has reached its terminal pseudo-stationary regime. Indeed, simulations predict the time-resolved 3D surface of the drop, the dynamics of which can be analysed in detail to highlight the existence of multimode oscillations. However, this data was not saved in the present study, so simulations must be run again to extract suitable (and very large) 3D data. Nevertheless, a close examination of the variation in the axis ratio in Figure 10 when the drop has reached its mean terminal velocity reveals that the amplitude of the axis ratio oscillations appears to be periodically modulated. This suggests the presence of multiple oscillation modes, as observed by Szakall et al. (2009, DOI: 10.1175/2008JAS2777.1, Figure 3). For this reason, we believe that the simulation probably predicts multiple oscillation modes, but we did not quantify them.Line 206: Can the aerosol of 2 mm size be considered as one with negligible fall speed wrt the drop?
Authors answer: Here, we assume that the reviewer is referring to aerosols with the largest considered aerodynamic diameter, i.e. 20 micrometres (not 2mm). Indeed, aerosols of this size have a negligible sedimentation velocity compared to that of the drop (typically 100 to 500 times less for the drop diameters considered in the present paper). However, note that even if the computations are performed in the assumed Galilean coordinate system of the moving drop, changing the coordinate system of the Navier–Stokes equation does not affect particle acceleration due to gravity. Hence, the model fully accounts for the difference in fall velocity between the aerosols and the drop.Line 244: Are there any old literature results of particles collection efficiencies? Analytical or experimental?
Authors answer: Indeed, the connection with other available literature is probably not obvious. An overview of the available literature results for these drop sizes (Re = 30, 70) and similar flow regimes (i.e. laminar axisymmetric) would be as follows:
1) Analytical :
- so-called “model II” or “flux model” by H.R. Pruppacher team (P. K. Wang, S. N. Grover and H. R. Pruppacher 1978) : Brownian motion only, no inertia, “moderate” Reynolds number in the axisymmetric laminar flow regime
- Slinn 1977 : largely inaccurate semi-empirical model (does not fit well the other numerical or experimental work listed here)
2) Simulations:
- Grover et al. work, beginning with Beard and Grover 1974 and successive papers (so-called “model I” by H.R. Pruppacher team) : lagrangian modelling without Brownian motion
- Wang et al. 2016 (Study on inertial capture of particles by a droplet in a wide Reynolds number range) : inertial aerosol only, no Brownian motion
- Yu et al. 2022 (Effects of rotation on collection characteristics of fine particles by droplets) : only one inertial point at Re=72, aerodynamic diameter 3.8 micrometer.
- Cherrier et. al. 2016 : unify both experimental and numerical results with fair accuracy for Reg<100 and Brownian/inertial particles : for this reason, data of Cherrier et al. 2016 were chosen as reference for the validation of the current model, without repeating other available results that are similar.
3) Experimental:
- Starr and Mason 1966 : only inertial particles and pendant drop technique (2 aerodynamic diameter > 4 micrometers)
- Horn et al 1988 (Collection efficiency of aerosol particles by raindrops) : only 2 points, aerodyn. diam. of 0.7 and 3.3 micrometers at Reg=66.
- Yu et al. 2022 (Effects of rotation on collection characteristics of fine particles by droplets) : only one experimental point at Re=72, aerodynamic diameter 3.8 micrometer (inertial particle, no influence of Brownian motion).
For the laminar, axisymmetric flow regime past a drop, the results of Cherrier et al. (2016) thus cover the widest range of Reynolds numbers and aerodynamic diameters. They link the purely Brownian and the purely inertial behaviours of the aerosol particles and retrieve data from other authors (experimental, theoretical, or numerical) (Cherrier et al., 2016; Depée et al., 2021). For this reason, it was chosen as a reference in the present paper. As this justification is not clearly evident in the paper, we propose adding the following sentence after line 243:
“As stated in the introduction, the simulation data of Cherrier et al. (2016) were chosen as the reference, as they cover the widest range of Reynolds numbers and aerosol aerodynamic diameters. This data links the purely Brownian and purely inertial behaviours of the aerosol particles, and retrieves data from other authors, either analytical, numerical of experimental (Cherrier et al., 2016; Depée et al., 2021)”Line 287: In my opinion the deformation of a 2 mm drop is still not really substantial
Authors answer: Indeed, we should remain objective. We therefore propose reformulating the sentence “In this flow regime, the droplets experience substantial deformations, oscillations, and vortex releases” as “In this flow regime, the droplets experience noticeable deformations, oscillations, and vortex releases (see Table 2)”.Figure 10, axis ratio: in Table 1 the axis ratio values are referred to data from Szakall et al. 2010. In Fig. 10 they are from Beard et al. 1991. Is there any difference?
Authors answer: The information in Table 1 is actually imprecise. Szakall et al. (2010) collected literature information and incorporated the values of Beard et al. (1991) (drop of 1.39 mm, used in Fig. 10) and Thurai et al. (2009) (drop of 2 mm). We propose modifying the headers in Table 2 for clarity (see revised paper).Line 303: Are the fluctuations seen in the model at the beginning of the simulations of physical or of numerical origin?
Author’s answer: We could say that they would be physical if the initial conditions given in the simulation were replicated in an experiment; in other words, these fluctuations are not the result of a numerical error. However, in the natural process of a raindrop falling, this initial condition does not reflect the reality of raindrop formation. Nevertheless, we demonstrate that the steady-state free-fall situation is independent of this initial condition, whether it is physical or not, and that the predicted free-fall dynamics of the drop is consistent with the literature - therefore rendering the fluctuation event inconsequential.Line 400: Is it possible to provide an estimation on the magnitude of the phoretic forces (probably it would be just enough to move the corresponding discussion from the Conclusions section to this line).
Authors answer: We propose to do as suggested: in line also with your initial general suggestion, we have moved the discussion paragraphs from the former “discussion and conclusion” section to the results section.Citation: https://doi.org/10.5194/ar-2026-1-AC1 -
RC2: 'Reply on AC1', Anonymous Referee #1, 13 Apr 2026
reply
I thank the authors for their careful responses. My comments have been satisfactorily addressed, and I have no further remarks.
Citation: https://doi.org/10.5194/ar-2026-1-RC2
- We propose to add the following justification to the introduction of the paper :
-
AC1: 'Reply on RC1', Emmanuel Belut, 09 Apr 2026
reply
-
RC3: 'Comment on ar-2026-1', Anonymous Referee #2, 14 Apr 2026
reply
The manuscript addresses an important problem in multiphase flow and atmospheric aerosol physics: the collection of aerosol particles by deformable, oscillating droplets. The use of an Eulerian–Lagrangian framework with DNS-based flow resolution and CLSVOF interface tracking is a clear strength of the study. Overall, the methodology is sound and well-executed, and the numerical framework captures key features of droplet deformation, oscillation, and settling dynamics across a range of Reynolds numbers. The validation against established results for both spherical and deformable regimes is also a positive aspect of the work. However, the manuscript, in its current form, exhibits significant limitations that prevent acceptance and therefore requires major revision. The most significant concern is the quantitative discrepancy observed in the predicted collection efficiency, particularly in the deformable droplet regime. While the model reproduces qualitative trends, the deviations from available experimental data are not sufficiently analyzed or explained. Given that collection efficiency is the central quantity of interest, this issue requires deeper investigation and a clearer physical or numerical interpretation. In addition, the sensitivity of the results to numerical choices, particularly interface treatment, interpolation schemes near the liquid–gas boundary, and grid resolution, has not been adequately assessed. The discussion of these aspects remains too limited for a DNS-based study of this complexity. A more systematic error and convergence analysis would significantly strengthen confidence in the reported results. The manuscript also overlooks several relevant and recent studies, including Journal of Fluid Mechanics (2026, 1031, A21), Physics of Fluids (2020, 32, 112105), Theoretical and Computational Fluid Dynamics (2020, 34, 133–144), and Physical Review E (2019, 99, 023107), which should be properly acknowledged and discussed in relation to the present findings. Furthermore, the manuscript would benefit from a clearer separation between methodological development and physical interpretation. Some modeling assumptions, particularly the definition of particle capture based on geometric contact with a deforming interface, require additional justification in the context of oscillatory droplet dynamics. Thus, while the study is technically strong and scientifically relevant, it requires substantial revision to address issues related to quantitative accuracy, numerical robustness, physical interpretation, and proper positioning within the existing literature.
Citation: https://doi.org/10.5194/ar-2026-1-RC3
Video supplement
Collection of aerosol particles by falling deformable drops Emmanuel Reyes https://av.tib.eu/series/1993
Viewed
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 185 | 57 | 15 | 257 | 10 | 7 |
- HTML: 185
- PDF: 57
- XML: 15
- Total: 257
- BibTeX: 10
- EndNote: 7
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
The wet removal of aerosol particles from the atmosphere, i.e. their collection by cloud droplets and raindrops, is a highly efficient atmospheric cleansing process. This scavenging mechanism is of crucial importance in heavily polluted industrial regions; moreover, in the case of nuclear accidents or volcanic eruptions, the removal of hazardous particles from the atmosphere has significant health and economic implications. Therefore, the topic of the present manuscript is highly relevant not only for the aerosol community but also for the broader atmospheric physics and chemistry communities.
Experimental investigations of scavenging processes are challenging, and the results are often uncertain due to difficulties in accurately characterising aerosol size distributions and environmental parameters such as temperature and humidity. In addition, drop size plays a key role in determining scavenging efficiency. For these reasons, numerical investigations are often preferred for studying this problem. However, such numerical tools must be both accurate and computationally efficient. This is one of the main objectives of the authors of the present manuscript, who introduce a model to numerically investigate the dynamics of freely falling water drops in air laden with aerosol particles.
In general, the paper is very well written, easy to read and to follow the concept. I recommend the manuscript for publication in Aerosol Research. I have really just a few comments and remarks before publication:
First a structural suggestion: Please consider to move some part from the Discussion and conclusions section to the Results section. It is more common to have a Results and Discussion section and a stand-alone Conclusion section. The discussion of the results fits there better.
Minor issues: