Research

(1) Rain Forecast: Effect of background air turbulence on droplet size growth rate in a polydisperse droplet field

In warm rain initiation, air turbulence is understood to be the bottleneck mechanism that determines the rate at which small droplets (30 μm diameter) grow towards sizes (90-100 μm diameter) required for precipitation (Falkovich et al. 2002, Wang et al. 2006, Xue et al. 2008). It is recognized that a cloud droplet could increase in size up to around of 30 μm diameter within a reasonable time by condensation (Lamb and Verlinde 2011, see Fig. 1.3). Size growth in larger droplet diameter classes (> 80 μm) is predominantly by the collection of smaller droplets by larger droplets through gravitational settling. Mechanisms driving droplet size growth through the bottleneck diameter range of 30-100 μm (Wang and Grabowski 2009) are not well understood, with air turbulence being one of the primary candidates (Falkovich et al. 2002). Falkovich et al. (2002) numerically demonstrated the effect of turbulence on the widening of the droplet spectrum for conditions representative of real clouds. In the last few decades, research on particle interactions has focused on understanding the underlying mechanisms that enhance particle/droplet interactions (especially collisions) by scaling down the large scale cloud problem to small scale droplet-turbulence interactions . The effects of relative velocity and clustering on droplet size growth in a turbulent air flow, some aspects are still not fully understood. Specifically

• How to determine the droplet size growth rate experimentally in a polydisperse droplet field that encounters several of the aforementioned mechanisms?

• What are the roles of relative velocity and clustering in a droplet field of relatively large polydispersity? How do the turbulence characteristics influence the collective effects of relative velocity and clustering?

• What are the effects of initial droplet characteristics on droplet size growth?

A genuine attempt has been made to address the above questions. An experimental set-up has been designed and developed, and three different flow measurement techniques: Phase Doppler Interferometry (PDI), Laser Doppler Velocimetry (LDV) and Long Distance Microscopy (LDM) have been deployed to achieve these objectives.

Fig. (a) Schematic of the experimental set-up, with all dimensions in mm. The axial and transverse directions are specified by the x- and y-axes, respectively, with the origin placed at the spray nozzle exit. (b) Top view of the AA′ plane indicated in (a), along with the optical arrangements for the phase Doppler interferometry (PDI) and long-distance microscopy (LDM) measurements.(c) A representative image obtained using LDM over a 4.5 mm×4.5 mm window centred around (x,y)=(302.25,0) mm. 

• We identify an optimum air turbulent intensity that maximizes the rate at which the average droplet diameter increases with time 

• We show that the onset of clustering suppresses the intuitive effect of an increase in droplet collision rate with air turbulent intensity, resulting in the existence of an optimum air turbulent intensity that maximizes the average droplet size growth rate due to droplet coalescence 

• We measure clustering and relative velocity in a polydisperse droplet field with background air turbulence, to directly demonstrate the physical coupling between these collision enhancement factors

• This coupling is shown to cause an inverse relation between clustering and relative velocity in the mean-flow–dominated turbulent flow we study, thus suppressing the intuitive effect of an increase in droplet collision rate with background air turbulence

Reference:

• Falkovich, G., A. Fouxon, and M. Stepanov (2002). Acceleration of rain initiation by cloud turbulence. Nature(London), 419(6903), 151

• Wang, L.-P., Y. Xue, O. Ayala, and W. W. Grabowski (2006). Effects of stochastic coalescence and air turbulence on the size distribution of cloud droplets. Atmos. Res.,82(1), 416–432

• Xue, Y., L.-P. Wang, and W. W. Grabowski (2008). Growth of cloud droplets by turbulent collision–coalescence. J. Atmos. Sci., 65(2), 331–356.

• Lamb, D. and J. Verlinde, Physics and chemistry of clouds. Cambridge University Press, 2011

• Kumar, M. S., Chakravarthy, S. R., & Mathur, M. (2019). Optimum air turbulence intensity for polydisperse droplet size growth. Physical Review Fluids, 4(7), 074607

(2) Spray visualization using digital inline holography (DIH) 

Accurate characterization of agricultural sprays is crucial to predict in-field performance of liquid applied crop protection products. In this paper, we introduce a robust and efficient machine learning (ML) based Digital Inline Holography (DIH) algorithm to accurately characterize the droplet field for a wide range of commonly used agricultural spray nozzles. Compared to non-ML based DIH processing, the ML-based algorithm enhances accuracy, generalizability, and processing speed. The ML-based approach employs two neural networks: a modified U-Net to obtain the 3D droplet field from the numerically reconstructed optical field, followed by a VGG16 classifier to reduce false positives from the U-Net prediction. The modified U-Net is trained using holograms generated using a single spray nozzle (XR11003) at three different spray locations; center, half-span, and the spray edge to create training data with different number densities and droplet size ranges. VGG16 is trained using the minimum intensity projection of the droplet 3D point spread function (PSF). 

Reference:

• Kumar, M. S., Hogan, C. J., Fredericks, S. A., & Hong, J. (2024). Visualization and characterization of agricultural sprays using machine learning based digital inline holography. Computers and Electronics in Agriculture, 216, 108486. 

• Kumar, M.S., He, R., Feng, L., Olin, P., Chew, H.P., Jardine, P., Anderson, G.C. and Hong, J.,(2023). Particle generation and dispersion from high-speed dental drilling. Clinical oral investigations, 27(9), 5439-5448. 

(3) Machine learning based model development for hologram processing

Despite the advancements in DL, many models developed thus far suffer from a lack of generalizability, with their effectiveness heavily influenced by factors like particle concentration, morphology, size ranges, and optical properties. This often results in inaccurate predictions that necessitate further post-processing, thus increasing the overall processing time. Efforts to enhance generalizability frequently result in compromises on model performance, potentially impeding the real-time processing of holograms in diverse applications such as product quality control in manufacturing, environment monitoring, and medical diagnostics . In response to these challenges, our current work introduces a novel DL model designed to robustly process holograms across a wide spectrum of particle concentrations, shapes, and polydispersity. To achieve this, our model architecture is designed to be both physics-informed and tailored to prevent overfitting, thereby enhancing its generalizability.

Reference:

• Kumar M, S., & Hong, J. (2024). Generalizable deep learning approach for 3D particle imaging using holographic microscopy (HM). Optics Express, 32(27), 48159-48173. 

(4) Bacteria Tracking from Digital Inline Holography

Bacteria tracking is crucial for biofilm formation studies because biofilms are structured communities of bacteria that adhere to surfaces and develop over time. Understanding bacterial motion and behavior at different stages of biofilm formation provides key insights into microbial dynamics, antibiotic resistance, and infection control. We have started using the generalizable ML model (Kumar, S. M., & Hong, J., 2024) for tracking bacteria. Here are some initial results: