Surface coverage by impact of droplets from a monodisperse spray

  • A. DaliliEmail author
  • K. Sidawi
  • S. Chandra


A novel pneumatic monodisperse spray was fabricated to validate the results of a probabilistic model and a stochastic model that were developed to predict surface area coverage of the monodisperse spray. Multiple droplets of a highly viscous 87 wt% aqueous glycerin solution were deposited on a flat, transparent, plexiglass substrate. The uniformly sized droplets (2.5 mm in diameter) impacted, spread, and coalesced on the substrate which led to the creation of a liquid sheet. Using a high-speed camera placed underneath the transparent substrate, droplet impact and resultant area coverage were recorded. When impinging droplets overlapped those already on the surface, surface tension forces pulled impacting droplets towards them, agglomerating the liquid, in a phenomenon known as drawback. The area covered by the liquid was measured from photographs using image analysis software. In the numerical models, droplets were set to impinge at random locations and drawback effects between droplets were accounted for by using a semiempirical correlation. While both models showed good agreement with the experimental results at lower area fractions, the stochastic model gave better estimates at larger area fraction due to its incorporation of drawback effects.


Sprays Coatings Liquid films Droplet coalescence Droplet drawback Spray impact Surface coverage Paint sprays 

List of symbols


Droplet area (mm2)


Drag coefficient


Diameter (mm)


Droplet spread diameter (mm)




Area fraction not covered


Area fraction covered


Local gravitational field (m/s2)


Nozzle to substrate height (mm)


Average thickness of liquid film (mm)


Droplet center-to-center distance (mm)


Number of droplets


Time (s)


Droplet impact velocity (m/s)


Weber number


Reynolds number

Greek letters


Droplet spread factor


Volume ratio


Equilibrium contact angle (°)


Advancing contact angle (°)




Overlap ratio


Viscosity (cP)


Density (kg/m3)


Surface tension (mN/m)


Dimensionless droplet length



The authors gratefully acknowledge funding for this work provided by the Natural Sciences and Engineering Research Council (NSERC) of Canada.


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Copyright information

© American Coatings Association 2019

Authors and Affiliations

  1. 1.Department of Mechanical and Industrial Engineering, Centre for Advanced Coatings TechnologiesUniversity of TorontoTorontoCanada

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