Abstract
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.
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Abbreviations
- \(A_{i}\) :
-
Droplet area (mm2)
- \(C_{\text{d}}\) :
-
Drag coefficient
- \(D\) :
-
Diameter (mm)
- \(D_{\text{s}}\) :
-
Droplet spread diameter (mm)
- F :
-
Force
- \(F_{b}\) :
-
Area fraction not covered
- \(F_{c}\) :
-
Area fraction covered
- g :
-
Local gravitational field (m/s2)
- h :
-
Nozzle to substrate height (mm)
- \(h_{avg}\) :
-
Average thickness of liquid film (mm)
- L :
-
Droplet center-to-center distance (mm)
- n :
-
Number of droplets
- t :
-
Time (s)
- U :
-
Droplet impact velocity (m/s)
- We :
-
Weber number
- Re :
-
Reynolds number
- \(\zeta\) :
-
Droplet spread factor
- \(\eta\) :
-
Volume ratio
- \(\theta\) :
-
Equilibrium contact angle (°)
- \(\theta_{\text{a}}\) :
-
Advancing contact angle (°)
- \(\kappa\) :
-
Curvature
- \(\lambda\) :
-
Overlap ratio
- \(\mu\) :
-
Viscosity (cP)
- \(\rho\) :
-
Density (kg/m3)
- \(\sigma\) :
-
Surface tension (mN/m)
- \(\psi\) :
-
Dimensionless droplet length
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Acknowledgment
The authors gratefully acknowledge funding for this work provided by the Natural Sciences and Engineering Research Council (NSERC) of Canada.
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Dalili, A., Sidawi, K. & Chandra, S. Surface coverage by impact of droplets from a monodisperse spray. J Coat Technol Res 17, 207–217 (2020). https://doi.org/10.1007/s11998-019-00258-7
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DOI: https://doi.org/10.1007/s11998-019-00258-7