Particle dispersion and deposition in evaporating sessile droplets

• Applicant: Professor Dr. Berend van Wachem
• Subject Area: Mechanical Process Engineering ; Fluid Mechanics
• Term: from 2021 to 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 452916560

• Final Report Year: 2025

Final Report Abstract

The objective of this project was to model particle dispersion and deposition in evaporating sessile droplets, aiming to predict particle distribution, internal velocity, vapor concentration, and temperature fields in and around the droplet. A two-stage numerical framework was developed, coupling a Volume of Fluid (VOF) method for multiphase flow with a Discrete Element Method (DEM) for particle tracking, enabling the simulation of evaporation, flow, and particle transport. The model was validated against experimental and analytical data, confirming its accuracy and relevance for industrial applications such as coating, printing, and microfluidics. The influence of Marangoni stresses on monodisperse particles was first analyzed. Temperature gradients from heated substrates induce internal flows that suppress coffee-ring formation by redistributing particles away from the contact line. The model was then extended to bidisperse systems under constant contact angle evaporation. Simulations showed Marangoni flow drives self-sorting: smaller particles form a core at the droplet apex, while larger particles form a surrounding shell. This mechanism demonstrates how deposition patterns can be tuned via substrate temperature, particle properties, and droplet dynamics. The simulation tool captures all key physical effects, including capillary interactions at the gas-liquid interface, and provides a robust approach to predicting particle organization in evaporating droplets.

Publications

• Breaching the capillary time-step constraint using a coupled VOF method with implicit surface tension. Journal of Computational Physics, 459, 111128.
  Denner, Fabian; Evrard, Fabien & van Wachem, Berend
  
• Data for the paper A fully-coupled algorithm with implicit surface tension treatment for interfacial flows with large density ratios
  Janodet, R., van Wachem, B. & Denner, F.
  
• Data for the paper Dispersion of particles in a sessile droplet evaporating on a heated substrate
  Jain, A., Denner, F. & van Wachem, B.
  
• Dispersion of particles in a sessile droplet evaporating on a heated substrate. International Journal of Multiphase Flow, 180, 104956.
  Jain, Aman Kumar; Denner, Fabian & van Wachem, Berend
  
• Numerical Analysis of the Dispersion and Deposition of Particles in Evaporating Sessile Droplets. Langmuir, 40(26), 13428-13445.
  Erdem, Ali Kerem; Denner, Fabian & Biancofiore, Luca
  
• A fully-coupled algorithm with implicit surface tension treatment for interfacial flows with large density ratios. Journal of Computational Physics, 520, 113520.
  Janodet, Romain; van Wachem, Berend & Denner, Fabian
  
• Data for the paper Self-sorting of bidisperse particles in evaporating sessile droplets
  Jain, A., Denner, F. & van Wachem, B.
  
• Self-sorting of bidisperse particles in evaporating sessile droplets
  Jain, A.K., Denner, F. & van Wachem, B.