Macroscopic Model for Head-On Binary Droplet Collisions in a Gaseous Medium

Area of Science:

• Fluid Dynamics
• Interfacial Phenomena
• Computational Physics

Background:

• Binary droplet collisions are crucial in many industrial processes.
• Understanding the transition between droplet coalescence and bouncing is essential for controlling these processes.
• Existing models often rely on empirical parameters or lack accuracy across wide length scales.

Purpose of the Study:

• To develop a novel macroscopic model for predicting droplet collision outcomes based on fundamental physics.
• To accurately simulate coalescence-bouncing transitions in head-on binary droplet collisions.
• To investigate the influence of gas film properties and intermolecular forces on collision dynamics.

Main Methods:

• Modification of Navier-Stokes equations incorporating lubrication theory to account for rarefied gas films.
• Inclusion of intermolecular van der Waals forces via a disjoint pressure model.
• Employment of a state-of-the-art moving adaptive mesh method to resolve multiple length scales.
• Numerical simulations of tetradecane and water droplet collisions.

Main Results:

• The model successfully predicts coalescence-bouncing and bouncing-coalescence transitions.
• Simulations capture transitions observed with increasing collision intensity.
• Predicted transition Weber numbers show good agreement with experimental data for tetradecane and water droplets.
• The study elucidates the roles of gas density, droplet size, and mean free path in gas film rupture.

Conclusions:

• The developed macroscopic model provides accurate predictions for droplet collision dynamics without empirical parameters.
• The model's ability to span over five orders of magnitude in length scales enhances its applicability.
• Findings offer new insights into the physics governing droplet collision outcomes and gas film behavior.