Obstructed breakup of slender drops in a microfluidic T junction

Area of Science:

• Fluid dynamics
• Microfluidics
• Interface physics

Background:

• Droplet breakup in microfluidic devices is crucial for various applications.
• Understanding the physics of droplet deformation and breakup is essential for controlling microfluidic processes.
• Previous studies have explored droplet dynamics, but a comprehensive theoretical model for obstructed T junctions was lacking.

Purpose of the Study:

• To develop a theoretical model for droplet breakup in a microfluidic T junction with a permanent obstruction.
• To analyze the scaling of droplet deformation with time and capillary number.
• To investigate the self-similar behavior during droplet breakup.

Main Methods:

• Theoretical analysis using a geometric construction for interface shape.
• Application of Tanner's law for local contact angle.
• Rigorous analysis employing the lubrication approximation.

Main Results:

• The proposed theory accurately predicts droplet deformation.
• The model shows excellent agreement with direct numerical simulations and experimental data.
• A self-similar behavior analogous to droplet spreading on a liquid film was identified.

Conclusions:

• The developed theory provides a robust framework for understanding droplet breakup in obstructed microfluidic T junctions.
• The findings offer insights into controlling droplet dynamics in microfluidic systems.
• The study highlights the applicability of lubrication theory to complex interface phenomena.