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Transit Time Theory for a Droplet Passing through a Slit in Pressure-Driven Low Reynolds Number Flows
Spencer W Borbas1, Kevin Shen2, Catherine Ji3
1Richard and Loan Hill Department of Biomedical Engineering, University of Illinois at Chicago, 1200 W Harrison St., Chicago, IL 60607, USA.
Micromachines
|November 25, 2023
Summary
We developed analytical and numerical solutions for viscous droplet transit through rectangular slits, crucial for understanding cell passage and microfluidic applications. Our findings reveal how pressure, viscosity, and droplet size impact transit time, offering insights into biological and engineering processes.
Area of Science:
- Fluid dynamics
- Biophysics
- Microfluidics
Background:
- Soft object transit through constrictions is vital for biological processes (e.g., red blood cell passage) and microfluidic applications.
- Understanding droplet dynamics in slits is essential for blood filtration, disease progression, and droplet manipulation/separation.
Purpose of the Study:
- To derive analytical and numerical solutions for viscous droplet transit through a rectangular slit.
- To investigate the influence of various parameters on droplet transit time in slits.
Main Methods:
- Combined planar Poiseuille flow and Young-Laplace equations to derive ODEs.
- Modified equations to include the lubrication layer between droplet and slit wall.
- Employed Roscoe solution for flow entering/exiting rectangular slits and solved ODEs numerically for finite surface tension and lubrication layers.
Main Results:
- Derived closed-form solutions for transit time when surface tension and lubrication are negligible.
- Identified linear relationships between pressure and inverse transit time, and viscosity and transit time.
- Demonstrated increased transit time with larger droplet size relative to slit dimensions; noted surface tension's dual role.
Conclusions:
- Provided quantitative calculations for cell passage through slit-like constrictions.
- Offers insights for designing droplet microfluidic experiments and understanding physiological transit phenomena.
- Highlighted critical surface tension and pressure values that can impede droplet transit.
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