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08:02
Fabricating High-viscosity Droplets using Microfluidic Capillary Device with Phase-inversion Co-flow Structure
Published on: April 17, 2018
Viscous withdrawal of miscible liquid layers
Laura E Schmidt1, Wendy W Zhang
1The Department of Physics & The James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA.
Physical Review Letters
|March 21, 2008
Summary
We developed a new scaling law for viscous withdrawal, predicting how much liquid is entrained between layers. This model accounts for global geometry, resolving issues with previous local-flow approximations for improved accuracy.
Area of Science:
- Fluid dynamics
- Rheology
- Interfacial phenomena
Background:
- Viscous withdrawal involves an upper layer's converging flow entraining a lower, stably stratified layer.
- Previous models using local straining flow approximations for thin tendrils were degenerate.
Purpose of the Study:
- To propose a scaling law for the volume flux of entrained liquid in miscible layers.
- To resolve the degeneracy of long-wavelength models by incorporating global geometry.
Main Methods:
- Utilizing the concept of local straining flow acting on thin tendrils.
- Developing a long-wavelength model that incorporates global withdrawal flow geometry.
Main Results:
- A scaling law for entrained volume flux was derived.
- Incorporating global geometry removed model degeneracy, yielding a unique solution.
- The refined model shows only a logarithmic dependence on global flow parameters.
Conclusions:
- The proposed scaling law accurately predicts viscous entrainment.
- Global geometry is crucial for resolving model degeneracy in viscous withdrawal.
- The findings advance understanding of fluid entrainment in stratified systems.
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