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Related Experiment Video

Updated: Dec 10, 2025

Parameterizing V-notch Weir Equations for Flow Monitoring in a Drainage Control Structure
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Parameterizing V-notch Weir Equations for Flow Monitoring in a Drainage Control Structure

Published on: April 25, 2025

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Self-Similar Draining near a Vertical Edge.

Nan Xue1, Howard A Stone1

  • 1Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA.

Physical Review Letters
|August 27, 2020
PubMed
Summary

Researchers discovered a new 3D self-similar shape for draining liquid films near vertical edges. This finding simplifies complex fluid dynamics equations and matches experimental measurements.

Area of Science:

  • Fluid dynamics
  • Surface science
  • Physics

Background:

  • Liquid films draining on vertical surfaces exhibit complex, nonuniform behavior near edges.
  • Existing models often simplify the fluid dynamics, particularly in three dimensions.

Purpose of the Study:

  • To experimentally characterize the three-dimensional (3D) self-similar shape of a draining liquid film near a vertical edge.
  • To develop a new theoretical scaling for the 3D film shape.
  • To validate the theoretical model with experimental data.

Main Methods:

  • Utilized interferometry to precisely measure the liquid film thickness.
  • Collected data on film thickness as a function of position and time.
  • Developed a new 3D self-similar scaling based on the 2D solution.

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Main Results:

  • Identified and experimentally confirmed a novel 3D self-similar shape for the draining film.
  • The new scaling successfully reduced the complexity of the governing partial differential equation.
  • Experimental measurements showed excellent agreement with the theoretical predictions.

Conclusions:

  • The study reveals a fundamental 3D self-similar structure in draining liquid films.
  • This work provides a simplified model for understanding edge effects in thin film dynamics.
  • The findings have implications for various applications involving thin liquid films.