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Harmonic moment dynamics in Laplacian growth
Alexander Leshchiner1, Matthew Thrasher, Mark B Mineev-Weinstein
1Center for Nonlinear Dynamics, Physics Department, University of Texas at Austin, Austin, Texas 78712, USA.
Summary
Harmonic moments describe bubble growth in oil layers. For nonzero surface tension, these moments decay over time, validating a new theoretical expression and yielding accurate surface tension measurements.
Area of Science:
- Fluid dynamics
- Interface phenomena
- Laplacian growth
Background:
- Harmonic moments linearize zero surface tension Laplacian growth problems.
- Previous models predicted conserved moments (except area) in zero surface tension scenarios.
Purpose of the Study:
- Investigate harmonic moments for bubble growth with nonzero surface tension.
- Derive and validate a theoretical expression for the time evolution of harmonic moments.
- Measure surface tension using harmonic moment dynamics.
Main Methods:
- Experimental determination of harmonic moments for a growing air bubble in oil.
- Derivation of an expression relating the time derivative of harmonic moments to physical parameters.
- Comparison of experimental observations with the derived theoretical expression.
Main Results:
- For nonzero surface tension, harmonic moments (except area) decay over time, unlike theoretical predictions for zero surface tension.
- The derived expression for dM(k)/dt accurately describes laboratory observations.
- The method yielded a surface tension value within 20% of the accepted value.
Conclusions:
- Harmonic moments provide a robust and physically realizable framework for describing interface dynamics.
- The study confirms the conservation of higher-order harmonic moments only in the zero surface tension limit.
- The experimental validation supports the utility of harmonic moments in fluid dynamics and surface tension measurements.
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