Curvature and shape relaxation in surface-viscous domains
Joseph M Barakat1, Todd M Squires1
1Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara, CA 93106.
Physical Review Fluids
|June 10, 2024
Summary
This study models curved, viscous fluid interfaces, revealing how surface curvature generates flow and affects domain shape. A critical capillary number (Ca) indicates shape instability distinct from Saffman-Taylor fingering.
Area of Science:
- Fluid Mechanics
- Surface Science
- Rheology
Background:
- Modeling rheologically complex interfaces is crucial for engineering and biological applications.
- Existing models often simplify interfaces as planar or of fixed curvature, neglecting dynamic curvature effects.
- Understanding surfactant-laden, curved interfaces requires dynamic models that account for surface viscosity and changing geometry.
Purpose of the Study:
- To investigate a dynamical model of a two-phase surface fluid on a curved interface.
- To understand how surface curvature changes generate 2D Stokes flows within a viscous domain.
- To analyze the resulting resistance to curvature deformation and domain shape distortion.
Main Methods:
- Developed a dynamical model for a surface-viscous domain on a spherical interface with time-varying radius.
- Utilized the Boussinesq-Scriven constitutive equation for surface stress under small-amplitude curvature deformation.
- Analyzed frequency-dependent dynamics under sinusoidal oscillation of pressure difference, defining a Peclet number (Pe).
Main Results:
- Curvature relaxation is diffusive, characterized by the Peclet number (Pe).
- At high Pe, sharp boundary layers form, leading to discontinuous domain curvature.
- A shape instability emerges above a critical surface capillary number (Ca), driven by surface-viscous stresses, distinct from Saffman-Taylor fingering.
Conclusions:
- Surface viscosity significantly influences the dynamics of curved interfaces and domain shape.
- The study defines key dimensionless numbers (Pe, Ca) governing interface behavior under deformation.
- The findings provide a foundation for modeling more complex interfacial phenomena, including viscoelasticity and large deformations.
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