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The various IMFs between identical molecules of a substance are examples of cohesive forces. The molecules within a liquid are surrounded by other molecules and are attracted equally in all directions by the cohesive forces within the liquid. However, the molecules on the surface of a liquid are attracted only by about one-half as many molecules. Because of the unbalanced molecular attractions on the surface molecules, liquids contract to form a shape that minimizes the number...
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Related Experiment Video

Updated: Jan 25, 2026

Fabricating High-viscosity Droplets using Microfluidic Capillary Device with Phase-inversion Co-flow Structure
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Free-Surface Variational Principle for an Incompressible Fluid with Odd Viscosity.

Alexander G Abanov1, Gustavo M Monteiro2

  • 1Simons Center for Geometry and Physics and Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA.

Physical Review Letters
|May 4, 2019
PubMed
Summary

We developed new fluid dynamics models incorporating odd viscosity, revealing unique boundary behaviors. These findings introduce novel free surface conditions with geometric interpretations for fluid flow analysis.

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Area of Science:

  • Fluid dynamics
  • Theoretical physics
  • Mathematical physics

Background:

  • Incompressible fluid dynamics with free surfaces is crucial in many scientific and engineering fields.
  • Odd viscosity, a less-studied fluid property, introduces unique phenomena not captured by classical models.
  • Understanding boundary dynamics is key to accurately modeling fluid behavior.

Purpose of the Study:

  • To develop variational and Hamiltonian formulations for incompressible fluid dynamics including odd viscosity and free surface effects.
  • To investigate the physical and geometric interpretation of odd viscosity contributions at the fluid boundary.
  • To establish new, potentially universal boundary conditions for fluid systems with odd viscosity.

Main Methods:

  • Application of variational principles to fluid dynamics.
  • Hamiltonian mechanics formulation.
  • Analysis of geometric boundary terms.
  • Derivation of modified Poisson brackets (Zakharov's).

Main Results:

  • Odd viscosity contributions manifest as geometric boundary terms within the variational principle.
  • These terms modify Zakharov's Poisson brackets, leading to novel boundary dynamics.
  • A new type of boundary condition is derived, relating free surface pressure to angular velocity.

Conclusions:

  • The derived boundary conditions offer a geometric interpretation of odd viscosity effects.
  • These conditions are proposed as universal due to their basis in system symmetries.
  • The study advances the theoretical framework for fluid dynamics with non-standard properties.