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Related Experiment Video

Updated: May 7, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

Dispersive hydrodynamics in viscous fluid conduits.

N K Lowman¹, M A Hoefer

¹Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 17, 2013

Summary

This summary is machine-generated.

This study derives a precise theoretical model for viscous fluid conduits, revealing how nonlinearity and dispersion govern their evolution. The findings describe large amplitude dynamics and validate experimental observations.

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Area of Science:

Fluid dynamics
Nonlinear dynamics
Wave phenomena

Background:

The interface between fluids of different viscosities rising buoyantly is complex.
Previous models lacked precise theoretical treatment for this free-boundary two-fluid system.

Purpose of the Study:

To derive a precise theoretical model for the interfacial dynamics of viscous fluid conduits.
To analyze the interplay between nonlinearity and dispersion in this system.

Main Methods:

Utilized a multiple scales, perturbation technique applied to the Navier-Stokes equations.
Considered perturbations around a vertically uniform, laminar conduit flow.
Employed the ratio of interior to exterior viscosities as the small parameter for asymptotic analysis.

Main Results:

Derived a scalar, nonlinear partial differential equation governing the cross-sectional area dynamics.
Identified a balance between buoyancy-driven self-steepening and viscous, interfacial stress-induced dispersion.
Characterized the leading order behavior and the regime of model validity.

Conclusions:

The derived model accurately describes large amplitude dynamics of viscous fluid conduits.
The model's validity aligns with previous experimental findings.
Viscous fluid conduits serve as a robust system for studying nonlinear, dispersive wave phenomena.