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Fabrication, Operation and Flow Visualization in Surface-acoustic-wave-driven Acoustic-counterflow Microfluidics

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Stability of vortex flow in a modulated channel.

Ehab Abu-Ramadan¹, Roger E Khayat

¹Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, Canada N6A 5B9.

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

|March 16, 2007

Summary

This study numerically analyzes fluid flow in a modulated channel. Increasing wall modulation decreases the critical Reynolds number, promoting instability and vortex formation.

Area of Science:

Fluid dynamics
Hydrodynamic stability

Background:

Investigates linear stability of two-dimensional periodic steady flow.
Focuses on spatially modulated symmetric channels with sinusoidal wall modulations.

Purpose of the Study:

Numerically analyze flow stability in modulated channels.
Examine the influence of geometric parameters on instability thresholds.
Investigate vortex flow effects on stability.

Main Methods:

Employs a regular perturbation expansion for base flow calculation.
Utilizes Floquet theory and a two-point boundary value method for disturbance analysis.
Validates a simple, direct, and efficient numerical procedure.

Main Results:

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Critical Reynolds number decreases with increasing wall modulation amplitude or wave number.
Modulated channel flow exhibits recirculation regions or vortices above a critical threshold.
Stable vortex flow parameter regime expands with modulation wave number, especially at low values.

Conclusions:

Hydrodynamic instability is promoted by wall modulation.
Vortex formation is linked to instability onset.
Wall modulation wave number significantly impacts stable vortex flow regimes.