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Transient two-layer thin-film flow inside a channel.

Kamran Alba¹, Patrice Laure, Roger E Khayat

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

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

|September 21, 2011

Summary

This study numerically investigates two superimposed Newtonian fluid layers flowing in a channel under a pressure gradient. It develops averaging equations that accurately predict the stability and nonlinear behavior of these two-layer flows.

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Area of Science:

Fluid Dynamics
Non-Newtonian Fluid Mechanics
Computational Fluid Dynamics

Background:

Investigates the flow of two superimposed Newtonian fluid layers in a channel driven by a pressure gradient.
Builds upon existing models for incompressible Newtonian film flow and stability analysis.

Purpose of the Study:

To numerically investigate the flow of two superimposed Newtonian layers in a channel.
To develop and validate averaging equations for two-layer Poiseuille flow stability.
To analyze the nonlinear behavior of interfacial instabilities in such flows.

Main Methods:

Introduced scaled conservation equations for two-layer incompressible Newtonian film flow.
Employed a weighted residual approach for depth averaging.
Performed linear stability analysis and numerical simulations using a finite difference scheme.
Utilized Gaster's relation to calculate perturbation spatial growth rates.

Main Results:

Averaging equations recovered asymptotic stability formulas derived from Navier-Stokes equations.
Numerical simulations accurately predicted perturbation amplification based on flow parameters.
The developed averaging equations successfully described nonlinear interfacial instabilities.
Quantitative agreement was found between Gaster's relation and numerical simulations.

Conclusions:

The derived averaging equations provide an accurate model for two-layer Newtonian film flow stability.
The study successfully mimics disturbance effects on coextrusion flow through perturbation analysis.
The model captures the nonlinear dynamics of interfacial instabilities in two-layer Poiseuille flow.