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Scaling properties of coating flows in rectangular channels.

A de Lózar¹, A L Hazel, A Juel

¹Manchester Centre for Nonlinear Dynamics and School of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom.

Physical Review Letters

|February 1, 2008

Summary

The aspect ratio of rectangular channels significantly influences two-phase displacement flows. A new scaling law shows flow behavior depends on a modified capillary number above a threshold, simplifying predictions.

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Area of Science:

Fluid Dynamics
Multiphase Flow
Channel Flow

Background:

Two-phase displacement flows are crucial in various industrial applications.
Understanding flow behavior in channels of varying aspect ratios is complex.
Previous studies have not fully captured the aspect-ratio dependence in rectangular channels.

Purpose of the Study:

To experimentally investigate the influence of channel aspect ratio on two-phase displacement flows.
To identify key dimensionless parameters governing these flows.
To develop a predictive model for flow behavior across different rectangular channel geometries.

Main Methods:

Experimental setup involving controlled two-phase displacement in rectangular channels.
Systematic variation of channel aspect ratio (alpha).
Measurement of flow characteristics and determination of capillary number (Ca).

Main Results:

A buoyancy-dependent threshold capillary number (Ca[over ;]_{t}) was identified.
Above this threshold, flow behavior scales with a modified capillary number, Ca[over ;]=[1+0.12(alpha-1)+0.018(alpha-1);{2}]Ca.
The aspect ratio's influence is captured by this modified capillary number.

Conclusions:

The aspect ratio's impact on two-phase displacement flows can be unified under a modified capillary number.
This finding simplifies the prediction of flow behavior in any rectangular channel.
Practical applications can benefit from this generalized scaling law for flow management.