Effect of Flow Profiles on the Flow Subjected to Oscillation Forcing: An Example of Droplet Mobilization in Constricted Tubes


Poiseuille flow was widely assumed in the analysis of fluid flow in porous media due to its simple form. It can describe the flow behavior at creeping flow conditions very well. However, errors were reported in the literature by the use of this parabolic velocity profile in some dynamic circumstances. The effect of velocity profiles on the capillary flow was discussed in this study when oscillation forcing was applied to the flow. An example of the response of nonwetting droplets to the oscillation forcing in a constricted capillary was analyzed: the velocity profiles of Poiseuille flow, starting flow and oscillatory flow were used in this analysis for a comparison. The easiness of implementing these velocity profiles in the theoretical analysis is in this order: Poiseuille flow, starting flow, and oscillatory flow, but the accuracy is in the order: oscillatory flow, starting flow, and Poiseuille flow. By using theoretical approach, we quantified the dimensionless numbers at which the velocity profile of Poiseuille flow profile can be used to approximate the velocity profiles of starting flow or oscillatory flow. The sensitivity of the viscosity ratio was also discussed in this study. When certain conditions of the dimensionless numbers are met, the use of the velocity profile of Poiseuille flow can be justified even though the flow is in a dynamic condition. Otherwise, the approximation by using Poiseuille flow could cause significant errors when the flow is subjected to oscillation forcing.


Civil, Architectural and Environmental Engineering

Research Center/Lab(s)

Center for Research in Energy and Environment (CREE)


This material is based upon work supported as part of the University of Missouri Research Board at the University of Missouri system. W. Deng also acknowledges the support from TOPRS Tech Co LTD.

Keywords and Phrases

Flow profiles; Oscillation forcing; Oscillatory flow; Poiseuille flow; Starting flow; Two-phase flow

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Article - Journal

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© 2019 Elsevier B.V., All rights reserved.

Publication Date

01 aPR 2020