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Motion of a viscous slug on heterogeneous surfaces: crossover from stick–slip to steady sliding

Published online by Cambridge University Press:  10 October 2023

Bauyrzhan K. Primkulov Open the ORCID record for Bauyrzhan K. Primkulov [Opens in a new window] ,
Amir A. Pahlavan Open the ORCID record for Amir A. Pahlavan [Opens in a new window] ,
Luis Cueto-Felgueroso Open the ORCID record for Luis Cueto-Felgueroso [Opens in a new window]  and
Ruben Juanes Open the ORCID record for Ruben Juanes [Opens in a new window]
Bauyrzhan K. Primkulov
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Amir A. Pahlavan
Affiliation:
Department of Mechanical Engineering and Materials Science, Yale University, New Haven, CT 06520, USA
Luis Cueto-Felgueroso
Affiliation:
Department of Civil Engineering: Hydraulics, Energy and Environment, Universidad Politécnica de Madrid, 28040 Madrid, Spain
Ruben Juanes*
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: juanes@mit.edu
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Abstract

We present a theoretical study of viscous slug motion inside a microscopically rough capillary tube, where pronounced stick–slip motion can emerge at slow displacement rates. The mathematical description of this intermittent motion can be reduced to a system of ordinary differential equations, which also describe the motion of a pendulum inside a fluid-filled rotating drum. We use this analogy to show that the stick–slip motion transitions to steady sliding at high displacement rates. We characterize this crossover with a simple scaling relation and show that the crossover is accompanied by a shift in the dominant energy dissipation mechanisms within the system.

JFM classification

Interfacial Flows (free surface): Capillary flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 973 , 25 October 2023 , A2
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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Primkulov et al. Supplementary Movie

Video shows a transition from stick--slip to steady sliding with phase-field simulation of fluid-fluid displacement in a 2D channel. The crossover occurs as the capillary number increases from 1E-4 to 3E-2. Here, a dashed line represents an axis of symmetry in the 2D channel.

Download Primkulov et al. Supplementary Movie(Video)
Video 15.7 MB