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Capillarity 2021, 4(2): 31-44 https://doi.org/10.46690/capi.2021.02.02
Original Article | Open Access | Issue | Published: 03 June 2021

Investigation of the dynamics of immiscible displacement of a ganglion in capillaries

Show Author's Information Amgad Salama1( ),  Jianchao Cai2,  Jisheng Kou3,  Shuyu Sun4,  Mohamed F. El-Amin5,  Yi Wang6
Process System Engineering, Faculty of Engineering and Applied Science, University of Regina, SK S4S 0A2, Canada
State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, P. R. China
School of Civil Engineering, Shaoxing University, Shaoxing 312000, P. R. China
Computational Transport Phenomena Laboratory, Physical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia
College of Engineering, Effat University, Jeddah 21478, Saudi Arabia
National Engineering Laboratory for Pipeline Safety, China University of Petroleum, Beijing 102249, P. R. China
Keywords:
Imbibition, capillarity, drainage, ganglion
Cite this article:
Salama A, Cai J, Kou J, et al. Investigation of the dynamics of immiscible displacement of a ganglion in capillaries. Capillarity, 2021, 4(2): 31-44. https://doi.org/10.46690/capi.2021.02.02
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Abstract Full text About this article

In this work the problem of displacing a ganglion of a fluid by another immiscible one in capillaries is investigated. A modeling approach is developed to predict the location of the ganglion with time. The model describes two patterns; namely, when the ganglion totally exists inside the tube, and when the advancing interface of the ganglion has broken through the exit of the tube. The model is valid for the case in which the ganglion is wetting as well as when it is nonwetting to the wall of the tube. It also considers the situation in which both the advancing and the receding interfaces assume, generally, different contact angles. For the special case when the displacement process is quasistatic, both the receding and the advancing contact angles may be considered the same. Under these conditions, interfacial tension force plays no role and the ganglion moves as a plug inside the tube with a constant velocity. When the viscosity ratio between the invading fluid and the ganglion is one (i.e., both phases are having the same viscosity) the motion reduces to the Hagen-Poiseuille flow in pipes. Once the advancing interface breaks through the exit of the tube, interfacial tension starts to take part in the displacement process and the ganglion starts to accelerate or decelerate according to the viscosity ratio. When the ganglion is nonwetting, interfacial tension becomes in the direction of the flow and is opposite to the flow otherwise. The model accounts for external forces such as pressure and gravity in addition to capillarity. A computational fluid dynamics analysis of this system is conducted for both types of wettability scenarios and shows very good match with the results of the developed model during both the two modes of flow patterns. This builds confidence in the developed modeling approach. Other cases have also been explored to highlight the effects of other scenarios.


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About this article

Investigation of the dynamics of immiscible displacement of a ganglion in capillaries

Show Author's information Amgad Salama1( ), Jianchao Cai2, Jisheng Kou3, Shuyu Sun4, Mohamed F. El-Amin5, Yi Wang6
Process System Engineering, Faculty of Engineering and Applied Science, University of Regina, SK S4S 0A2, Canada
State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, P. R. China
School of Civil Engineering, Shaoxing University, Shaoxing 312000, P. R. China
Computational Transport Phenomena Laboratory, Physical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia
College of Engineering, Effat University, Jeddah 21478, Saudi Arabia
National Engineering Laboratory for Pipeline Safety, China University of Petroleum, Beijing 102249, P. R. China

Abstract

In this work the problem of displacing a ganglion of a fluid by another immiscible one in capillaries is investigated. A modeling approach is developed to predict the location of the ganglion with time. The model describes two patterns; namely, when the ganglion totally exists inside the tube, and when the advancing interface of the ganglion has broken through the exit of the tube. The model is valid for the case in which the ganglion is wetting as well as when it is nonwetting to the wall of the tube. It also considers the situation in which both the advancing and the receding interfaces assume, generally, different contact angles. For the special case when the displacement process is quasistatic, both the receding and the advancing contact angles may be considered the same. Under these conditions, interfacial tension force plays no role and the ganglion moves as a plug inside the tube with a constant velocity. When the viscosity ratio between the invading fluid and the ganglion is one (i.e., both phases are having the same viscosity) the motion reduces to the Hagen-Poiseuille flow in pipes. Once the advancing interface breaks through the exit of the tube, interfacial tension starts to take part in the displacement process and the ganglion starts to accelerate or decelerate according to the viscosity ratio. When the ganglion is nonwetting, interfacial tension becomes in the direction of the flow and is opposite to the flow otherwise. The model accounts for external forces such as pressure and gravity in addition to capillarity. A computational fluid dynamics analysis of this system is conducted for both types of wettability scenarios and shows very good match with the results of the developed model during both the two modes of flow patterns. This builds confidence in the developed modeling approach. Other cases have also been explored to highlight the effects of other scenarios.

Keywords: Imbibition, capillarity, drainage, ganglion

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Received: 10 May 2021
Revised: 30 May 2021
Accepted: 01 June 2021
Published: 03 June 2021
Issue date: June 2021

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