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Investigation of the imbibition/drainage of two immiscible fluids in capillaries with arbitrary axisymmetric cross-sections: a generalized model.

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Title: Investigation of the imbibition/drainage of two immiscible fluids in capillaries with arbitrary axisymmetric cross-sections: a generalized model.
Authors: Salama, Amgad1 (AUTHOR) amgad.salama@uregina.ca
Source: Journal of Fluid Mechanics. 9/25/2022, Vol. 947, p1-35. 35p.
Subjects: Viscosity, Capillaries, Gravitation, Drainage, Fluids, Capillary tubes, Axial flow
Abstract: In this work, we investigate the problem of imbibition/drainage of a fluid in capillaries of arbitrary axisymmetric cross-sections filled initially with another immiscible one. The model predicts the location of the meniscus and its speed along the tube length with time. The two immiscible fluids may assume any density and viscosity contrasts. In addition, the axisymmetric profile of the tube maintains a relatively small angle of tangency to warrant that the axial velocity distribution assumes, approximately, a parabolic profile. The driving forces that may be encountered in this system include the capillary force, pressure force, gravitational force and an opposing viscous force. The orientation of the capillary force can be in the direction of the flow (e.g. during imbibition) or opposite to the flow (e.g. during drainage). Likewise, the gravitational force can be in the direction of the flow or opposite to it. In this work we account for all these possibilities. A differential equation is developed that defines the location of the meniscus with time. A fourth-order-accurate Runge–Kutta scheme has been developed to provide solutions for the different scenarios associated with this system. It is shown that the developed model reduces to those appropriate for straight tubes, which builds confidence in the modelling approach. The effects of changing the tangent along the profile of the tube, which influences the calculation of the radius of curvature of the meniscus, is also considered. Unlike the cases of straight capillary tubes, in tubes with arbitrary symmetric profiles, the friction force depends on the variations of the tube profile. Examples of converging/diverging capillary tubes that follow straight and power law profiles are investigated. In addition, the case of sinusoidal profiles has also been considered. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Fluid Mechanics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 159191020
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PubTypeId: academicJournal
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  Label: Title
  Group: Ti
  Data: Investigation of the imbibition/drainage of two immiscible fluids in capillaries with arbitrary axisymmetric cross-sections: a generalized model.
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  Data: <searchLink fieldCode="AR" term="%22Salama%2C+Amgad%22">Salama, Amgad</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> amgad.salama@uregina.ca</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Fluid+Mechanics%22">Journal of Fluid Mechanics</searchLink>. 9/25/2022, Vol. 947, p1-35. 35p.
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  Data: <searchLink fieldCode="DE" term="%22Viscosity%22">Viscosity</searchLink><br /><searchLink fieldCode="DE" term="%22Capillaries%22">Capillaries</searchLink><br /><searchLink fieldCode="DE" term="%22Gravitation%22">Gravitation</searchLink><br /><searchLink fieldCode="DE" term="%22Drainage%22">Drainage</searchLink><br /><searchLink fieldCode="DE" term="%22Fluids%22">Fluids</searchLink><br /><searchLink fieldCode="DE" term="%22Capillary+tubes%22">Capillary tubes</searchLink><br /><searchLink fieldCode="DE" term="%22Axial+flow%22">Axial flow</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In this work, we investigate the problem of imbibition/drainage of a fluid in capillaries of arbitrary axisymmetric cross-sections filled initially with another immiscible one. The model predicts the location of the meniscus and its speed along the tube length with time. The two immiscible fluids may assume any density and viscosity contrasts. In addition, the axisymmetric profile of the tube maintains a relatively small angle of tangency to warrant that the axial velocity distribution assumes, approximately, a parabolic profile. The driving forces that may be encountered in this system include the capillary force, pressure force, gravitational force and an opposing viscous force. The orientation of the capillary force can be in the direction of the flow (e.g. during imbibition) or opposite to the flow (e.g. during drainage). Likewise, the gravitational force can be in the direction of the flow or opposite to it. In this work we account for all these possibilities. A differential equation is developed that defines the location of the meniscus with time. A fourth-order-accurate Runge–Kutta scheme has been developed to provide solutions for the different scenarios associated with this system. It is shown that the developed model reduces to those appropriate for straight tubes, which builds confidence in the modelling approach. The effects of changing the tangent along the profile of the tube, which influences the calculation of the radius of curvature of the meniscus, is also considered. Unlike the cases of straight capillary tubes, in tubes with arbitrary symmetric profiles, the friction force depends on the variations of the tube profile. Examples of converging/diverging capillary tubes that follow straight and power law profiles are investigated. In addition, the case of sinusoidal profiles has also been considered. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Fluid Mechanics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1017/jfm.2022.642
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 35
        StartPage: 1
    Subjects:
      – SubjectFull: Viscosity
        Type: general
      – SubjectFull: Capillaries
        Type: general
      – SubjectFull: Gravitation
        Type: general
      – SubjectFull: Drainage
        Type: general
      – SubjectFull: Fluids
        Type: general
      – SubjectFull: Capillary tubes
        Type: general
      – SubjectFull: Axial flow
        Type: general
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      – TitleFull: Investigation of the imbibition/drainage of two immiscible fluids in capillaries with arbitrary axisymmetric cross-sections: a generalized model.
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            NameFull: Salama, Amgad
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            – D: 25
              M: 09
              Text: 9/25/2022
              Type: published
              Y: 2022
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              Value: 947
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            – TitleFull: Journal of Fluid Mechanics
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