Analytical Solution of Electro-Osmotic Peristalsis of Fractional Jeffreys Fluid in a Micro-Channel

The electro-osmotic peristaltic flow of a viscoelastic fluid through a cylindrical micro-channel is studied in this paper. The fractional Jeffreys constitutive model, including the relaxation time and retardation time, is utilized to describe the viscoelasticity of the fluid. Under the assumptions o...

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Published inMicromachines (Basel) Vol. 8; no. 12; p. 341
Main Authors Guo, Xiaoyi, Qi, Haitao
Format Journal Article
LanguageEnglish
Published Switzerland MDPI AG 23.11.2017
MDPI
Subjects
Computational fluid dynamics
electro-osmotic flow
Fluid flow
fractional calculus
Jeffreys fluid
Laplace transform
Mathematical models
Maxwell fluids
Numerical analysis
peristalsis
Relaxation time
Reynolds number
Stream functions (fluids)
Viscoelastic fluids
Viscoelasticity
electro-osmotic flow
peristalsis
fractional calculus
Laplace transform
Jeffreys fluid
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Abstract The electro-osmotic peristaltic flow of a viscoelastic fluid through a cylindrical micro-channel is studied in this paper. The fractional Jeffreys constitutive model, including the relaxation time and retardation time, is utilized to describe the viscoelasticity of the fluid. Under the assumptions of long wavelength, low Reynolds number, and Debye-Hückel linearization, the analytical solutions of pressure gradient, stream function and axial velocity are explored in terms of Mittag-Leffler function by Laplace transform method. The corresponding solutions of fractional Maxwell fluid and generalized second grade fluid are also obtained as special cases. The numerical analysis of the results are depicted graphically, and the effects of electro-osmotic parameter, external electric field, fractional parameters and viscoelastic parameters on the peristaltic flow are discussed.
AbstractList The electro-osmotic peristaltic flow of a viscoelastic fluid through a cylindrical micro-channel is studied in this paper. The fractional Jeffreys constitutive model, including the relaxation time and retardation time, is utilized to describe the viscoelasticity of the fluid. Under the assumptions of long wavelength, low Reynolds number, and Debye-Hückel linearization, the analytical solutions of pressure gradient, stream function and axial velocity are explored in terms of Mittag-Leffler function by Laplace transform method. The corresponding solutions of fractional Maxwell fluid and generalized second grade fluid are also obtained as special cases. The numerical analysis of the results are depicted graphically, and the effects of electro-osmotic parameter, external electric field, fractional parameters and viscoelastic parameters on the peristaltic flow are discussed.
Author Qi, Haitao
Guo, Xiaoyi
AuthorAffiliation 2 School of Mathematics and Statistics, Shandong University, Weihai 264209, China; htqi@sdu.edu.cn
1 School of Mathematics and Statistics, Linyi University, Linyi 276000, China
AuthorAffiliation_xml – name: 2 School of Mathematics and Statistics, Shandong University, Weihai 264209, China; htqi@sdu.edu.cn
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  surname: Guo
  fullname: Guo, Xiaoyi
  email: guoxiaoyi@lyu.edu.cn
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  givenname: Haitao
  orcidid: 0000-0001-9518-249X
  surname: Qi
  fullname: Qi, Haitao
  email: htqi@sdu.edu.cn
  organization: School of Mathematics and Statistics, Shandong University, Weihai 264209, China. htqi@sdu.edu.cn
BackLink https://www.ncbi.nlm.nih.gov/pubmed/30400531$$D View this record in MEDLINE/PubMed
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Issue 12
Keywords electro-osmotic flow
peristalsis
fractional calculus
Laplace transform
Jeffreys fluid
Language English
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Snippet The electro-osmotic peristaltic flow of a viscoelastic fluid through a cylindrical micro-channel is studied in this paper. The fractional Jeffreys constitutive...
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StartPage 341
SubjectTerms Computational fluid dynamics
electro-osmotic flow
Fluid flow
fractional calculus
Jeffreys fluid
Laplace transform
Mathematical models
Maxwell fluids
Numerical analysis
peristalsis
Relaxation time
Reynolds number
Stream functions (fluids)
Viscoelastic fluids
Viscoelasticity
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Title Analytical Solution of Electro-Osmotic Peristalsis of Fractional Jeffreys Fluid in a Micro-Channel
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