Linear Stability of a Viscoelastic Liquid Film on an Oscillating Plane.
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| Title: | Linear Stability of a Viscoelastic Liquid Film on an Oscillating Plane. |
|---|---|
| Authors: | Zhang, Jing1 (AUTHOR), Liu, Quansheng1 (AUTHOR), Zhang, Ruigang1 (AUTHOR), Ding, Zhaodong1 (AUTHOR) dingzhd@imu.edu.cn |
| Source: | Nanomaterials (2079-4991). Apr2025, Vol. 15 Issue 8, p610. 17p. |
| Subjects: | Viscoelastic materials, Stream function, Boundary value problems, Analytical solutions, Bandwidths, Free convection, Liquid films |
| Abstract: | This paper investigates the linear stability of the liquid film of Oldroyd-B fluid on an oscillating plate. The time-dependent Orr–Sommerfeld boundary-value problem is formulated through the assumption of a normal modal solution and the introduction of the stream function, which is further transformed into the Floquet system. A long-wavelength expansion analysis is performed to derive the analytical solution of the Orr–Sommerfeld equation. The results indicate that long-wave instability occurs only within specific bandwidths related to the Ohnesorge number ( O h ). Fixing the elasticity parameter ( E l ) and increasing the relaxation-to-delay time ratio ( λ ˜ ) from 2 to 4 or fixing ( λ ˜ ) and increasing ( E l ) from 0.001 to 0.01 decreases the number of unstable bandwidths while enhancing the intensity of unstable modes. Increasing the surface-tension-related parameter ( ζ ∗ ) from 0 to 100 suppresses the wave growth rate, stabilizing the system. Additionally, increasing ( λ ˜ ) from 2 to 4 reduces the maximum values of the coupling of viscoelastic, gravitational, and surface-tension forces, as well as the maximum value of the Floquet exponent, further stabilizing the system. These findings provide supplements to the theoretical research on the stability of viscoelastic fluids and also offer a scientific basis for engineering applications in multiple fields. [ABSTRACT FROM AUTHOR] |
| Copyright of Nanomaterials (2079-4991) is the property of MDPI 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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| Header | DbId: egs DbLabel: Engineering Source An: 184794841 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Linear Stability of a Viscoelastic Liquid Film on an Oscillating Plane. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Zhang%2C+Jing%22">Zhang, Jing</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Liu%2C+Quansheng%22">Liu, Quansheng</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zhang%2C+Ruigang%22">Zhang, Ruigang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Ding%2C+Zhaodong%22">Ding, Zhaodong</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> dingzhd@imu.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Nanomaterials+%282079-4991%29%22">Nanomaterials (2079-4991)</searchLink>. Apr2025, Vol. 15 Issue 8, p610. 17p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Viscoelastic+materials%22">Viscoelastic materials</searchLink><br /><searchLink fieldCode="DE" term="%22Stream+function%22">Stream function</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Analytical+solutions%22">Analytical solutions</searchLink><br /><searchLink fieldCode="DE" term="%22Bandwidths%22">Bandwidths</searchLink><br /><searchLink fieldCode="DE" term="%22Free+convection%22">Free convection</searchLink><br /><searchLink fieldCode="DE" term="%22Liquid+films%22">Liquid films</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper investigates the linear stability of the liquid film of Oldroyd-B fluid on an oscillating plate. The time-dependent Orr–Sommerfeld boundary-value problem is formulated through the assumption of a normal modal solution and the introduction of the stream function, which is further transformed into the Floquet system. A long-wavelength expansion analysis is performed to derive the analytical solution of the Orr–Sommerfeld equation. The results indicate that long-wave instability occurs only within specific bandwidths related to the Ohnesorge number ( O h ). Fixing the elasticity parameter ( E l ) and increasing the relaxation-to-delay time ratio ( λ ˜ ) from 2 to 4 or fixing ( λ ˜ ) and increasing ( E l ) from 0.001 to 0.01 decreases the number of unstable bandwidths while enhancing the intensity of unstable modes. Increasing the surface-tension-related parameter ( ζ ∗ ) from 0 to 100 suppresses the wave growth rate, stabilizing the system. Additionally, increasing ( λ ˜ ) from 2 to 4 reduces the maximum values of the coupling of viscoelastic, gravitational, and surface-tension forces, as well as the maximum value of the Floquet exponent, further stabilizing the system. These findings provide supplements to the theoretical research on the stability of viscoelastic fluids and also offer a scientific basis for engineering applications in multiple fields. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Nanomaterials (2079-4991) is the property of MDPI 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: BibEntity: Identifiers: – Type: doi Value: 10.3390/nano15080610 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 17 StartPage: 610 Subjects: – SubjectFull: Viscoelastic materials Type: general – SubjectFull: Stream function Type: general – SubjectFull: Boundary value problems Type: general – SubjectFull: Analytical solutions Type: general – SubjectFull: Bandwidths Type: general – SubjectFull: Free convection Type: general – SubjectFull: Liquid films Type: general Titles: – TitleFull: Linear Stability of a Viscoelastic Liquid Film on an Oscillating Plane. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Zhang, Jing – PersonEntity: Name: NameFull: Liu, Quansheng – PersonEntity: Name: NameFull: Zhang, Ruigang – PersonEntity: Name: NameFull: Ding, Zhaodong IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 04 Text: Apr2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 20794991 Numbering: – Type: volume Value: 15 – Type: issue Value: 8 Titles: – TitleFull: Nanomaterials (2079-4991) Type: main |
| ResultId | 1 |
