A dense suspension of the cornstarch flowing on a very inclined wall finally forms some ridge-like patterns of the free surface. The onset of pattern formation is the primary target to elucidate the mechanism. In this work, based on the continuity of fluids and the force balance, we show that the flat free surface is unstable when the second normal stress difference N2 is negatively proportional to shear stress and the gravity component perpendicular to the wall is weak enough. Such instability is inevitable for the growth of a ridge-like surface profile oriented parallel to the flow direction. We use the instability criterion to predict the critical slope angle for the formation of ridge patterns. The estimated critical angle was found to be in agreement with experimental observations for a cornstarch suspension.
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February 2024
Research Article|
February 07 2024
Ridge instability in dense suspensions caused by the second normal stress difference
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Zhongqiang Xiong (熊钟强)
;
Zhongqiang Xiong (熊钟强)
(Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Validation, Writing – original draft)
1
Wenzhou Key Laboratory of Biomaterials and Engineering, Wenzhou Institute, University of Chinese Academy of Sciences
, Wenzhou 325000, China
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Peter Angerman;
Peter Angerman
(Conceptualization, Data curation, Investigation, Methodology, Visualization, Writing – original draft)
2
Complex Fluids Research Group, Department of Chemical Engineering, Swansea University
, Swansea SA1 8EN, United Kingdom
3
Basque Center for Applied Mathematics (BCAM)
, Alameda de Mazarredo 14, Bilbao 48009, Spain
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Marco Ellero
;
Marco Ellero
(Conceptualization, Funding acquisition, Project administration, Resources, Supervision, Writing – review & editing)
3
Basque Center for Applied Mathematics (BCAM)
, Alameda de Mazarredo 14, Bilbao 48009, Spain
4
IKERBASQUE, Basque Foundation for Science
, Calle de Maria Diaz de Haro 3, Bilbao 48013, Bizkaia, Spain
5
Zienkiewicz Center for Computational Engineering (ZCCE), Swansea University
, Bay Campus, Swansea SA1 8EN, United Kingdom
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Bjornar Sandnes
;
Bjornar Sandnes
(Conceptualization, Funding acquisition, Resources, Supervision, Writing – review & editing)
2
Complex Fluids Research Group, Department of Chemical Engineering, Swansea University
, Swansea SA1 8EN, United Kingdom
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Ryohei Seto (瀬戸亮平)
Ryohei Seto (瀬戸亮平)
a)
(Conceptualization, Funding acquisition, Resources, Supervision, Validation, Writing – review & editing)
1
Wenzhou Key Laboratory of Biomaterials and Engineering, Wenzhou Institute, University of Chinese Academy of Sciences
, Wenzhou 325000, China
6
Oujiang Laboratory (Zhejiang Lab for Regenerative Medicine, Vision and Brain Health)
, Wenzhou 325000, China
7
Graduate School of Information Science, University of Hyogo
, Kobe 650-0047, Japan
a)Author to whom correspondence should be addressed: seto@ucas.ac.cn
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a)Author to whom correspondence should be addressed: seto@ucas.ac.cn
Physics of Fluids 36, 024111 (2024)
Article history
Received:
November 17 2023
Accepted:
January 14 2024
Citation
Zhongqiang Xiong, Peter Angerman, Marco Ellero, Bjornar Sandnes, Ryohei Seto; Ridge instability in dense suspensions caused by the second normal stress difference. Physics of Fluids 1 February 2024; 36 (2): 024111. https://doi.org/10.1063/5.0188004
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