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<p>In this paper, we derive an extension of the Reynolds law for quasi-Newtonian fluid flows through a thin domain with thickness <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(0&lt;\varepsilon \ll 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0</mn> <mo>&lt;</mo> <mi>ε</mi> <mo>≪</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> with viscosity obeying the Carreau law without high-rate viscosity, by applying asymptotic analysis with respect to <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\varepsilon \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ε</mi> </math></EquationSource> </InlineEquation>. This provides a framework for understanding how the non-Newtonian effects and the thickness of the domain (which is significantly smaller than the other dimensions) influence its flow behavior.</p>

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Mathematical modelling of a thin-film flow obeying Carreau’s law without high-rate viscosity

  • 期刊论文

  • 发表日期：

    2026年5月11日

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  • María Anguiano,
  • Francisco Javier Suárez-Grau

摘要

In this paper, we derive an extension of the Reynolds law for quasi-Newtonian fluid flows through a thin domain with thickness \(0<\varepsilon \ll 1\) 0 < ε ≪ 1 with viscosity obeying the Carreau law without high-rate viscosity, by applying asymptotic analysis with respect to \(\varepsilon \) ε . This provides a framework for understanding how the non-Newtonian effects and the thickness of the domain (which is significantly smaller than the other dimensions) influence its flow behavior.