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<p>The newly formulated non-Newtonian rivulet flows streaming down an inclined planar surface, with additional periodic perturbations arising from the application of the 2nd Stokes problem to the investigation of rivulet dynamics, are demonstrated in the current research. Hereby, the 2nd Stokes problem assumes that the surface, with a thin shared layer of the fluid on it, oscillates in a harmonic manner along the <i>x</i>-axis of the rivulet flow, which coincides with the main flow direction streaming down the underlying surface. We obtain the exact extension of the rivulet flow family, clarifying the structure of the pressure field, which fully absorbs the arising perturbation. The profile of the velocity field is assumed to be Gaussian-type with a non-zero level of plasticity. Hence, the absolutely non-Newtonian case of the viscoplastic flow solution, which satisfies the motion and continuity equations, is considered (with particular cases of exact solutions for pressure). The perturbed governing equations of motion for rivulet flows then result in the Riccati-type ordinary differential equation (ODE), describing the dynamics of the coordinate <i>x</i>(<i>t</i>). The approximated schematic dynamics are presented in graphical plots.</p>

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Non-Newtonian rivulet flows on an inclined planar surface applying the 2nd Stokes problem

  • 期刊论文

  • 发表日期：

    2026年1月2日

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  • S. V. Ershkov,
  • E. S. Baranovskii,
  • A. V. Yudin

摘要

The newly formulated non-Newtonian rivulet flows streaming down an inclined planar surface, with additional periodic perturbations arising from the application of the 2nd Stokes problem to the investigation of rivulet dynamics, are demonstrated in the current research. Hereby, the 2nd Stokes problem assumes that the surface, with a thin shared layer of the fluid on it, oscillates in a harmonic manner along the x-axis of the rivulet flow, which coincides with the main flow direction streaming down the underlying surface. We obtain the exact extension of the rivulet flow family, clarifying the structure of the pressure field, which fully absorbs the arising perturbation. The profile of the velocity field is assumed to be Gaussian-type with a non-zero level of plasticity. Hence, the absolutely non-Newtonian case of the viscoplastic flow solution, which satisfies the motion and continuity equations, is considered (with particular cases of exact solutions for pressure). The perturbed governing equations of motion for rivulet flows then result in the Riccati-type ordinary differential equation (ODE), describing the dynamics of the coordinate x(t). The approximated schematic dynamics are presented in graphical plots.