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<p>In this paper, we derive a new effective interface condition governing the transition between porous and free flow regions of a fluid domain via asymptotic analysis. The proposed non-standard condition represents a Darcy-type law acting across the imaginary interface, asserting that the trace of the free-flow velocity is proportional to the difference in stresses on both sides of the interface. Higher-order asymptotics reveals that the leading-order approximation corresponds to a no-slip condition, the first-order to a non-penetration condition with tangential slip, whereas the second-order approximation acknowledges the leaking across the interface. This hierarchical behavior is particularly relevant in modeling blood flow in the arteries, where the arterial wall behaves as a porous medium, allowing slow blood seepage relative to the main flow.</p>

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A New Light on the Interface Condition Between the Flow in a Porous Medium and the Free Flow

  • 期刊论文

  • 发表日期：

    2026年5月14日

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  • Eduard Marušić-Paloka,
  • Igor Pažanin

摘要

In this paper, we derive a new effective interface condition governing the transition between porous and free flow regions of a fluid domain via asymptotic analysis. The proposed non-standard condition represents a Darcy-type law acting across the imaginary interface, asserting that the trace of the free-flow velocity is proportional to the difference in stresses on both sides of the interface. Higher-order asymptotics reveals that the leading-order approximation corresponds to a no-slip condition, the first-order to a non-penetration condition with tangential slip, whereas the second-order approximation acknowledges the leaking across the interface. This hierarchical behavior is particularly relevant in modeling blood flow in the arteries, where the arterial wall behaves as a porous medium, allowing slow blood seepage relative to the main flow.