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<p>In this paper we investigate the stress concentration problem between two closely spaced general convex rigid particles immersed in an incompressible Stokes flow. The main novelty of this paper is the optimal and explicit characterization of the singular behavior of the stress in the narrow region between two spherical particles in two and three dimensions. For the general case of <i>m</i>-convex inclusions, where <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="526_2025_2955_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="47" /> </InlineMediaObject> <EquationSource Format="TEX">\(m\ge 3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>m</mi> <mo>≥</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>, we also obtain the corresponding asymptotic expansion in two dimensions and a pointwise upper bound of the gradient in three dimensions. Our results indicate that as the value of <i>m</i> increases, the degree of stress concentration decreases. Additionally, we derive the second order partial derivative estimates for all <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="526_2025_2955_Article_IEq2.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="47" /> </InlineMediaObject> <EquationSource Format="TEX">\(m\ge 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>m</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Characterization of the stress concentration between two adjacent rigid particles in stokes flow

  • 期刊论文

  • 发表日期：

    2025年3月13日

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  • Haigang Li,
  • Junhua Zhang,
  • Peihao Zhang

摘要

In this paper we investigate the stress concentration problem between two closely spaced general convex rigid particles immersed in an incompressible Stokes flow. The main novelty of this paper is the optimal and explicit characterization of the singular behavior of the stress in the narrow region between two spherical particles in two and three dimensions. For the general case of m-convex inclusions, where \(m\ge 3\) m ≥ 3 , we also obtain the corresponding asymptotic expansion in two dimensions and a pointwise upper bound of the gradient in three dimensions. Our results indicate that as the value of m increases, the degree of stress concentration decreases. Additionally, we derive the second order partial derivative estimates for all \(m\ge 2\) m ≥ 2 .