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<p>The present research explores the uniform flow of an axisymmetric, steady Stokesian flow past a spherical shell containing couple stress liquid core. The Newtonian fluid is able to flow within the permeable boundary, but cannot pass through the permeable porous boundary of the spherical shell. It is presumed that the couple stress liquid does not mix with the Newtonian fluid. The Brinkman equation is taken as the governing equation of motion in permeable porous regions. The drag force experienced by the shell is evaluated. Evaluations are done on the stream function expressions for the permeable, inner, and outer regions. The streamlines are displayed for various values of couple stress parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\lambda \)</EquationSource> </InlineEquation> and ratio of viscosities <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\Phi \)</EquationSource> </InlineEquation>. The analysis indicates that couple stress fluid shows circulation of various intensities corresponding to variations in the couple stress parameter and viscosity ratio; however, the flow pattern of Newtonian fluid remains unaltered. Variation of the drag coefficient <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(D_n\)</EquationSource> </InlineEquation> with respect to permeability parameter <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> </InlineEquation>, couple stress parameter <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\lambda \)</EquationSource> </InlineEquation>, ratio of viscosities <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\Phi \)</EquationSource> </InlineEquation> are graphically examined for various values of flow parameters and discussed.</p>

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Stokes Flow of Newtonian Fluid Past a Composite Sphere Filled with Couple Stress Liquid Core

  • 期刊论文

  • 发表日期：

    2026年5月25日

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  • Satish Kumar,
  • Satya Deo,
  • Pankaj Kumar Maurya

摘要

The present research explores the uniform flow of an axisymmetric, steady Stokesian flow past a spherical shell containing couple stress liquid core. The Newtonian fluid is able to flow within the permeable boundary, but cannot pass through the permeable porous boundary of the spherical shell. It is presumed that the couple stress liquid does not mix with the Newtonian fluid. The Brinkman equation is taken as the governing equation of motion in permeable porous regions. The drag force experienced by the shell is evaluated. Evaluations are done on the stream function expressions for the permeable, inner, and outer regions. The streamlines are displayed for various values of couple stress parameter \(\lambda \) and ratio of viscosities \(\Phi \) . The analysis indicates that couple stress fluid shows circulation of various intensities corresponding to variations in the couple stress parameter and viscosity ratio; however, the flow pattern of Newtonian fluid remains unaltered. Variation of the drag coefficient \(D_n\) with respect to permeability parameter \(\alpha \) , couple stress parameter \(\lambda \) , ratio of viscosities \(\Phi \) are graphically examined for various values of flow parameters and discussed.