Oscillatory interactions of two spheres in an unbounded couple stress fluid
Abstract This study investigates the rectilinear oscillations of two coaxially aligned spherical particles in an unbounded couple stress fluid at low Reynolds numbers, addressing a fundamental problem in microfluidics and biomechanics where microstructure effects dominate. The importance lies in app...
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Nature Portfolio
2025-07-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-025-11707-2 |
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| author | Shreen El-Sapa Azza M. Algatheem |
| author_facet | Shreen El-Sapa Azza M. Algatheem |
| author_sort | Shreen El-Sapa |
| collection | DOAJ |
| description | Abstract This study investigates the rectilinear oscillations of two coaxially aligned spherical particles in an unbounded couple stress fluid at low Reynolds numbers, addressing a fundamental problem in microfluidics and biomechanics where microstructure effects dominate. The importance lies in applications such as drug delivery and material processing, where understanding particle-fluid interactions is critical. The unsteady Stokes equations were solved using a superposition of fundamental solutions in spherical coordinates, centered on each particle, with no-slip boundary conditions enforced via a collocation method. Key results include the quantification of in-phase and out-of-phase drag force coefficients, revealing that increasing the couple stress parameter ( $$\bar{\eta }$$ ) enhances drag forces by up to 50% for $$\bar{\eta } = 0.9$$ compared to Newtonian cases ( $$\bar{\eta } = 0$$ ). Numerical simulations demonstrated robust convergence across dimensionless parameters (e.g., separation distance $$\delta$$ , frequency $$\alpha$$ ), with tabulated data showing agreement within % of established solutions for steady-state and single-sphere oscillations. Novelty arises from extending prior work on viscous fluids to couple stress fluids, uncovering how microstructural effects amplify drag and alter oscillation dynamics. For instance, at $$\alpha = 60$$ , drag forces increased by 30% for closely spaced spheres ( $$\delta = 1.05$$ ), highlighting the interplay between frequency and microstructure. This work advances predictive models for complex fluids and provides design insights for microfluidic systems. |
| format | Article |
| id | doaj-art-5d6b4968d57d4b1088fda28d5c99c5a0 |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Nature Portfolio |
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| series | Scientific Reports |
| spelling | doaj-art-5d6b4968d57d4b1088fda28d5c99c5a02025-08-20T03:42:35ZengNature PortfolioScientific Reports2045-23222025-07-0115112010.1038/s41598-025-11707-2Oscillatory interactions of two spheres in an unbounded couple stress fluidShreen El-Sapa0Azza M. Algatheem1Department of Mathematical Sciences, College of Sciences, Princess Nourah bint Abdulrahman UniversityDepartment of Mathematics, Faculty of Science, University of BishaAbstract This study investigates the rectilinear oscillations of two coaxially aligned spherical particles in an unbounded couple stress fluid at low Reynolds numbers, addressing a fundamental problem in microfluidics and biomechanics where microstructure effects dominate. The importance lies in applications such as drug delivery and material processing, where understanding particle-fluid interactions is critical. The unsteady Stokes equations were solved using a superposition of fundamental solutions in spherical coordinates, centered on each particle, with no-slip boundary conditions enforced via a collocation method. Key results include the quantification of in-phase and out-of-phase drag force coefficients, revealing that increasing the couple stress parameter ( $$\bar{\eta }$$ ) enhances drag forces by up to 50% for $$\bar{\eta } = 0.9$$ compared to Newtonian cases ( $$\bar{\eta } = 0$$ ). Numerical simulations demonstrated robust convergence across dimensionless parameters (e.g., separation distance $$\delta$$ , frequency $$\alpha$$ ), with tabulated data showing agreement within % of established solutions for steady-state and single-sphere oscillations. Novelty arises from extending prior work on viscous fluids to couple stress fluids, uncovering how microstructural effects amplify drag and alter oscillation dynamics. For instance, at $$\alpha = 60$$ , drag forces increased by 30% for closely spaced spheres ( $$\delta = 1.05$$ ), highlighting the interplay between frequency and microstructure. This work advances predictive models for complex fluids and provides design insights for microfluidic systems.https://doi.org/10.1038/s41598-025-11707-2InteractionAxisymmetricFrequencyCouple stress theoryNumerical methodTransient |
| spellingShingle | Shreen El-Sapa Azza M. Algatheem Oscillatory interactions of two spheres in an unbounded couple stress fluid Scientific Reports Interaction Axisymmetric Frequency Couple stress theory Numerical method Transient |
| title | Oscillatory interactions of two spheres in an unbounded couple stress fluid |
| title_full | Oscillatory interactions of two spheres in an unbounded couple stress fluid |
| title_fullStr | Oscillatory interactions of two spheres in an unbounded couple stress fluid |
| title_full_unstemmed | Oscillatory interactions of two spheres in an unbounded couple stress fluid |
| title_short | Oscillatory interactions of two spheres in an unbounded couple stress fluid |
| title_sort | oscillatory interactions of two spheres in an unbounded couple stress fluid |
| topic | Interaction Axisymmetric Frequency Couple stress theory Numerical method Transient |
| url | https://doi.org/10.1038/s41598-025-11707-2 |
| work_keys_str_mv | AT shreenelsapa oscillatoryinteractionsoftwospheresinanunboundedcouplestressfluid AT azzamalgatheem oscillatoryinteractionsoftwospheresinanunboundedcouplestressfluid |