Interaction Between Two Rigid Hydrophobic Spheres Oscillating in an Infinite Brinkman–Stokes Fluid
This study investigates the dynamics of two oscillating rigid spheres moving through an infinite porous medium saturated with Stokes fluid flow, addressing the problem of how fluid properties, permeability, frequency, and slip length influence the system. The objective is to model the interactions b...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/2/218 |
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| author | Azza M. Algatheem Hala H. Taha Shreen El-Sapa |
| author_facet | Azza M. Algatheem Hala H. Taha Shreen El-Sapa |
| author_sort | Azza M. Algatheem |
| collection | DOAJ |
| description | This study investigates the dynamics of two oscillating rigid spheres moving through an infinite porous medium saturated with Stokes fluid flow, addressing the problem of how fluid properties, permeability, frequency, and slip length influence the system. The objective is to model the interactions between the spheres, which differ in size and velocity as they move along the axis connecting their centers while applying slip boundary conditions to their surfaces. We derive the governing field equations using a semi-analytical method and solve the resulting system of equations numerically through a collocation technique. Our novel quantitative results include insights into the drag force coefficients for both in-phase and out-of-phase oscillations of each hydrophobic sphere, considering parameters such as diameter ratio, permeability, frequency, velocity ratios, slip lengths, and the distances between the spheres. Notably, when the spheres are sufficiently far apart, the normalized drag force coefficients behave as if each sphere is moving independently. Additionally, we present streamlines that illustrate the interactions between the spheres across a range of parameters, highlighting the novelty of our findings. A purely viscous medium and no-slip conditions are used to validate the numerical approach and results. |
| format | Article |
| id | doaj-art-05e921ddcc4245a59bc3a0b6bf195a4f |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-05e921ddcc4245a59bc3a0b6bf195a4f2025-01-24T13:39:47ZengMDPI AGMathematics2227-73902025-01-0113221810.3390/math13020218Interaction Between Two Rigid Hydrophobic Spheres Oscillating in an Infinite Brinkman–Stokes FluidAzza M. Algatheem0Hala H. Taha1Shreen El-Sapa2Department of Mathematics, Faculty of Science, University of Bisha, Bisha 61922, Saudi ArabiaDepartment of Mathematical Sciences, College of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaDepartment of Mathematics and Computer Science, Faculty of Science, Damanhour University, Damanhour 22511, EgyptThis study investigates the dynamics of two oscillating rigid spheres moving through an infinite porous medium saturated with Stokes fluid flow, addressing the problem of how fluid properties, permeability, frequency, and slip length influence the system. The objective is to model the interactions between the spheres, which differ in size and velocity as they move along the axis connecting their centers while applying slip boundary conditions to their surfaces. We derive the governing field equations using a semi-analytical method and solve the resulting system of equations numerically through a collocation technique. Our novel quantitative results include insights into the drag force coefficients for both in-phase and out-of-phase oscillations of each hydrophobic sphere, considering parameters such as diameter ratio, permeability, frequency, velocity ratios, slip lengths, and the distances between the spheres. Notably, when the spheres are sufficiently far apart, the normalized drag force coefficients behave as if each sphere is moving independently. Additionally, we present streamlines that illustrate the interactions between the spheres across a range of parameters, highlighting the novelty of our findings. A purely viscous medium and no-slip conditions are used to validate the numerical approach and results.https://www.mdpi.com/2227-7390/13/2/218interactionfluctuationsdrag forcehydrophobiccollocation methodpermeability |
| spellingShingle | Azza M. Algatheem Hala H. Taha Shreen El-Sapa Interaction Between Two Rigid Hydrophobic Spheres Oscillating in an Infinite Brinkman–Stokes Fluid Mathematics interaction fluctuations drag force hydrophobic collocation method permeability |
| title | Interaction Between Two Rigid Hydrophobic Spheres Oscillating in an Infinite Brinkman–Stokes Fluid |
| title_full | Interaction Between Two Rigid Hydrophobic Spheres Oscillating in an Infinite Brinkman–Stokes Fluid |
| title_fullStr | Interaction Between Two Rigid Hydrophobic Spheres Oscillating in an Infinite Brinkman–Stokes Fluid |
| title_full_unstemmed | Interaction Between Two Rigid Hydrophobic Spheres Oscillating in an Infinite Brinkman–Stokes Fluid |
| title_short | Interaction Between Two Rigid Hydrophobic Spheres Oscillating in an Infinite Brinkman–Stokes Fluid |
| title_sort | interaction between two rigid hydrophobic spheres oscillating in an infinite brinkman stokes fluid |
| topic | interaction fluctuations drag force hydrophobic collocation method permeability |
| url | https://www.mdpi.com/2227-7390/13/2/218 |
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