The slow motion of a solid spherical particle which is immersed in a non-Newtonian nanofluid and flowing through a curved peristaltic channel is studied. The more important physical application of this type of motion is the motion of clots through blood arteries and the motion gallstones in the bile duct. The biviscosity model is applied to represent the rheological property of the non-Newtonian fluid. Also, the biviscosity model is one of the most important models that can be considers to describe rheological properties of the blood flow and the other biological fluids in the human body. Also, the flow motion in the blood vessels and other vital vessels undergo peristaltic movement. So, this type of motion has many medical and biological applications. In the mathematical treatment, due to the symmetry of the flow channel, the stress tensor components of the biviscosity model are obtained twice. Firstly, in the polar coordinates due to the curvature of the channel. Secondly, due to the spherical coordinates for the spherical motion of the particle to obtain the general form of the stream function which represents the flow motion. The peristaltic motion is studied generally without the ordinary longwave approximation and without assuming the small value of Reynolds number. This gives more generalization to the results. The most important factor in this type of motion is the drag force that effect on the spherical body (clot or stone) motion in the vessel. So, the problem is solved analytically, and the drag force is obtained numerically. Also, the heat and the volume fraction distributions are obtained. The results illustrate that the existence of the nanoparticles reduces the drag force, which contributes to increasing the sliding motion of the spherical particle and contributes on removing the blood clot and stone through the vital vessel. Some other important parameters, which effects on the motion, are considered such as the radius ratio, curvature parameter, the wave speed, the wave amplitude, and the slip parameter. The results illustrated that the increase of the fluid viscosity enhances the friction force. Meanwhile, the Brownian motion of the nanoparticles enhances the flow motion which intern enhances the slipping motion of the particle.
| Published in | Science Discovery Physics (Volume 1, Issue 1) |
| DOI | 10.11648/j.sdp.20260101.11 |
| Page(s) | 1-28 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2026. Published by Science Publishing Group |
Spherical Particle Slow Motion, Peristaltic Channel, Non-newtonian Nano-fluid, Curved Channel, Drag Force
| [1] | S. Leichtberg, T. R. Pfeffer, S. Weinbaum, Stokes Flow Past Finite Coaxial Clusters of Spheres In A Circular Cylinder, Int. J. Multiphase Flow. 3, 147-169 (1976). |
| [2] | T. C. Lee, H. J. Keh, Slow motion of a spherical particle in a spherical cavity with slip surfaces, Int. J. Engng. Sci. 69, 1–15 (2013). |
| [3] | H. J. Keh, Y. C. Chang, Creeping motion of a slip spherical particle in a circular cylindrical pore, Int. J. Multiphase Flow, 33, 726-741 (2007). |
| [4] | H. H. Sherief, M. S. Faltas, E. A. Ashmawy, M. G. Nashwan, Slow motion of a slip spherical particle along the axis of a circular cylindrical pore in a micropolar fluid, J. Molecular Liquids 200, 273–282 (2014). |
| [5] | M. Trofa, G. D’Avino, M. A. Hulsen, F. Greco, P. L. Maffettone, Numerical simulations of the dynamics of a slippery particlein Newtonian and viscoelastic fluids subjected to shear and Poiseuille flows, J. Non-Newtonian Fluid Mech., 228, 46–54 (2016). |
| [6] | M. Trofa, G. D’Avino, M. A. Hulsen, P. L. Maffettone, The effect of wall slip on the dynamics of a spherical particle in Newtonian and viscoelastic fluids subjected to shear and Poiseuille flows, J. Non-Newtonian Fluid Mech., 236, 123–131 (2016). |
| [7] | D. Tripathi, S. Bhushan, O. A. Bég, Analytical study of electro-osmosis modulated capillary peristaltic hemodynamics, J. Mech. Med. Biol., 17(3) 1-22 (2017). |
| [8] | M. K. Chaube, A. Yadav, D. Tripathi, Electroosmotically induced alterations in peristaltic microflows of power law fluids through physiological vessels, J. Brazilian Soc. Mech. Sci. Engng., 40(423) 1-9 (2018). |
| [9] | D. Tripathi, A. Yadav, O. Anwar Bég, R. Kumar, Study of microvascular non-Newtonian blood flow modulated by electroosmosis, Microvascular research 117, 28-36 (2018). |
| [10] | M. Nakamura, T. Sawada., Numerical study on the flow of a non-Newtonian fluid through an axisymmetric stenosis., J. Biomechanical, 110, 137–143 (1988). |
| [11] | Kh. S. Mekheimer, W. M. Hasona, R. E. Abo-Elkhair, A. Z. Zaher, Peristaltic blood flow with gold nanoparticles as a third grade nanofluid in catheter: Application of cancer therapy, Phys. Lett. A 382, 85–93 (2018). |
| [12] | S. Mosayebidorcheh, M. Hatami, Analytical investigation of peristaltic nanofluid flow and heat transfer in an asymmetric wavy wall channel (Part I: Straight channel), Int. J. Heat Mass Trans., 126, 790–799 (2018). |
| [13] | S. Mosayebidorcheh, M. Hatami, Analytical investigation of peristaltic nanofluid flow and heat transfer in an asymmetric wavy wall channel (Part II: Divergent channel), Int. J. Heat Mass Trans., 126, 800–808 (2018). |
| [14] | N. Ali, M. Sajid, T. Javed, Z. Abbas, Heat transfer analysis of peristaltic flow in a curved channel, Int. J. Heat Mass Trans., 53, 3319–3325 (2010). |
| [15] | T. Hayat, Maryiam Javed, Awatif A. Hendi, Peristaltic transport of viscous fluid in a curved channel with compliant walls, Int. J. Heat Mass Trans., 54, 1615–1621(2011). |
| [16] | T. Hayat, S. Hina, Awatif A. Hendi, S. Asghar, Effect of wall properties on the peristaltic flow of a third grade fluid in a curved channel with heat and mass transfer, Int. J. Heat Mass Trans., 54, 5126–5136 (2011). |
| [17] | S. A. Shehzad, F. M. Abbasi, T. Hayat, F. Alsaadi, G. Mousa, Peristalsis in a curved channel with slip condition and radial magnetic field, Int. J. Heat Mass Trans., 91, 562-569 (2015). |
| [18] | S. Hina, T. Hayat, A. Alsaedi, Heat and mass transfer effects on the peristaltic flow of Johnson–Segalman fluid in a curved channel with compliant walls, Int. J. Heat Mass Trans., 55, 3511–3521 (2012). |
| [19] | T. Hayat, S. Farooq, B. Ahmad, A. Alsaedi, Numerical simulations of Oldroyd 8-constant fluid flow and heat transfer in a curved channel, Int. J. Heat Mass Trans., 94, 500–508 (2016). |
| [20] | A. Tanveer, T. Hayat, A. Alsaedi, B. Ahmad, Mixed convective peristaltic flow of Sisko fluid in curved channel with homogeneous-heterogeneous reaction effects, J. Mol. Liq., 233, 131–138 (2017). |
| [21] | T. Hayat, S. Farooq, B. Ahmad, A. Alsaedi, Homogeneous-heterogeneous reactions and heat source/sink effects in MHD peristaltic flow of micropolar fluid with Newtonian heating in a curved channel, J. Mol. Liq., 223, 469–488(2016). |
| [22] | S. Hina, M. Mustafa, T. Hayat, N. D. Alotaibi, On peristaltic motion of pseudoplastic fluid in a curved channel with heat/mass transfer and wall properties, Appl. Math. Comp., 263, 378–391 (2015). |
| [23] | S. Hina, M. Mustafa, T. Hayat, A. Alsaedi, Peristaltic transport of Powell–Eyring fluid in a curved channel with heat/mass transfer and wall properties, Int. J. Heat Mass Trans., 101, 156–165 (2016). |
| [24] | T. Hayat, S. Farooq, A. Alsaedi, Mixed convection peristaltic motion of copper-water nanomaterial with velocity slip effects in a curved channel, Comp. Meth. Prog. Biom., 142, 117–128 (2017). |
| [25] | T. Hayat, Naseema Aslam, A. Alsaedi, M. Rafiq, Numerical study for MHD peristaltic transport of Sisko nanofluid in a curved channel, Int. J. Heat Mass Trans., 109, 1281–1288 (2017). |
| [26] | M. A. Hassan, Slow motion of a slip spherical particle through a viscoelastic Giesekus fluid in a peristaltic tube, Physica Scripta, Phys. Scr. 94 (2019) 105011 (17pp) |
| [27] | M. A. Hassan, Peristaltic Flow of Viscoelastic Giesekus Fluid through Concentric Annuli with Heat Transfer, J. Appl. Nonlinear Dyn., 10, (3), 577-603 (2021). |
| [28] | M. A. Hassan, Linear Instability of Electromagnetic Viscoelastic Nanofluid: Analytical and Numerical Study, Diff. Eq. Dyn. Sys., |
| [29] | Galal M. Moatimid, Mohamed A. Hassan, Mona A. A. Mohamed, Temporal instability of a confined nano-liquid film with the Marangoni convection effect: viscous potential theory, Microsystem Tech., |
| [30] | A. H. Shapiro, M. Y. Jaffrin, S. L. Weinberg, Peristaltic pumping with long wavelengths at low Reynolds number, J. Fluid Mech., 37, 4, 799-825 (1969). |
| [31] | T. Hayat, Nida Alvi, N. Ali, Peristaltic mechanism of a Maxwell fluid in an asymmetric channel, Non. Anal.: Real World Appl., 9, 1474 – 1490 (2008). |
| [32] | H. J. Keh, C. H. Huang, Slow motion of axisymmetric slip particles along their axes of revolution, Int. J. Engng. Sci., 42, 1621–1644 (2004). |
| [33] | M. Lorenzini, I. Daprà, G. Scarpi, Heat transfer for a Giesekus fluid in a rotating concentric annulus, App. Ther. Engng., 122, 118–125 (2017). |
| [34] | L. Dintenfass, Viscosity and Clotting of Blood in Venous Thrombosis and Coronary Occlusions, Circulation Research, V. XIV, No. 1, 1-16 (1964). |
| [35] | G. Romero, M. LuisaMartinez, J. Maroto, J. Felez, Blood Clot Simulation Model by Using the Bond-Graph Technique, Sci. World J., V. 2013, Article ID 519047, 10 pages |
| [36] | S. Nadeem, S. Ijaz, Single wall carbon nanotube (SWCNT) examination on blood flow through a multiple stenosed artery with variable nanofluid viscosity, AIP Adv., 5, 107217 (2015). |
| [37] |
Search for " linear-expansion-coefficients". Web site:
https://www.engineeringtoolbox.com (accessed 31-Mar-2019). |
| [38] | D. Coglitore, Nanoparticle dynamics in simple fluids, Ph.D., Thesis, Univ. Liverpool, 2016. |
| [39] | Wikipedia, adverse pressure pumping, accessed November, 2018, from: |
| [40] | A. N. Ilinskaya and M. A. Dobrovolskaia, Nanoparticles and the blood coagulation system. Part II: safety concerns, Nanomed. (Lond)., 8(6): 969–981 (2013). |
APA Style
Hassan, M. A. (2026). Slipping of a Spherical Particle Through Peristaltic Curved Tube Filled with Non-newtonian Nanofluid. Science Discovery Physics, 1(1), 1-28. https://doi.org/10.11648/j.sdp.20260101.11
ACS Style
Hassan, M. A. Slipping of a Spherical Particle Through Peristaltic Curved Tube Filled with Non-newtonian Nanofluid. Sci. Discov. Phys. 2026, 1(1), 1-28. doi: 10.11648/j.sdp.20260101.11
AMA Style
Hassan MA. Slipping of a Spherical Particle Through Peristaltic Curved Tube Filled with Non-newtonian Nanofluid. Sci Discov Phys. 2026;1(1):1-28. doi: 10.11648/j.sdp.20260101.11
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.sdp.20260101.11,
author = {Mohamed Ahmed Hassan},
title = {Slipping of a Spherical Particle Through Peristaltic Curved Tube Filled with Non-newtonian Nanofluid},
journal = {Science Discovery Physics},
volume = {1},
number = {1},
pages = {1-28},
doi = {10.11648/j.sdp.20260101.11},
url = {https://doi.org/10.11648/j.sdp.20260101.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sdp.20260101.11},
abstract = {The slow motion of a solid spherical particle which is immersed in a non-Newtonian nanofluid and flowing through a curved peristaltic channel is studied. The more important physical application of this type of motion is the motion of clots through blood arteries and the motion gallstones in the bile duct. The biviscosity model is applied to represent the rheological property of the non-Newtonian fluid. Also, the biviscosity model is one of the most important models that can be considers to describe rheological properties of the blood flow and the other biological fluids in the human body. Also, the flow motion in the blood vessels and other vital vessels undergo peristaltic movement. So, this type of motion has many medical and biological applications. In the mathematical treatment, due to the symmetry of the flow channel, the stress tensor components of the biviscosity model are obtained twice. Firstly, in the polar coordinates due to the curvature of the channel. Secondly, due to the spherical coordinates for the spherical motion of the particle to obtain the general form of the stream function which represents the flow motion. The peristaltic motion is studied generally without the ordinary longwave approximation and without assuming the small value of Reynolds number. This gives more generalization to the results. The most important factor in this type of motion is the drag force that effect on the spherical body (clot or stone) motion in the vessel. So, the problem is solved analytically, and the drag force is obtained numerically. Also, the heat and the volume fraction distributions are obtained. The results illustrate that the existence of the nanoparticles reduces the drag force, which contributes to increasing the sliding motion of the spherical particle and contributes on removing the blood clot and stone through the vital vessel. Some other important parameters, which effects on the motion, are considered such as the radius ratio, curvature parameter, the wave speed, the wave amplitude, and the slip parameter. The results illustrated that the increase of the fluid viscosity enhances the friction force. Meanwhile, the Brownian motion of the nanoparticles enhances the flow motion which intern enhances the slipping motion of the particle.},
year = {2026}
}
TY - JOUR T1 - Slipping of a Spherical Particle Through Peristaltic Curved Tube Filled with Non-newtonian Nanofluid AU - Mohamed Ahmed Hassan Y1 - 2026/02/09 PY - 2026 N1 - https://doi.org/10.11648/j.sdp.20260101.11 DO - 10.11648/j.sdp.20260101.11 T2 - Science Discovery Physics JF - Science Discovery Physics JO - Science Discovery Physics SP - 1 EP - 28 PB - Science Publishing Group UR - https://doi.org/10.11648/j.sdp.20260101.11 AB - The slow motion of a solid spherical particle which is immersed in a non-Newtonian nanofluid and flowing through a curved peristaltic channel is studied. The more important physical application of this type of motion is the motion of clots through blood arteries and the motion gallstones in the bile duct. The biviscosity model is applied to represent the rheological property of the non-Newtonian fluid. Also, the biviscosity model is one of the most important models that can be considers to describe rheological properties of the blood flow and the other biological fluids in the human body. Also, the flow motion in the blood vessels and other vital vessels undergo peristaltic movement. So, this type of motion has many medical and biological applications. In the mathematical treatment, due to the symmetry of the flow channel, the stress tensor components of the biviscosity model are obtained twice. Firstly, in the polar coordinates due to the curvature of the channel. Secondly, due to the spherical coordinates for the spherical motion of the particle to obtain the general form of the stream function which represents the flow motion. The peristaltic motion is studied generally without the ordinary longwave approximation and without assuming the small value of Reynolds number. This gives more generalization to the results. The most important factor in this type of motion is the drag force that effect on the spherical body (clot or stone) motion in the vessel. So, the problem is solved analytically, and the drag force is obtained numerically. Also, the heat and the volume fraction distributions are obtained. The results illustrate that the existence of the nanoparticles reduces the drag force, which contributes to increasing the sliding motion of the spherical particle and contributes on removing the blood clot and stone through the vital vessel. Some other important parameters, which effects on the motion, are considered such as the radius ratio, curvature parameter, the wave speed, the wave amplitude, and the slip parameter. The results illustrated that the increase of the fluid viscosity enhances the friction force. Meanwhile, the Brownian motion of the nanoparticles enhances the flow motion which intern enhances the slipping motion of the particle. VL - 1 IS - 1 ER -
Faculty of Education Mathematics Department, Ain Shams University, Cairo, Egypt
Information