Read More.

Call for Paper - December – 2023 Edition   

(SJIF Impact Factor: 5.966) (IJIFACTOR 3.8, RANKING: A+) (PIF: 3.460)

IJATCA solicits original research papers for the December – 2023 Edition.
Last date of manuscript submission is December 30, 2023.


Cell Model of Viscous Flow Past a Semipermeable Cylinder

Volume: 1 Issue: 1
Year of Publication: 2019
Authors: M. Krishna Prasad, Tina Bucha


Stokes steady incompressible viscous fluid flow through a partially permeable cylinder is analytically studied using cell model technique. Considered flow is divided into two regions, outer viscous fluid region and inner semipermeable region which are governed by Stokes and Darcy\"s law respectively. Boundary conditions for the fluid porous interface are continuity of normal component of velocity, vanishing of tangential component of velocity and continuity of pressure accompanying the boundary condition for cell surface. Exact solution and an expression for drag exerted on the cylinder is calculated using stream function. Variation of Kozeny constant against fractional void volume is studied numerically. As special case analytical and numerical results agrees with well known existing results.


  1. Brown, G. R. (1975). Doctoral dissertation, The institute of paper chemistry (1975).

  2. Brinkman, H. C. (1947). A calculation of viscous force exerted by flowing fluid on dense swarm of particles. Applied Science Research, A (1), 27-34.

  3. Carman, P. C. (1956). Flow of Gases through Porous media, Academic Press Inc., New York, (1956).

  4. Darcy, H. P. G. (1910). Les fontaines publiques de la ville de dijon. Proceedings of Royal Society of London Ser, 83, 357-369.

  5. Datta, S., & Shukla, M. (2003). Drag on flow past a cylinder with slip. Bulletin of the Calcutta Mathematical Society. 95(1), 63-72.

  6. Dassios, G., & Vafeas, P. (2004). The 3D Happel model for complete isotropic Stokes flow. Int. J. Math. M. Sci. ,46, 2429-2441.

  7. Deo, S., Filippov, A., Tiwari, A., Vasin, S., & Starov, V. (2011). Hydrodynamic permeability of aggregates of porous particles with an impermeable core. Advances in Colloid and Interface Science , 164(1-2), 21-37.

  8. Happel, J., & Brenner, H., (1965). Low Reynolds Number Hydrodynamics. Prentice-Hall, Englewood Cliffs, N.J.

  9. Happel, J. (1958). Viscous flow in multiparticle systems: slow motion of fluids relative to beds of spherical particles. American Institute of Chemical Engineers Journal, 4, 197 -201.

  10. Joseph, D. D., & Tao, L. N. (1964). The effect of permeability on the slow motion of a porous sphere. Zeitschrift. Angewandte Mathematik und Mechanik, 44, 361-364.

  11. Kuwabara, S. (1959). The forces experienced by randomly distributed parallel circular cylinders or spheres in a viscous flow at small Reynolds numbers. Journal of the Physical Society Japan, 14, 527-532.

  12. Kim, A. S., & Yuan, R. (2005). A new model for calculating specific resistance of aggregated colloidal cake layers in membrane filtration processes. Journal of Membrane Science, 249(1-2), 89-101.

  13. Pop, I., & Cheng, P. (1992). Flow past a circular cylinder embedded in a porous medium based on the Brinkman model. International Journal of Engineering Science, 30, 257-262.

  14. Prasad, M. K., & Srinivasacharya, D. (2017). Micropolar fluid flow through a cylinder and a sphere embedded in a porous medium. International Journal of Fluid Mechanics Research, 44 (3), 229-240.

  15. Prakash, J., Raja Sekhar, G. P., Kohr, M. (2011). Stokes flow of an assemblage of porous particle: stress jump condition. Zeitschrift. Angewandte Mathematik und Physik, 62, 1027.

  16. Prasad, M. K., & Bucha, T. (2019). Effect of magnetic field on the steady viscous fluid flow around a semipermeable spherical particle. International Journal of applied and computational mathematics, 5, 98, DOI: 10.1007/s40819-019-0668-1.

  17. Spielman, L., & Goren, S. L. (1968). Model for predicting pressure drop and filtration efficiency in fibrous media. Environ. Sci. Technolgy, 2, 279-287.

  18. Shapovalov, V. M. (2009). Viscous fluid flow around a semipermeable particle. Journal of Applied Mechanics and Technical Physics, 50(4), 584-588.

  19. Sherief, H. H., Faltas, M. S., Ashmawy, E. A., & Abdel-Hameid, A. M. (2014). European Physics Journal Plus, 129, 217.

  20. Saad, E. I. (2018). Effect of magnetic fields on the motion of porous particles for Happel and Kuwabara models. Journal of Porous media, 21(7), 637-664.


Semipermeable cylinder, Stokes flow, Darcy\"s law, drag force, cell models.

© 2023 International Journal of Advanced Trends in Computer Applications
Foundation of Computer Applications (FCA), All right reserved.
Vision & Mission | Privacy Policy | Terms and Conditions