RAS Energy, Mechanics & ControlПрикладная математика и механика Journal of Applied Mathematics and Mechanics

  • ISSN (Print) 0032-8235
  • ISSN (Online) 3034-5758

Sedimentation Waves in a Two-Phase Granular Liquid

PII
10.31857/S0032823523020145-1
DOI
10.31857/S0032823523020145
Publication type
Status
Published
Authors
Volume/ Edition
Volume 87 / Issue number 2
Pages
240-253
Abstract
The question of mathematical modeling of the flows of a suspension of solid particles without assumptions about low concentrations is considered. The difference between the velocities of the particles and the binding liquid is taken into account by applying the two-continuum approach, in which the particles and the liquid are treated as two different viscous liquids. The role of buoyancy forces and gravitational mobility on particle settling is investigated. A qualitative comparison is made with the theory of Kinch concentration waves for the case of one-dimensional vertical flows. The role of vortices on the transverse migration of particles during sedimentation in a two-dimensional vessel is noted.
Keywords
суспензии седиментация силы плавучести поперечная миграция частиц
Date of publication
01.02.2023
Year of publication
2023
Number of purchasers
0
Views
22

References

  1. 1. Schwarze R., Gladkyy A., Uhlig F., Luding S. Rheology of weakly wetted granular materials: a comparison of experimental and numerical data // Granular Matter. 2013. V. 15. P. 455–465.
  2. 2. Herminghaus S. Dynamics of wet granular matter // Adv. Phys. 2005. V. 54. P. 221–261.
  3. 3. Hsiau S.S., Liao C.C., Tai C.H., Wan C.Y. The dynamics of wet granular matter under a vertical vibration bed // Granul. Matter. 2013. V. 15. P. 437–446.
  4. 4. Jop P., Forterre Y., Pouliquen O. A constitutive law for dense granular flows // Nature. 2006. V. 441. P. 727–730.
  5. 5. Gabrieli F., Lambert P., Cola S., Calvetti F. Micromechanical modelling of erosion due to evaporation in a partially wet granular slope // Int. J. Numer. Anal. Meth. Geomech. 2012. V. 36. P. 918–943.
  6. 6. Pietsch W. Agglomeration Processes. Weinheim: Wiley, 2002.
  7. 7. Guo Y., Wu C.Y., Thornton C. The effects of air and particle density difference on segregation of powder mixtures during die filling // Chem. Eng. Sci. 2011. V. 66. P. 661–673.
  8. 8. Beeley P.R. Foundry Technology. Oxford: Elsevier, 2001.
  9. 9. Schwarze R., Rudert A., Tilch W., Bast J. Rheological behavior of sand-binder mixtures measured by a coaxial cylinder rheometer // I. Foundry Res. 2008. V. 60. № 3. P. 2–6.
  10. 10. Anderson T., Jackson R. Fluid mechanical description of fluidized beds. Equations of motion // Ind. Eng. Chem. Fundamen. 1967. V. 6. P. 527–539.
  11. 11. Buyevich Y., Shchelchkova I. Flow of dense suspensions // Prog. Aerosp. Sci. 1978. V. 18. P. 121–150.
  12. 12. Zhang D., Prosperetti A. Momentum and energy equations for disperse two-phase flows and their closure for dilute suspensions // Int. J. Multiphase Flow. 1997. V. 23. P. 425–453.
  13. 13. Miller R., Singh J., Morris J. Suspensions flow modeling for general geometries // Chem. Eng. Sci. 2009. V. 64. P. 4597–4610.
  14. 14. Crowe C., Schwarzkopf J., Sommerfield M., Tsuji Y. Multiphase Flows with Droplets and Particles. Boca Raton: CRC Press, 2011.
  15. 15. Dontsov E.V., Peirce A.P. Slurry flow, gravitational settling and a proppant transport model for hydraulic fracture // J. Fluid Mech. 2014. V. 760. P. 567–590.
  16. 16. Nevskii Yu.A., Osiptsov A.N. Slow gravitational convection of disperse systems in domain with inclined boundaries // Fluid Dyn. 2011. V. 46. № 2. P. 225–239.
  17. 17. Ландау Л.Д., Лифшиц Е.М. Теоретическая физика. Т. VI. Гидродинамика. М.: Наука, 1986. 736 с.
  18. 18. Shelukhin V.V., Neverov V.V. Dense suspension flows: a mathematical model consistent with thermodynamics // J. Fluids Eng. ASME. 2022. V. 144. Iss. 021402. P. 1–13.
  19. 19. Kynch G.F. A theory of sedimentation // Trans. Faraday Soc. 1952. V. 48. P. 166–176.
  20. 20. Bustos M.C., Concha F., Bürger R., Tory E.M. Sedimentation and Thickening Phenomenological Foundation and Mathematical Theory. Dordrecht: Springer, 1999.
  21. 21. Shelukhin V.V. Thermodynamics of two-phase granular fluids // J. Non-Newton. Fluid Mech. 2018. V. 262. P. 25–37.
  22. 22. Krieger I.M., Dougerty T. A mechanism for non-Newtonian flow in suspensions of rigid spheres // Trans. Soc. Rheol. 1959. V. 3. P. 137–152.
  23. 23. Ishii V., Mishima K. Two-fluid model and hydrodynamic constitutive relations // Nucl. Eng.&Des. 1984. V. 82. P. 107–126.
  24. 24. Baumgarten A.S., Kamrin K. A general fluid-sediment mixture model and constitutive theory validated in many flow regimes // J. Fluid Mech. 2018. V. 861. P. 721–764.
  25. 25. Acrivos A., Herbolzheimer E. Enhanced sedimentation in settling tanks with inclined walls // J. Fluid Mech. 1979. V. 92. P. 435–457.
  26. 26. Richardson J.F., Zaki W.N. The sedimentation of a suspension of uniform spheres under conditions of viscous flow // Chem. Eng. Sci. 1954. V. 3. P. 65–73.
  27. 27. Шелухин В.В. Квазистационарная седиментация с адсорбцией // ПМТФ. 2005. Т. 46. № 4. С. 66–77.
QR
Translate

Индексирование

Scopus

Scopus

Scopus

Crossref

Scopus

Higher Attestation Commission

At the Ministry of Education and Science of the Russian Federation

Scopus

Scientific Electronic Library