EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 54 / No 5 (September-October 2020) ESAIM: M2AN, 54 5 (2020) 1597-1634 References
Open Access
Issue
ESAIM: M2AN
Volume 54, Number 5, September-October 2020
Page(s) 1597 - 1634
DOI https://doi.org/10.1051/m2an/2020002
Published online 28 July 2020
  1. G. Allaire, Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes I. Abstract framework, a volume distribution of holes. Arch. Ratio. Mech. Anal. 113 (1991) 209–259. [Google Scholar]
  2. G.K. Batchelor, Sedimentation in a dilute suspension of spheres. J. Fluid Mech. 52 (1972) 245–268. [Google Scholar]
  3. H.C. Brinkman, A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Flow Turbul. Combust. 1 (1949) 27. [Google Scholar]
  4. T. Champion, L. De Pascale and P. Juutinen, The #-Wasserstein distance: local solutions and existence of optimal transport maps. SIAMJ. Math. Anal. 40 (2008) 1–20. [Google Scholar]
  5. L. Desvillettes, F. Golse and V. Ricci, The mean field limit for solid particles in a Navier-Stokes flow. J. Stat. Phys. 131 (2008) 941–967. [Google Scholar]
  6. M. Doi and S.F. Edwards, The Theory of Polymer Dynamics. Oxford University Press (1986). [Google Scholar]
  7. A. Einstein, Eine neue bestimmung der moleküldimensionen. Ann. Physik. 19 (1906) 289–306. [Google Scholar]
  8. F. Feuillebois, Sedimentation in a dispersion with vertical inhomogeneities. J. Fluid Mech. 139 (1984) 145–171. [Google Scholar]
  9. G.P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Steady-State Problems. 2nd ed. Springer Monographs in Mathematics. Springer, New York (2011). [Google Scholar]
  10. D. Gérard-Varet and M. Hillairet, Analysis of the viscosity of dilute suspensions beyond Einstein’s formula. Preprint arXiv:1905.08208 (2019). [Google Scholar]
  11. E. Guazzelli and J.F. Morris, A Physical Introduction to Suspension Dynamics. Cambridge Texts Applied Mathematics (2012). [Google Scholar]
  12. B.M. Haines and A.L. Mazzucato, A proof of einstein’s effective viscosity for a dilute suspension of spheres. SIAM J. Math. Anal. 44 (2012) 2120–2145. [Google Scholar]
  13. H. Hasimoto, On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres. J. Fluid Mech. 5 (1959) 317–328. [Google Scholar]
  14. M. Hauray, Wasserstein distances for vortices approximation of Euler-type equations. Math. Models Methods Appl. Sci. 19 (2009) 1357–1384. [Google Scholar]
  15. M. Hauray and P.E. Jabin, Particle approximation of Vlasov equations with singular forces: propagation of chaos. Ann. Sci. Éc. Norm. Supér. 48 (2015) 891–940. [Google Scholar]
  16. C. Helzel and A.E. Tzavaras, A comparison of macroscopic models describing the collective response of sedimenting rod-like particles in shear flows. Phys. D 337 (2016) 18–29. [Google Scholar]
  17. C. Helzel and A.E. Tzavaras, A kinetic model for the sedimentation of rod–like particles. Multiscale Model Simul. 15 (2017) 500–536. [Google Scholar]
  18. M. Hillairet, On the homogenization of the Stokes problem in a perforated domain. Arch. Ratio. Mech. Anal. 230 (2018) 1179–1228. [Google Scholar]
  19. M. Hillairet, D. Wu, Effective viscosity of a polydispersed suspension Preprint arXiv:1905.12306 (2019). [Google Scholar]
  20. M. Hillairet, A. Moussa, F. Sueur, On the effect of polydispersity and rotation on the Brinkman force induced by a cloud of particles on a viscous incompressible flow Preprint arXiv:1705.08628v1 [math.AP] (2017). [Google Scholar]
  21. R.M. Höfer, Sedimentation of inertialess particles in Stokes flows. Commun. Math. Phys. 360 (2018) 55–101. [Google Scholar]
  22. R.M. Höfer, Sedimentation of particle suspensions in Stokes flow. Ph.D thesis, Rheinischen Friedrich-Wilhelms University, Bonn (2019). [Google Scholar]
  23. R.M. Höfer, J.J.L. Velàzquez, The method of reflections, homogenization and screening for Poisson and Stokes equations in perforated domains. Arch. Ration. Mech. Anal. 227 (2018) 1165–1221. [Google Scholar]
  24. P.E. Jabin and F. Otto, Identification of the dilute regime in particle sedimentation. Commun. Math. Phys. 250 (2004) 415–432. [Google Scholar]
  25. D.J. Jeffrey and Y. Onishi, Calculation of the resistance and mobility functions for two unequal spheres in low-Reynolds-number flow. J. Fluid Mech. 139 (1984) 261–290. [Google Scholar]
  26. J.B. Keller, L.A. Rubenfeld and J.E. Molyneux, Extremum principles for slow viscous flows with applications to suspensions. J. Fluid Mech. 30 (1967) 97–125. [Google Scholar]
  27. S. Kim and S.J. Karrila, Microhydrodynamics: Principles and Selected Applications. Courier Corporation (2005). [Google Scholar]
  28. P. Laurent, G. Legendre, J. Salomon, On the method of reflections. Available at: https://hal.archives-ouvertes.fr/hal-01439871 (2017).. [Google Scholar]
  29. C. Le Bris and T. Lelièvre, Micro-macro models for viscoelastic fluids: modelling, mathematics and numerics. Sci. China Math. 55 (2012) 353–384. [Google Scholar]
  30. T. Lévy and E. Sánchez-Palencia, Einstein-like approximation for homogenization with small concentration. II. Navier-Stokes equation. Nonlinear Anal. 9 (1985) 1255–1268. [Google Scholar]
  31. J.H.C. Luke, Convergence of a multiple reflection method for calculating Stokes flow in a suspension. Soc. Ind. Appl. Math. 49 (1989) 1635–1651. [Google Scholar]
  32. A. Mecherbet, Sedimentation of particles in Stokes flow. Kinet. Relat. Models 12 (2019) 995–1044. [Google Scholar]
  33. B. Niethammer and R. Schubert, A local version of Einstein’s formula for the effective viscosity of suspensions. Preprint arXiv:1903.08554 (2019) 5. [Google Scholar]
  34. J. Rubinstein, On the macroscopic description of slow viscous flow past a random array of spheres. J. Stat. Phys. 44 (1986) 849–863. [Google Scholar]
  35. J. Rubinstein and J. Keller, Particle distribution functions in suspensions. Phys. Fluids A 1 (1989) 1632–1641. [Google Scholar]
  36. E. Sánchez-Palencia, Einstein-like approximation for homogenization with small concentration. I. Elliptic problems. Nonlinear Anal. 9 (1985) 1243–1254. [Google Scholar]
  37. M. Smoluchowski, Über die Wechselwirkung von Kugeln, die sich in einer zähen Flüssigkeit bewegen. Bull. Acad. Sci. Cracovie A 1 (1911) 28–39. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you