-
Previous Article
About interface conditions for coupling hydrostatic and nonhydrostatic Navier-Stokes flows
- DCDS-S Home
- This Issue
-
Next Article
Coupling the shallow water equation with a long term dynamics of sand dunes
Rate of convergence for a multi-scale model of dilute emulsions with non-uniform surface tension
1. | Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609, United States, United States |
References:
[1] |
G. Allaire, Homogenization of Navier-Stokes equations in open sets perforated with tiny holes. I. Abstract framework, a volume distribution of holes,, Arch. Rat. Mech. Anal., 113 (1991), 209.
doi: 10.1007/BF00375065. |
[2] |
H. Ammari, P. Garapon, H. Kang and H. Lee, Effective viscosity properties of dilute suspensions of arbitrarily shaped particles,, J. Asymptotic Analysis, 80 (2012), 189.
|
[3] |
H. Attouch, Variational Convergence for Functions and Operators,, Pitman, (1984).
|
[4] |
E. Bonnetier, D. Manceau and F. Triki, Asymptotic of the velocity of a dilute suspension of droplets with interfacial tension,, Quart. Appl. Math., 71 (2013), 89.
doi: 10.1090/S0033-569X-2012-01275-7. |
[5] |
A. Brillard, Asymptotic analysis of incompressible and viscous fluid flow through porous media. Brinkman's law via epi-convergence methods,, Ann. Fac. Sci. Toulouse, 8 (1986), 225.
|
[6] |
D. Cioranescu and F. Murat, Un terme etrange venu d'ailleurs,, in Nonlinear partial differential equations and their applications, 70 (1982), 154.
|
[7] |
D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order,, Berlin-Heidelberg-New York-Tokyo, (1983).
doi: 10.1007/978-3-642-61798-0. |
[8] |
J. B. Keller, L. A. Rubenfeld and J. E. Molyneux, Extremum Principles for slow viscous flow,, J. Fluid Mech., 30 (1967), 97. Google Scholar |
[9] |
L. Leal, Laminar flow and convective transport processes,, Research article, (2007), 1137.
doi: 10.1080/07373939308916891. |
[10] |
R. Lipton and B. Vernescu, Homogenization of two-phase emulsions,, Proc. Roy. Soc. Edinburgh, 124 (1994), 1119.
doi: 10.1017/S0308210500030146. |
[11] |
J.-L. Lions, Quelques Methodes de Resolution Des Problemes Aux Limites Non Lineaires,, Dunod, (2002). Google Scholar |
[12] |
F. Maris and B. Vernescu, Random homogenization for a fluid flow through a membrane,, J. Asymptotic Analysis, 86 (2012), 17.
|
[13] |
A. Nadim, A concise introduction to surface rheology with application to dilute emulsions of viscous drops,, Chem. Engin. Comm., 148/150 (1996), 391.
doi: 10.1080/00986449608936527. |
[14] |
G. Nika and B. Vernescu, Dilute emulsions with surface tension,, Quart. Appl. Math., 74 (2016), 89.
doi: 10.1090/qam/1403. |
[15] |
G. Nika and B. Vernescu, Asymptotics for dilute emulsions with surface tension,, J. Elliptic & Parabolic Equat., 1 (2015), 215.
|
[16] |
G. I. Taylor, The viscosity of a fluid containing small drops of another fluid,, Proc. Roy. Soc. London Ser. A, 138 (1932), 41.
doi: 10.1098/rspa.1932.0169. |
[17] |
R. Temam, Navier-Stokes Equations. Theory and Numerical Analysis,, North-Holland, (1984).
|
[18] |
R. C. Tolman, The effect of droplet size on surface tension,, J. Chem. Phys., 17 (1949), 333.
doi: 10.1063/1.1747247. |
[19] |
B. Vernescu, Convergence results for the homogenization of flow in fractured porous media,, IMA Preprint Series, 732 (1990). Google Scholar |
show all references
References:
[1] |
G. Allaire, Homogenization of Navier-Stokes equations in open sets perforated with tiny holes. I. Abstract framework, a volume distribution of holes,, Arch. Rat. Mech. Anal., 113 (1991), 209.
doi: 10.1007/BF00375065. |
[2] |
H. Ammari, P. Garapon, H. Kang and H. Lee, Effective viscosity properties of dilute suspensions of arbitrarily shaped particles,, J. Asymptotic Analysis, 80 (2012), 189.
|
[3] |
H. Attouch, Variational Convergence for Functions and Operators,, Pitman, (1984).
|
[4] |
E. Bonnetier, D. Manceau and F. Triki, Asymptotic of the velocity of a dilute suspension of droplets with interfacial tension,, Quart. Appl. Math., 71 (2013), 89.
doi: 10.1090/S0033-569X-2012-01275-7. |
[5] |
A. Brillard, Asymptotic analysis of incompressible and viscous fluid flow through porous media. Brinkman's law via epi-convergence methods,, Ann. Fac. Sci. Toulouse, 8 (1986), 225.
|
[6] |
D. Cioranescu and F. Murat, Un terme etrange venu d'ailleurs,, in Nonlinear partial differential equations and their applications, 70 (1982), 154.
|
[7] |
D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order,, Berlin-Heidelberg-New York-Tokyo, (1983).
doi: 10.1007/978-3-642-61798-0. |
[8] |
J. B. Keller, L. A. Rubenfeld and J. E. Molyneux, Extremum Principles for slow viscous flow,, J. Fluid Mech., 30 (1967), 97. Google Scholar |
[9] |
L. Leal, Laminar flow and convective transport processes,, Research article, (2007), 1137.
doi: 10.1080/07373939308916891. |
[10] |
R. Lipton and B. Vernescu, Homogenization of two-phase emulsions,, Proc. Roy. Soc. Edinburgh, 124 (1994), 1119.
doi: 10.1017/S0308210500030146. |
[11] |
J.-L. Lions, Quelques Methodes de Resolution Des Problemes Aux Limites Non Lineaires,, Dunod, (2002). Google Scholar |
[12] |
F. Maris and B. Vernescu, Random homogenization for a fluid flow through a membrane,, J. Asymptotic Analysis, 86 (2012), 17.
|
[13] |
A. Nadim, A concise introduction to surface rheology with application to dilute emulsions of viscous drops,, Chem. Engin. Comm., 148/150 (1996), 391.
doi: 10.1080/00986449608936527. |
[14] |
G. Nika and B. Vernescu, Dilute emulsions with surface tension,, Quart. Appl. Math., 74 (2016), 89.
doi: 10.1090/qam/1403. |
[15] |
G. Nika and B. Vernescu, Asymptotics for dilute emulsions with surface tension,, J. Elliptic & Parabolic Equat., 1 (2015), 215.
|
[16] |
G. I. Taylor, The viscosity of a fluid containing small drops of another fluid,, Proc. Roy. Soc. London Ser. A, 138 (1932), 41.
doi: 10.1098/rspa.1932.0169. |
[17] |
R. Temam, Navier-Stokes Equations. Theory and Numerical Analysis,, North-Holland, (1984).
|
[18] |
R. C. Tolman, The effect of droplet size on surface tension,, J. Chem. Phys., 17 (1949), 333.
doi: 10.1063/1.1747247. |
[19] |
B. Vernescu, Convergence results for the homogenization of flow in fractured porous media,, IMA Preprint Series, 732 (1990). Google Scholar |
[1] |
Imam Wijaya, Hirofumi Notsu. Stability estimates and a Lagrange-Galerkin scheme for a Navier-Stokes type model of flow in non-homogeneous porous media. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1197-1212. doi: 10.3934/dcdss.2020234 |
[2] |
Alain Damlamian, Klas Pettersson. Homogenization of oscillating boundaries. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 197-219. doi: 10.3934/dcds.2009.23.197 |
[3] |
Monia Capanna, Jean C. Nakasato, Marcone C. Pereira, Julio D. Rossi. Homogenization for nonlocal problems with smooth kernels. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020385 |
[4] |
Eduard Marušić-Paloka, Igor Pažanin. Homogenization and singular perturbation in porous media. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020279 |
[5] |
Guido Cavallaro, Roberto Garra, Carlo Marchioro. Long time localization of modified surface quasi-geostrophic equations. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020336 |
[6] |
Martin Heida, Stefan Neukamm, Mario Varga. Stochastic homogenization of $ \Lambda $-convex gradient flows. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 427-453. doi: 10.3934/dcdss.2020328 |
[7] |
John Mallet-Paret, Roger D. Nussbaum. Asymptotic homogenization for delay-differential equations and a question of analyticity. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3789-3812. doi: 10.3934/dcds.2020044 |
[8] |
Hua Zhong, Xiaolin Fan, Shuyu Sun. The effect of surface pattern property on the advancing motion of three-dimensional droplets. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020366 |
[9] |
Tian Ma, Shouhong Wang. Topological phase transition III: Solar surface eruptions and sunspots. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 501-514. doi: 10.3934/dcdsb.2020350 |
[10] |
Shuxing Chen, Jianzhong Min, Yongqian Zhang. Weak shock solution in supersonic flow past a wedge. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 115-132. doi: 10.3934/dcds.2009.23.115 |
[11] |
Karoline Disser. Global existence and uniqueness for a volume-surface reaction-nonlinear-diffusion system. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 321-330. doi: 10.3934/dcdss.2020326 |
[12] |
Björn Augner, Dieter Bothe. The fast-sorption and fast-surface-reaction limit of a heterogeneous catalysis model. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 533-574. doi: 10.3934/dcdss.2020406 |
[13] |
Xing-Bin Pan. Variational and operator methods for Maxwell-Stokes system. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3909-3955. doi: 10.3934/dcds.2020036 |
[14] |
Caterina Balzotti, Simone Göttlich. A two-dimensional multi-class traffic flow model. Networks & Heterogeneous Media, 2020 doi: 10.3934/nhm.2020034 |
[15] |
Shuang Liu, Yuan Lou. A functional approach towards eigenvalue problems associated with incompressible flow. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3715-3736. doi: 10.3934/dcds.2020028 |
[16] |
Pablo D. Carrasco, Túlio Vales. A symmetric Random Walk defined by the time-one map of a geodesic flow. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020390 |
[17] |
Joan Carles Tatjer, Arturo Vieiro. Dynamics of the QR-flow for upper Hessenberg real matrices. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1359-1403. doi: 10.3934/dcdsb.2020166 |
[18] |
Petr Pauš, Shigetoshi Yazaki. Segmentation of color images using mean curvature flow and parametric curves. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1123-1132. doi: 10.3934/dcdss.2020389 |
[19] |
Xuhui Peng, Rangrang Zhang. Approximations of stochastic 3D tamed Navier-Stokes equations. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5337-5365. doi: 10.3934/cpaa.2020241 |
[20] |
Helmut Abels, Andreas Marquardt. On a linearized Mullins-Sekerka/Stokes system for two-phase flows. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020467 |
2019 Impact Factor: 1.233
Tools
Metrics
Other articles
by authors
[Back to Top]