Loading [MathJax]/jax/output/SVG/jax.js

The homogenized model of small oscillations of complex fluids

  • Received: 01 June 2007 Revised: 01 February 2008
  • Primary: 35B27, 35Q30, 74Q10; Secondary: 76M30, 76M50

  • We consider the system of equations that describes small non-stationary motions of viscous incompressible fluid with a large number of small rigid interacting particles. This system is a microscopic mathematical model of complex fluids such as colloidal suspensions, polymer solutions etc. We suppose that the system of particles depends on a small parameter ε in such a way that the sizes of particles are of order ε3, the distances between the nearest particles are of order ε, and the stiffness of the interaction force is of order ε2.
    We study the asymptotic behavior of the microscopic model as ε0 and obtain the homogenized equations that can be considered as a macroscopic model of diluted solutions of interacting colloidal particles.

    Citation: M. Berezhnyi, L. Berlyand, Evgen Khruslov. The homogenized model of small oscillations of complex fluids[J]. Networks and Heterogeneous Media, 2008, 3(4): 831-862. doi: 10.3934/nhm.2008.3.831

    Related Papers:

    [1] Nurtiti Sunusi, Giarno . Bias of automatic weather parameter measurement in monsoon area, a case study in Makassar Coast. AIMS Environmental Science, 2023, 10(1): 1-15. doi: 10.3934/environsci.2023001
    [2] RAHMOUN Ibrahim, BENMAMAR Saâdia, RABEHI Mohamed . Comparison between different Intensities of Rainfall to identify overflow points in a combined sewer system using Storm Water Management Model. AIMS Environmental Science, 2022, 9(5): 573-592. doi: 10.3934/environsci.2022034
    [3] Lei Wang, Huan Du, Jiajun Wu, Wei Gao, Linna Suo, Dan Wei, Liang Jin, Jianli Ding, Jianzhi Xie, Zhizhuang An . Characteristics of soil erosion in different land-use patterns under natural rainfall. AIMS Environmental Science, 2022, 9(3): 309-324. doi: 10.3934/environsci.2022021
    [4] Ronak P. Chaudhari, Shantanu R. Thorat, Darshan J. Mehta, Sahita I. Waikhom, Vipinkumar G. Yadav, Vijendra Kumar . Comparison of soft-computing techniques: Data-driven models for flood forecasting. AIMS Environmental Science, 2024, 11(5): 741-758. doi: 10.3934/environsci.2024037
    [5] Muhammad Rendana, Wan Mohd Razi Idris, Sahibin Abdul Rahim . Clustering analysis of PM2.5 concentrations in the South Sumatra Province, Indonesia, using the Merra-2 Satellite Application and Hierarchical Cluster Method. AIMS Environmental Science, 2022, 9(6): 754-770. doi: 10.3934/environsci.2022043
    [6] Swatantra R. Kethireddy, Grace A. Adegoye, Paul B. Tchounwou, Francis Tuluri, H. Anwar Ahmad, John H. Young, Lei Zhang . The status of geo-environmental health in Mississippi: Application of spatiotemporal statistics to improve health and air quality. AIMS Environmental Science, 2018, 5(4): 273-293. doi: 10.3934/environsci.2018.4.273
    [7] Dong Chen, Marcus Thatcher, Xiaoming Wang, Guy Barnett, Anthony Kachenko, Robert Prince . Summer cooling potential of urban vegetation—a modeling study for Melbourne, Australia. AIMS Environmental Science, 2015, 2(3): 648-667. doi: 10.3934/environsci.2015.3.648
    [8] Zinabu A. Alemu, Emmanuel C. Dioha, Michael O. Dioha . Hydro-meteorological drought in Addis Ababa: A characterization study. AIMS Environmental Science, 2021, 8(2): 148-168. doi: 10.3934/environsci.2021011
    [9] Robert Russell Monteith Paterson . Depletion of Indonesian oil palm plantations implied from modeling oil palm mortality and Ganoderma boninense rot under future climate. AIMS Environmental Science, 2020, 7(5): 366-379. doi: 10.3934/environsci.2020024
    [10] Meriatna, Zulmiardi, Lukman Hakim, Faisal, Suryati, Mizwa Widiarman . Adsorbent performance of nipa (nypafruticans) frond in methylene blue dye degradation: Response surface methodology optimization. AIMS Environmental Science, 2024, 11(1): 38-56. doi: 10.3934/environsci.2024003
  • We consider the system of equations that describes small non-stationary motions of viscous incompressible fluid with a large number of small rigid interacting particles. This system is a microscopic mathematical model of complex fluids such as colloidal suspensions, polymer solutions etc. We suppose that the system of particles depends on a small parameter ε in such a way that the sizes of particles are of order ε3, the distances between the nearest particles are of order ε, and the stiffness of the interaction force is of order ε2.
    We study the asymptotic behavior of the microscopic model as ε0 and obtain the homogenized equations that can be considered as a macroscopic model of diluted solutions of interacting colloidal particles.


  • This article has been cited by:

    1. Manuel Adrian Acuña-Zegarra, Daniel Olmos-Liceaga, Jorge X. Velasco-Hernández, The role of animal grazing in the spread of Chagas disease, 2018, 457, 00225193, 19, 10.1016/j.jtbi.2018.08.025
    2. Lauren A. White, James D. Forester, Meggan E. Craft, Thierry Boulinier, Dynamic, spatial models of parasite transmission in wildlife: Their structure, applications and remaining challenges, 2018, 87, 00218790, 559, 10.1111/1365-2656.12761
    3. Bruce Y. Lee, Sarah M. Bartsch, Laura Skrip, Daniel L. Hertenstein, Cameron M. Avelis, Martial Ndeffo-Mbah, Carla Tilchin, Eric O. Dumonteil, Alison Galvani, Ricardo E. Gürtler, Are the London Declaration’s 2020 goals sufficient to control Chagas disease?: Modeling scenarios for the Yucatan Peninsula, 2018, 12, 1935-2735, e0006337, 10.1371/journal.pntd.0006337
    4. Vanessa Steindorf, Norberto Aníbal Maidana, Modeling the Spatial Spread of Chagas Disease, 2019, 81, 0092-8240, 1687, 10.1007/s11538-019-00581-5
    5. Britnee A. Crawford, Christopher M. Kribs-Zaleta, Gaik Ambartsoumian, Invasion Speed in Cellular Automaton Models for T. cruzi Vector Migration, 2013, 75, 0092-8240, 1051, 10.1007/s11538-013-9840-7
    6. Christopher M. Kribs, Christopher Mitchell, Host switching vs. host sharing in overlapping sylvaticTrypanosoma cruzitransmission cycles, 2015, 9, 1751-3758, 247, 10.1080/17513758.2015.1075611
    7. N. El Saadi, A. Bah, T. Mahdjoub, C. Kribs, On the sylvatic transmission of T. cruzi, the parasite causing Chagas disease: a view from an agent-based model, 2020, 423, 03043800, 109001, 10.1016/j.ecolmodel.2020.109001
    8. Cheol Yong Han, Habeeb Issa, Jan Rychtář, Dewey Taylor, Nancy Umana, Marc Choisy, A voluntary use of insecticide treated nets can stop the vector transmission of Chagas disease, 2020, 14, 1935-2735, e0008833, 10.1371/journal.pntd.0008833
    9. Daniel Olmos, Ignacio Barradas, David Baca-Carrasco, On the Calculation of
    R0
    R 0 Using Submodels, 2017, 25, 0971-3514, 481, 10.1007/s12591-015-0257-7
    10. Md. Abdul Hye, M. A. Haider Ali Biswas, Mohammed Forhad Uddin, Mohammad Saifuddin, Mathematical Modeling of Covid-19 and Dengue Co-Infection Dynamics in Bangladesh: Optimal Control and Data-Driven Analysis, 2022, 33, 1046-283X, 173, 10.1007/s10598-023-09564-7
    11. A. Omame, H. Rwezaura, M. L. Diagne, S. C. Inyama, J. M. Tchuenche, COVID-19 and dengue co-infection in Brazil: optimal control and cost-effectiveness analysis, 2021, 136, 2190-5444, 10.1140/epjp/s13360-021-02030-6
    12. Edem Fiatsonu, Rachel E. Busselman, Gabriel L. Hamer, Sarah A. Hamer, Martial L. Ndeffo-Mbah, Luisa Magalhães, Effectiveness of fluralaner treatment regimens for the control of canine Chagas disease: A mathematical modeling study, 2023, 17, 1935-2735, e0011084, 10.1371/journal.pntd.0011084
    13. H. Rwezaura, S.Y. Tchoumi, J.M. Tchuenche, Impact of environmental transmission and contact rates on Covid-19 dynamics: A simulation study, 2021, 27, 23529148, 100807, 10.1016/j.imu.2021.100807
    14. Malicki Zorom, Babacar Leye, Mamadou Diop, Serigne M’backé Coly, Metapopulation Modeling of Socioeconomic Vulnerability of Sahelian Populations to Climate Variability: Case of Tougou, Village in Northern Burkina Faso, 2023, 11, 2227-7390, 4507, 10.3390/math11214507
    15. Xuan Dai, Xiaotian Wu, Jiao Jiang, Libin Rong, Modeling the impact of non-human host predation on the transmission of Chagas disease, 2024, 00255564, 109230, 10.1016/j.mbs.2024.109230
    16. M. Adrian Acuña-Zegarra, Mayra R. Tocto-Erazo, Claudio C. García-Mendoza, Daniel Olmos-Liceaga, Presence and infestation waves of hematophagous arthropod species, 2024, 376, 00255564, 109282, 10.1016/j.mbs.2024.109282
  • Reader Comments
  • © 2008 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(3066) PDF downloads(44) Cited by(5)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog