On hyperbolicity and solution properties of the continual models of micro/nanoparticle aggregation and sedimentation in concentrated suspensions
DOI:
https://doi.org/10.17721/1812-5409.2019/4.7Abstract
In continual mechanics sedimentation of aggregating particles in concentrated suspensions are determined by the mass and momentum conservation laws for each component of the suspension. The resulting quasilinear system of differential equations governing the flow could be hyperbolic, strongly strictly or weakly hyperbolic depending on the model accepted. The type and Eigenvalues of the matrix influence the characteristics of the pattern formation during the sedimentation that is essential for the model application in modern medical, microbiological and nanofluidic technologies. In this paper the hyperbolicity of the three-phase model of aggregation and sedimentation of micro/nanoparticles is studied.
Key words: Aggregation, Sedimentation, Multiphase Continuous Media, Hyperbolic Systems, Eigenvalues, Characteristics.
Pages of the article in the issue: 60 - 63
Language of the article: English
References
Sedimentation Engineering. (2018) A. AMINI (ed.). IntechOpen. 196 p.
SCHUCK P., ZHAO H. (2017) Sedimentation velocity analytical ultracentrifugation. CRC Press. - 271p.
FERNANDEZ-NIETO E.D., KONE E.H., DE LUNA T.M., BURGER R. (2013) A multilayer shallow water system for polydisperse sedimentation. J. Comput. Phys. Vol. 238. p. 281–314.
HOTZE E.M., PHENRAT T., LOWRY G.V. (2010) Nanoparticle Aggregation: Challenges to Understanding Transport and Reactivity in the Environment. J. Environ. Qual. Vol.39. p. 1909–1924.
Kizilova N., Batyuk L., Baranets V. Human Red Blood Cell Properties and Sedimentation Rate: a Biomechanical Study. // Biomechanics in Medicine and Biology: Proceedings of the International Conference of the Polish Society of Biomechanics, Zielona Góra, Poland, September 5-7, 2018. K. Arkusz, R. Będziński, T. Klekiel, S. Piszczatowski, eds. Springer Series “Advances in Intelligent Systems and Computing.” Vol.831. - 2019. - P. 3-22.
BARANETS V.А., KIZILOVA N.N., DATSOK O.M. (2019) Hardware-software complex for the study of sedimentation processes in technical and biological suspensions of aggregating micro- and nanoparticles. Visnyk of V.N. Karazin Kharkov National University, Ser. «Mathematical modeling. Information technologies. Automated control systems». Vol.42. p. 4-11.
BARANETS V.А., KIZILOVA N.N. (2018) Discrete modeling of aggregation and sedimentation of micro- and nanoparticles in suspensions. Visnyk of V.N. Karazin Kharkov National University, Ser. «Mathematical modeling. Information technologies. Automated control systems». Vol.40. p. 4-14.
BARANETS V., KIZILOVA N. Mathematical modeling of particle aggregation and sedimentation in the inclined tubes. Bulletin of Kyiv National University. Ser. “Physical and Mathematical Sciences.” – 2018. – N4. – Р.52-57.
RUIZ-BAIERA R., TORRES H. (2015) Numerical solution of a multidimensional sedimentation problem using finite volume-element methods. Applied Numerical Mathematics. Vol.95. p. 280-291.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
