KFU. Card publication. Mixed Boundary-Value Problem in Microfluidics: Aver'yanov-Blunt Model Revisited.

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MIXED BOUNDARY-VALUE PROBLEM IN MICROFLUIDICS: AVER'YANOV-BLUNT MODEL REVISITED.

Form of presentation

Articles in international journals and collections

Year of publication

2025

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Authors, employees of KFU

Obnosov Yuriy Viktorovich, author

Other authors

Kacimov Anvar Rashidovich, author

Bibliographic description in the original language

Kacimov A.R., Obnosov Yu.V. Mixed Boundary-Value Problem in Microfluidics: Aver'yanov-Blunt Model Revisited. ANZIAM J., v.67, e16 (2025) pp.1-14 (Cambridge University Press) (IF 0.9, Q3)

Annotation

Macroscopically, a Darcian unsaturated moisture flow in the top soil is usually represented by an one -dimensional volume scale of evaporation from a static water table. On the microscale, simple pore-level models posit bundles of small-radius capillary tubes of a constant circular cross-section, fully occupied by a mobile water moving in the Hagen-Poiseuille (HP) regime, while large diameter pores are occupied by a stagnant air. In our paper, cross-sections of cylindrical pores are polygonal. Steady, laminar, fully-developed 2-D flows of a Newtonian water in prismatic conduits, driven by a constant pressure gradient along poresgradient, are more complex than the HP formula is based on, viz. the pores are only partially occupied by water and immobile air. The Poisson equation in a circular tetragon, with a no-slip or mixed (no-shear stress) boundary conditions on the two adjacent pore walls and two menisci, is solved by the methods of complex analysis. The velocity distribution obtained via the Keldysh-Sedov type of singular integrals and the flow rate is evaluated for several sets of menisci radii by integration of the velocity over the corresponding tetragons.

Keywords

Mixed boundary value problem for holomorphic function; 2D Poisson equation; longitudinal pore-scale velocity; evapotranspiration from ``solonchak's'' shallow water table

The name of the journal

ANZIAM Journal

URL

https://doi.org/doi:10.1017/S1446181124000051

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=312417&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Obnosov Yuriy Viktorovich	ru_RU
dc.contributor.author	Kacimov Anvar Rashidovich	ru_RU
dc.date.accessioned	2025-01-01T00:00:00Z	ru_RU
dc.date.available	2025-01-01T00:00:00Z	ru_RU
dc.date.issued	2025	ru_RU
dc.identifier.citation	Kacimov A.R., Obnosov Yu.V. Mixed Boundary-Value Problem in Microfluidics: Aver'yanov-Blunt Model Revisited. ANZIAM J., v.67, e16 (2025) pp.1-14 (Cambridge University Press) (IF 0.9, Q3)	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=312417&p_lang=2	ru_RU
dc.description.abstract	ANZIAM Journal	ru_RU
dc.description.abstract	Macroscopically, a Darcian unsaturated moisture flow in the top soil is usually represented by an one -dimensional volume scale of evaporation from a static water table. On the microscale, simple pore-level models posit bundles of small-radius capillary tubes of a constant circular cross-section, fully occupied by a mobile water moving in the Hagen-Poiseuille (HP) regime, while large diameter pores are occupied by a stagnant air. In our paper, cross-sections of cylindrical pores are polygonal. Steady, laminar, fully-developed 2-D flows of a Newtonian water in prismatic conduits, driven by a constant pressure gradient along poresgradient, are more complex than the HP formula is based on, viz. the pores are only partially occupied by water and immobile air. The Poisson equation in a circular tetragon, with a no-slip or mixed (no-shear stress) boundary conditions on the two adjacent pore walls and two menisci, is solved by the methods of complex analysis. The velocity distribution obtained via the Keldysh-Sedov type of singular integrals and the flow rate is evaluated for several sets of menisci radii by integration of the velocity over the corresponding tetragons.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject		ru_RU
dc.title	Mixed Boundary-Value Problem in Microfluidics: Aver'yanov-Blunt Model Revisited.	ru_RU
dc.type	Articles in international journals and collections	ru_RU