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Fluid flow during phase transition : from viscous fluid to viscoelastic solid via variable-order calculus
ID
Istenič, Enej
(
Author
),
ID
Brojan, Miha
(
Author
)
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https://pubs.aip.org/aip/pof/article/35/12/123103/2925737/Fluid-flow-during-phase-transition-From-viscous
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Abstract
In this paper, we consider a pressure-driven flow of a viscoelastic fluid in a straight rectangular channel undergoing a solidification phase change due to polymerization. We treat the viscoelastic response of the fluid with a model based on the formalism of variable-order calculus; more specifically, we employ a model utilizing a variable-order Caputo-type differential operator. The order parameter present in the model is determined by the extent of polymerization induced by light irradiation. We model this physical quantity with a simple equation of kinetics, where the reaction rate is proportional to the amount of material available for polymerization and optical transmittance. We treat cases when the extent of polymerization is a function of either time alone or both position and time, and solve them using either analytical or semi-analytical methods. Results of our analysis indicate that in both cases, solutions evolve in time according to a variable-order decay law, with the solution in the first case having a hyperbolic cosine-like spatial dependence, while the spatial dependence in the second case conforms to a bell curve-like function. We infer that our treatment is physically sound and may be used to consider problems of more general viscoelastic flows during solidification, with the advantage of requiring fewer experimentally determined parameters.
Language:
English
Keywords:
viscous fluid flow
,
phase change
,
variable-order integro-differential operator
Work type:
Article
Typology:
1.01 - Original Scientific Article
Organization:
FS - Faculty of Mechanical Engineering
Publication status:
Published
Publication version:
Version of Record
Year:
2023
Number of pages:
Str. 1-21
Numbering:
Vol. 35, iss. 12, art. 123103
PID:
20.500.12556/RUL-152741
UDC:
532:536.42
ISSN on article:
1070-6631
DOI:
10.1063/5.0177121
COBISS.SI-ID:
174918659
Publication date in RUL:
05.12.2023
Views:
388
Downloads:
37
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Record is a part of a journal
Title:
Physics of fluids
Shortened title:
Phys. fluids
Publisher:
American Institute of Physics
ISSN:
1070-6631
COBISS.SI-ID:
37828865
Licences
License:
CC BY 4.0, Creative Commons Attribution 4.0 International
Link:
http://creativecommons.org/licenses/by/4.0/
Description:
This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.
Secondary language
Language:
Slovenian
Keywords:
tok viskoznega fluida
,
fazna sprememba
,
diferencialno-integralski operator variabilnega reda
Projects
Funder:
ARRS - Slovenian Research Agency
Project number:
J2-2499
Name:
Razvoj kvazi-periodičnih deformacijskih vzorcev v viskoelastičnih strukturah
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