Fluid flow during phase transition : from viscous fluid to viscoelastic solid via variable-order calculus

Istenič, Enej (author), Brojan, Miha (author)

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

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