Analytical Evaluation of Temperature Field Evolution at the Viscoelastic Medium-Solid Interface with Nanoscale Gas Inclusions

Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy


2018, Vol. 4. №4

Analytical Evaluation of Temperature Field Evolution at the Viscoelastic Medium-Solid Interface with Nanoscale Gas Inclusions

For citation: Amelkin S. V. 2018. “Analytical Evaluation of Temperature Field Evolution at the Viscoelastic Medium-Solid Interface with Nanoscale Gas Inclusions”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 4, no 4, pp. 33-47. DOI: 10.21684/2411-7978-2018-4-4-33-47

About the author:

Sergey V. Amelkin, Cand. Sci. (Phys.-Math.), Researcher, Multiphase Hydrodynamics Laboratory, Tyumen Branch of the Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences;


The processes on a contact of a viscoelastic medium with a solid (substrate, pore body matrix) are of practical interest for the operating of a variety of technical systems and technological processes. The physicochemical phenomena induced by pulse heating of the viscoelastic medium in contact with the solid have been investigated extensively in recent years. These phenomena may lead to transient metastability of the viscoelastic phase and to long-term or irreversible continuity violations of the contact.

Surface nanobubbles are assumed suitable model subjects for study of the phenomena under consideration. The surface nanobubbles may be formed from metastable gaseous nanodomens under interfacial shear stress arising from the temperature dependence of the interface energy. The computation of the temperature gradients during heat transfer through the non-uniform contact is therefore relevant problem.

It would be appropriate to possess simple analytical evaluation of the temperature field and the temperature gradients evolution at the viscoelastic medium-solid interface with the nanoscale gas inclusions to interpret concerning experimental data. Here we find some asymptotical solutions of the thermal contact problem in the case where the viscoelastic medium thermal diffusivity much lower than the solid one.


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