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Polymers
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Polymer Rheology II: Fundamentals and Applications
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Polymer Rheology II: Fundamentals and Applications

A special issue of Polymers (ISSN 2073-4360). This special issue belongs to the section "Polymer Processing and Engineering".

Deadline for manuscript submissions: closed (15 October 2021) | Viewed by 2338

Special Issue Editors

Prof. Dr. Valery Kulichikhin

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Guest Editor
Institute of Petrochemical Synthesis, Russian Academy of Sciences, Moscow, Russia
Interests: polymer physical chemistry; colloid chemistry; rheology; polymer processing; fiber spinning; additive technologies
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Alexander Malkin

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Guest Editor
Institute of Petrochemical Synthesis, Russian Academy of Sciences, Moscow, Russia
Interests: mechanics of polymers; rheology of polymer melts and solutions; colloid; multicomponent compositions; nanocomposites; polymer technology and pocessing
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Research

16 pages, 527 KiB  
Article
Analytical Solutions for Simple Turbulent Shear Flows on a Basis of a Generalized Newton’s Law
by Dmitry Nikushchenko, Valery Pavlovsky and Elena Nikushchenko
Polymers 2022, 14(16), 3308; https://doi.org/10.3390/polym14163308 - 14 Aug 2022
Cited by 1 | Viewed by 1613
Abstract
In the presented article a generalization of Newton’s formula for the shear stress in a fluid is carried out by giving it a power-law form. After the introduction of the corresponding strain rate tensor, a generalization is made to the spatial case of [...] Read more.
In the presented article a generalization of Newton’s formula for the shear stress in a fluid is carried out by giving it a power-law form. After the introduction of the corresponding strain rate tensor, a generalization is made to the spatial case of flow and the rheological relation is presented in tensor form. Depending on the power value in this rheological ratio, one can come either to a description of a laminar flow regime (in the form of Navier–Stokes equations), or to a description of the flow in turbulent regime. In the latter case, a set of differential equations with the no-slip boundary condition is specified, which is significantly different from that for the laminar flow regime, but which also allows one to obtain analytical solutions for simple shear flows and obtain the Blasius resistance law for the flow in a pipe. Therefore, the considered approach to solving problems of turbulent flows compares favorably with modern differential turbulence models. Solutions are given for simple shear flows of a fluid, when there is only one longitudinal component of the velocity, which depends on the transversal coordinate only. These solutions in terms of velocity profiles and resistance coefficients are in satisfactory agreement with the experimental data. Full article
(This article belongs to the Special Issue Polymer Rheology II: Fundamentals and Applications)
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