Pressure and temperature dependent viscosity of two glass forming liquids: Glycerol and dibutyl phthalate

1994 ◽  
Vol 100 (7) ◽  
pp. 5178-5189 ◽  
Author(s):  
Richard L. Cook ◽  
H. E. King ◽  
Chris A. Herbst ◽  
Dudley R. Herschbach
Keyword(s):  
Dibutyl Phthalate ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Glass Forming ◽  
Dependent Viscosity

scholarly journals A Novel Viscosity-Temperature Model of Glass-Forming Liquids by Modifying the Eyring Viscosity Equation

2020 ◽  
Vol 10 (2) ◽  
pp. 428 ◽  
Author(s):  
Chunyu Chen ◽  
Huidan Zeng ◽  
Yifan Deng ◽  
Jingtao Yan ◽  
Yejia Jiang ◽  
...  
Keyword(s):  
Mathematical Expression ◽  
Impact Factors ◽  
Viscosity Data ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Regression Methods ◽  
Glass Forming ◽  
Viscosity Models ◽  
Polymer Liquids ◽  
Dependent Viscosity

Many models have been created and attempted to describe the temperature-dependent viscosity of glass-forming liquids, which is the foundational feature to lay out the mechanism of obtaining desired glass properties. Most viscosity models were generated along with several impact factors. The complex compositions of commercial glasses raise challenges to settle these parameters. Usually, this issue will lead to unsatisfactory predicted results when fitted to a real viscosity profile. In fact, the introduction of the reliable viscosity-temperature data to viscosity equations is an effective approach to obtain the accurate parameters. In this paper, the Eyring viscosity equation, which is widely adopted for molecular and polymer liquids, was applied in this case to calculate the viscosity of glass materials. On the basis of the linear variation of molar volume with temperature during glass cooling, a modified temperature-dependent Eyring viscosity equation was derived with a distinguished mathematical expression. By means of combining high-temperature viscosity data and the glass transition temperature (Tg), nonlinear regression analysis was employed to obtain the accurate parameters of the equation. In addition, we have demonstrated that the different regression methods exert a great effect on the final prediction results. The viscosity of a series of glasses across a wide temperature range was accurately predicted via the optimal regression method, which was further used to verify the reliability of the modified Eyring equation.

scholarly journals Non-Isothermal Creeping Flows in a Pipeline Network: Existence Results

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1300
Author(s):  
Evgenii S. Baranovskii ◽  
Vyacheslav V. Provotorov ◽  
Mikhail A. Artemov ◽  
Alexey P. Zhabko
Keyword(s):  
Nonlinear Boundary ◽  
Galerkin Approximation ◽  
Large Data ◽  
Temperature Dependent ◽  
Weak Formulation ◽  
Temperature Dependent Viscosity ◽  
Pipeline Network ◽  
Flux Boundary Conditions ◽  
Creeping Flows ◽  
Dependent Viscosity

This paper deals with a 3D mathematical model for the non-isothermal steady-state flow of an incompressible fluid with temperature-dependent viscosity in a pipeline network. Using the pressure and heat flux boundary conditions, as well as the conjugation conditions to satisfy the mass balance in interior junctions of the network, we propose the weak formulation of the nonlinear boundary value problem that arises in the framework of this model. The main result of our work is an existence theorem (in the class of weak solutions) for large data. The proof of this theorem is based on a combination of the Galerkin approximation scheme with one result from the field of topological degrees for odd mappings defined on symmetric domains.

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