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A Semi-Analytical Method for Channel and Pipe Flows for the Linear Phan-Thien-Tanner Fluid Model with a Solvent
Matheus Tozo de Araujo1, Laison Furlan1, Analice Brandi2
1Department of Applied Mathematics and Statistics, University of Sao Paulo, Sao Carlos 13566-590, Brazil.
Polymers
|November 11, 2022
Summary
A new semi-analytical method accurately models viscoelastic fluid flow in channels and pipes using the Linear Phan-Thien-Tanner model. This approach validates results against established models and reveals parameter influences on flow dynamics.
Area of Science:
- Fluid dynamics
- Rheology
- Computational modeling
Background:
- Viscoelastic fluids exhibit complex flow behaviors not captured by standard Newtonian models.
- Accurate modeling of non-Newtonian fluid flow is crucial in various industrial applications.
Purpose of the Study:
- To present a novel semi-analytical method for simulating laminar steady-state flows of viscoelastic fluids.
- To validate the proposed method against analytical solutions and investigate parameter effects.
Main Methods:
- Developed a semi-analytical method based on the Linear Phan-Thien-Tanner (LPTT) constitutive equation, including solvent viscosity.
- Compared results with Oldroyd-B and simplified LPTT models for validation.
- Analyzed the influence of dimensionless parameters like Reynolds number and Weissenberg number.
Main Results:
- The semi-analytical method successfully obtains laminar solutions for viscoelastic fluid flow.
- Demonstrated the impact of solvent viscosity contribution and other parameters on velocity and stress distributions.
- Validated the method's accuracy against established analytical solutions.
Conclusions:
- The proposed semi-analytical method is effective for modeling non-Newtonian fluid flow with the LPTT model.
- Provides insights into the complex interplay of parameters governing viscoelastic fluid dynamics in confined geometries.
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