Simulate the Flow of Non-Newtonian Fluids with the Polymer Flow Module
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Modeling Software for Single and Multiphase Flows in Non-Newtonian Fluids
What You Can Model with the Polymer Flow Module
Polymer Melts, Paints, and Protein Suspensions
Viscoelastic fluid models account for the elasticity in these types of fluids. As the fluid is deformed, there is a certain amount of force that works toward returning the fluid to its undeformed state. Important aspects of modeling are to estimate the deformation of the fluid with time, that is the shape of the air–liquid interface, the local forces on the surfaces that may interact with these fluids, and the pressure losses in a system where the fluid flow occurs. Typical examples of these fluids are polymer melts, paints, and suspensions of proteins.
Benchmark model for the thinning of a viscoelastic filament under the action of surface tension. The filament forms a beads-on-a-string structure with almost spherical drops connected by exponentially thinning threads. The plot shows the flow velocity as the fluid beads are formed.
Colloidal Suspensions, Ketchup, and Lotions
Colloidal suspensions may exhibit shear thickening behavior, where viscosity increases substantially with shear rate. Other suspensions may be shear thinning, for example syrups and ketchup, where the viscosity decreases with shear rate. Thixotropic fluids also have a time dependency, where the viscosity decreases with the duration of the shear rate. The models describing these fluids are all inelastic, but they describe highly non-Newtonian behavior. The purpose of modeling and simulation is similar to that for viscoelastic fluids above: estimate the shape of the air–liquid interface, the local forces on the surfaces that may interact with these fluids, and the pressure losses in a system where the fluid flow occurs. Additionally, the dependency on temperature and composition may be important for the design of manufacturing processes, for example, with the curing of rubber melts.
Mold filling of a molten rubber solution. The model uses the Power Law to describe the behavior of the rubber melt and Newtonian flow for the air flow out of the mold. The phase field method is used to track the interface between phases.
Features and Functionality in the Polymer Flow Module
Viscoelastic Fluid Models
The Polymer Flow Module features a variety of viscoelastic fluid models. These models differ in the constitutive relations describing the deformation and the forces caused by the fluid's deformation. The Oldroyd-B model uses a linear relation, which can be described as a suspension of Hookean springs in a Newtonian solvent, while the others describe nonlinear elastic effects and shear thinning.
- Oldroyd-B
- Gisekus
- FENE-P
- LPTT
Blood flow in an aneurism modeled using the Oldroyd-B viscoelastic fluid model.
Inelastic Non-Newtonian Models
In addition to the viscoelastic models, the Polymer Flow Module features a wide range of inelastic non-Newtonian models. Many of the models are generic, used to describe shear thinning and shear thickening. For more specific applications, there are models for viscoplastic and thixotropic fluids.
- Power Law
- Carreau
- Carreau–Yasuda
- Cross
- Cross–Williamson
- Ellis
- Bingham–Papanastasiou (Viscoplastic)
- Casson–Papanastasiou (Viscoplastic)
- Herschel–Bulkley–Papanastasiou
- Robertsson–Stiff–Papanastasiou
- DeKee–Turcotte–Papanastasiou Houska thixotropy (Thixotropic)
Colloidal suspension modeled with the Power Law model. The viscosity increases dramatically away from the impeller yielding very poor mixing higher up in the mixer. The model shows that a second impeller closer to the liquid surface may be required.
The phase boundary, the velocity field in the non-Newtonian fluid coating, and the velocity field in air surrounding the system are computed in order to understand and optimize the clot die coating process.
Multiphase Flow Models
To make it possible to model the liquid–air interface when simulating coatings, free surfaces, and mold filling, the Polymer Flow Module includes three different separated multiphase flow models based on surface tracking methods. The Level Set method tracks the interface position by solving a transport equation for the level-set function. The Phase Field method tracks the interface position by solving two transport equations for the phase field variable and the mixing energy density. The Moving Mesh method tracks the interface position with a mesh that changes shape.
Solidification of a rubber melt in a mold. The curing properties and the curing process are described using thermal functions.
Thermal Functions for Temperature Dependence
A common method of polymer extrusion and mold filling is to melt the rubber or polymer mixture. The mixture is then allowed to cure inside the mold. The Polymer Flow Module includes the thermal models required to model these processes: the Arrhenius, Williams–Landel–Ferry, and Exponential models are all available.
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