Polymer Flow Module

Simulate the Flow of Non-Newtonian Fluids

The Polymer Flow Module is an add-on to the COMSOL Multiphysics® software that is used for defining and solving problems involving non-Newtonian fluids with viscoelastic, thixotropic, shear thickening, or shear thinning properties. You can account for the properties of the fluids as a function of temperature and composition to model curing and polymerization. When combining other modules in COMSOL Multiphysics®, you can also model fully coupled and time-dependent fluid–structure interactions.

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A slot die coating process model in metallic gray with a rainbow slice plot.

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. When modeling, it is important 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.

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, such as with the curing of rubber melts, for example.

Features and Functionality in the Polymer Flow Module

The Polymer Flow Module offers specialized functionality for many fluid models and properties.

A closeup view of the Fluid Properties settings with the Material model list expanded and Oldroyd-B selected, and an aortic aneurysm model in the Graphics window.

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
A closeup view of the Model Builder with the Two-Phase Flow, Phase Field node highlighted and a slot die coating model at 0.1 seconds in the Graphics window.

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.

A closeup view of the Fluid Properties settings with the Inelastic model list expanded and Power law selected, and a non-Newtonian fluid mixer in the Graphics window.

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 and used for describing 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)
A closeup view of the Two-Phase Flow, Phase Field settings with the Thermal function list expanded and Williams-Landel-Ferry selected; and a rubber injection mold in the Graphics window.

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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