A level set method to study foam processing: a validation study

Rao, Rekha R.; Mondy, Lisa Ann; Noble, David R.; Moffat, Harry K.; Adolf, Douglas Brian; Notz, Patrick

doi:10.1002/fld.2671

Cited by 22 publications

(21 citation statements)

References 34 publications

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“…In Braun et al (2008) a level set method is presented which is based on a 3-D set of triangulated points, which makes it a hybrid between tracers and level set functions. The level set method is primarily used in other fields of computational science such as twophase flows (Oka and Ishii, 1999) and fluid dynamics (Rao et al, 2011). An overview of the method and applications can be found in Osher and Fedkiw (2001).…”

Section: Introductionmentioning

confidence: 99%

Using the level set method in geodynamical modeling of multi-material flows and Earth's free surface

et al. 2014

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Abstract. The level set method allows for tracking material surfaces in 2-D and 3-D flow modeling and is well suited for applications of multi-material flow modeling. The level set method utilizes smooth level set functions to define material interfaces, which makes the method stable and free of oscillations that are typically observed in case step-like functions parameterize interfaces. By design the level set function is a signed distance function and gives for each point in the domain the exact distance to the interface as well as on which side it is located. In this paper we present four benchmarks which show the validity, accuracy and simplicity of using the level set method for multi-material flow modeling. The benchmarks are simplified setups of dynamical geophysical processes such as the Rayleigh-Taylor instability, post-glacial rebound, subduction and slab detachment. We also demonstrate the benefit of using the level set method for modeling a free surface with the sticky air approach. Our results show that the level set method allows for accurate material flow modeling and that the combination with the sticky air approach works well in mimicking Earth's free surface. Since the level set method tracks material interfaces instead of materials themselves, it has the advantage that the location of these interfaces is accurately known and that it represents a viable alternative to the more commonly used tracer method.

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Section: Introductionmentioning

confidence: 99%

Using the level set method in geodynamical modeling of multi-material flows and Earth's free surface

et al. 2014

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“…This work was documented by Rao et al (2011) and will only be briefly summarized here. The details of the level set method can also be found in these published papers (Rao et al, 2012a;Rao et al 2012b). The level set method, being an Eulerian method, can handle topological changes such as the merging of layers.…”

Section: Three-dimensional Free Surface Flow In the Splittermentioning

confidence: 96%

Multilayer Coextrusion of Polymer Composites to Develop Organic Capacitors

Mondy

Mrozek

Rao

et al. 2015

International Polymer Processing

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Multilayer coextrusion is applied to produce at ape containing layers of alternating electrical properties to demonstrate the potential for using coextrusion to manufacture capacitors. To obtain the desired properties, we develop two filled polymer systems, one for conductive layers and one for dielectric layers. We describe numerical models used to help determine the material and processing parameters that impact processing and layer stability. These models help quantify the critical ratios of densities and viscosities of the two layers to maintain stable layers, as well as the effect of increasing the flow rate of one of the two materials. The conducting polymer is based on polystyrene filled with ab lend of low-meltingpoint eutectic metal and nickel particulate filler, as described by Mrozek et al. (2010). The appropriate concentrations of fillers are determined by balancing measured conductivity with processability in at win screw extruder. Based on results of the numerical models and estimates of the viscosity of emulsions and suspensions, ad ielectric layer composed of polystyrene filled with barium titanate is formulated. Despite the fact that the density of the dielectric filler is less than the metallic filler of the conductive phase, as well as rheological measurements that later showed that the dielectric formulation is not an ideal match to the viscosity of the conductive material, the two materials can be successfully coextruded if the flow rates of the two materials are not identical. Am easurable capacitance of the layered structure is obtained. 1I ntroductionMultilayer coextrusion combines multiple polymers into a layered structure to produce composite properties that are not found in asingle polymer. Coextrusion processes have been in use for over 40 years, and multilayered film structures have found commercial application in the area of food and beverage packaging for their barrier properties and as protective coatings (Wagner, 2010). The multilayer coextrusione quipment used here is based on work by Zhao and Macosko (2002). The equipment combines the polymer flows from two single screw extruders into an initial layered structure that then passes through aseries of dies to multiply the number of layers. The first die splits the flow vertically; the two components are stacked and recombined to effectively double the number of layers. As the number of layers is increased in the same die cross-sectional area, the individual layer thickness decreases. This method has successfully been implemented by companies like 3M and Dow to produce multilayered structures of * 20 m ma nd 110 nm, respectively (3M 2005(3M , Dow 2007). In our equipment the initial layered structure consists of 8layers. As aresult, the number of multiplication sections, n, will result in 2 n+3 layers in a1mmtape.

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“…The commonly adopted material law in the literature for chemorheological fluids proposed by Castro and Macosko specifies the dependence of the mixture rheology on the degree of polymerization and the temperature of the system [15]. Rao et al assumed that the created gas in the system contributes to the viscosity following the Taylor-Mooney law derived for emulsion [16][17][18]. This model suggests an increase in the mixture viscosity as the gas fraction increases.…”

Section: Introductionmentioning

confidence: 99%

Numerical Studies of the Viscosity of Reacting Polyurethane Foam with Experimental Validation

et al. 2020

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Products made of polyurethane foam are manufactured by the chemical reaction of various low-viscosity raw materials and additives. The diversity of different formulations to meet the requirements of the market makes the characterization of their processing and flow properties important for a simple and error-free production. The modeling and simulation of such processes are equally of great importance. This provides additional findings without the expense of real tests and makes it easier to design components. The work described in this paper was carried out against this background. An experimental setup using a rheometer was developed to determine the flow and curing properties of reacting polyurethane foam reproducibly with comparable expansion conditions to industrial processes. The experiment was mathematically modelled to investigate the rheology of reacting polyurethane foams. The mathematical framework consists of coupled, non-linear, partial differential equations for the dynamics and the heat transfer processes in the system. These are solved numerically in 3D using finite volume techniques under adequate physical conditions. The accuracy of two viscosity laws according to the state of the art and their novel combination were investigated in this context. The proposed viscosity model of this study provides accurate results compared to the experiment.

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A level set method to study foam processing: a validation study

Cited by 22 publications

References 34 publications

Using the level set method in geodynamical modeling of multi-material flows and Earth's free surface

Using the level set method in geodynamical modeling of multi-material flows and Earth's free surface

Multilayer Coextrusion of Polymer Composites to Develop Organic Capacitors

Numerical Studies of the Viscosity of Reacting Polyurethane Foam with Experimental Validation

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