Modelluntersuchungen zur Restentgasung von Kunststoffschmelzen mit gasförmigen Schleppmitteln in einem statischen Entgasungsapparat – 1. Teil: Modellierung des Wachstums eines geschlossenzelligen Polymerschaums

Piesche, Manfred; Nonnenmacher, S.; Schütz, Steffen

doi:10.1002/cite.200700179

Cited by 3 publications

(19 citation statements)

References 10 publications

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“…For the sake of completeness, it is stated that the following considerations postulate physically existent, stable and mathematically unique solutions of the non-linear transport equations for mass, momentum and thermal energy [8] [9] [10]. As mentioned above, mimicking foaming processes occurs by employing two models that describe spherical foam and polyhedral foam, respectively.…”

Section: Model Equations For Foaming Processesmentioning

confidence: 99%

“…The gas volume fraction at time t = 0 is given by Figure 1. Spherical foam model (left) and growth of a single spherical bubble (right) [9]. …”

Section: Model Equations For Foaming Processesmentioning

confidence: 99%

“…As shown in [9], the conservation equation for mass in the liquid phase simplifies to an expression for the radial velocity component (see also Figure 1, right) ( )…”

Section: Model Equations For the Spherical Foammentioning

confidence: 99%

“…where p is the pressure, τ rr and τ θθ are the normal stresses in radial and polar direction, σ is the interface tension and ρ is the density of the liquid [9]. Inserting the continuity Equation (7) into the momentum Equation (8) …”

Section: Model Equations For the Spherical Foammentioning

confidence: 99%

“…Piesche, Nonnenmacher and Schütz [8] [9] [10] developed models to calculate foaming processes of polymer liquids in a static degassing system, which is supported by a gas dispersed into the polymer liquid under pressure before foaming.…”

Section: Introductionmentioning

confidence: 99%

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Numerical Simulation of Foaming Processes

Gladbach¹,

Delgado²,

Rauh³

2017

WJM

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The literature model studied in this article describes bubble formation and growth in a highly viscous polymer liquid with support of a gaseous matter dispersed under pressure before foaming. The foam growth is induced by the application of vacuum and mass transport of volatile components dissolved in the polymer liquid. Based on this literature model, aeration processes are calculated for intermediate viscosity and low viscosity biological systems, as they are of interest for biomatter foams, in particular for food foams in industrial processes. At the end of this article, the numerical results are presented and discussed.

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Section: Model Equations For Foaming Processesmentioning

confidence: 99%

“…The gas volume fraction at time t = 0 is given by Figure 1. Spherical foam model (left) and growth of a single spherical bubble (right) [9]. …”

Section: Model Equations For Foaming Processesmentioning

confidence: 99%

“…As shown in [9], the conservation equation for mass in the liquid phase simplifies to an expression for the radial velocity component (see also Figure 1, right) ( )…”

Section: Model Equations For the Spherical Foammentioning

confidence: 99%

Section: Model Equations For the Spherical Foammentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Numerical Simulation of Foaming Processes

Gladbach¹,

Delgado²,

Rauh³

2017

WJM

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show abstract

Modelluntersuchungen zur Restentgasung von Kunststoffschmelzen mit gasförmigen Schleppmitteln in einem statischen Entgasungsapparat – 2. Teil: Durchführung und Ergebnisse der Schäumversuche

Piesche

Nonnenmacher

Schütz

2008

Chemie Ingenieur Technik

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Modelling and Simulation of the Transport of Protein Foams

Gladbach¹,

Delgado²,

Rauh³

2014

Proc Appl Math and Mech

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The behaviour of foams at rest, but particularly during fluid mechanical transport is not sufficiently investigated yet. The present article deals with protein foams as they have a great importance in food production. In the first part, the foaming process of a highly viscous liquid due to gaseous materials dispersed under pressure in the liquid and mass transport of volatile components dissolved in the liquid is considered. The aim is to calculate the foam volume and the concentration of the dissolved, volatile components as a function of the material and process parameters. In the second part, material equations for bubble suspensions with gas volume fractions φ ≤ 0.6 and small bubble deformations (i.e. NCa 1) are presented. The basics form two constitutive laws which are used for describing a steady shear flow. If the rates of work of the two models are compared, material equations for the shear viscosity and the normal stress differences can be derived. Foaming processThe model presented in [4] and developed further in this article describes the foaming process of a highly viscous liquid due to gaseous materials dispersed under pressure in the liquid and mass transport of volatile components dissolved in the liquid. The model is divided into two model phases, which describe spherical foam and polyhedron foam, respectively. The increase of the foam volume is calculated by solving problem-specific conservation equations for mass, momentum and energy. Alike, concentration equations for the dissolved, volatile components, which are diffusing into the bubbles during the foaming process, are solved. The equations are subjected to a Lagrangian coordinate transformation and transformed into dimensionless equations by means of a set of dimensionless π-numbers. The equation of motion for the spherical foam is given bywhere R B is the bubble radius, R S is the radius of the liquid volume surrounding the bubble, P g is the internal pressure of the bubble, P ∞ is the ambient pressure, T Y Y and T θθ denote the normal stresses, T is the time and Y is the transformed spatial coordinate. The integral on the right side of equation (1) characterises the viscous elongation stresses around the bubble. The rheological behaviour of the liquid is described by the constitutive equation for Newtonian liquids or the generalised contravariant Maxwell-Oldroyd model for viscoelastic liquids. In the latter case, the extra stress tensor T results from the sum of the partial stresses T k based on a discrete spectrum that covers relaxation times λ R,k and viscosities η k , the sum of which is equal to the zero shear viscosity η 0 of the liquid:The function a takes account of viscosity changes due to changes in the temperature Θ and the concentration ξ i of the volatile components dissolved in the liquid. A similar differential equation is derived for the other relevant normal stress component T θθ of the extra stress tensor T. The equations for the partial stresses and the equation (1) are combined, resulting in a large system of non-linear ...

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Modelluntersuchungen zur Restentgasung von Kunststoffschmelzen mit gasförmigen Schleppmitteln in einem statischen Entgasungsapparat – 1. Teil: Modellierung des Wachstums eines geschlossenzelligen Polymerschaums

Cited by 3 publications

References 10 publications

Numerical Simulation of Foaming Processes

Numerical Simulation of Foaming Processes

Modelluntersuchungen zur Restentgasung von Kunststoffschmelzen mit gasförmigen Schleppmitteln in einem statischen Entgasungsapparat – 2. Teil: Durchführung und Ergebnisse der Schäumversuche

Modelling and Simulation of the Transport of Protein Foams

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