On simulations of spinning processes with a stationary one-dimensional upper convected Maxwell model

Lorenz, Maike; Marheineke, Nicole; Wegener, Raimund

doi:10.1186/2190-5983-4-2

Cited by 6 publications

(4 citation statements)

References 20 publications

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“…However, as seen in Appendix B, the terms q 2 and q 3 appear in the equations for u ,s and κ ,s , implying further limitations: when q 2 and q 3 approach zero, the equations for u ,s and κ ,s become singular; in addition, when q 2 and q 3 are negative, the aforementioned equations have no physically relevant stationary solutions and they would need a regularization. Therefore, to avoid any singularity issues that may arise in the solution of the set of (B1), for δ s → 0, we instead use the set of (2.95) but consider a small value of δ s = 10 −4 , to keep this set from becoming singular (see also Lorenz, Marheineke & Wegener 2014). Before we proceed, let us note a limitation on the assumptions used in our study.…”

Section: Polymer Melt Jet Modelling Constraintmentioning

confidence: 99%

Centrifugal spinning of viscoelastic nanofibres

et al. 2022

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The centrifugal spinning method is a recently invented technique to extrude polymer melts/solutions into ultra-fine nanofibres. Here, we present a superior integrated string-based mathematical model, to quantify the nanofibre fabrication performance in the centrifugal spinning process. Our model enables us to analyse the critical flow parameters covering an extensive range, by incorporating the angular momentum equations, the Giesekus viscoelastic constitutive model, the air-to-fibre drag effects and the energy equation into the string model equations. Using the model, we can analyse the dynamic behaviour of polymer melt/solution jets through the dimensionless flow parameters, namely, the Rossby ( $Rb$ ), Reynolds ( $Re$ ), Weissenberg ( $Wi$ ), Weber ( $We$ ), Froude ( $Fr$ ), air Péclet ( $Pe^*$ ) and air Reynolds ( $Re^*$ ) numbers as well as the viscosity ratio ( $\delta _s$ ), corresponding to rotational, inertial, viscous, viscoelastic, surface tension, gravitational, air thermal diffusivity, aerodynamic and viscosity ratio effects. We find that the nonlinear rheology remarkably affects the fibre trajectory, radius and normal stresses. Increasing $Wi$ leads to a thicker fibre, whereas increasing $\delta _s$ shows an opposite trend. In addition, by increasing $Wi$ , the fibre curvature is enhanced, causing the fibre to spiral closer to the rotation centre.

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Section: Polymer Melt Jet Modelling Constraintmentioning

confidence: 99%

Centrifugal spinning of viscoelastic nanofibres

et al. 2022

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“…In the steady uniaxial model this leads to singular system matrices and closing problems with appropriate boundary conditions making the numerical treatment extremely complicated. This issue has been addressed by [19] in the context of existence regimes for solutions of an uni-axial UCM fiber model under gravitational forces. We circumvent these problems when using the viscous fiber model where no mathematical regime changes take place.…”

Section: Setup and Model Closingmentioning

confidence: 99%

Melt-blowing of viscoelastic jets in turbulent airflows: Stochastic modeling and simulation

Wieland

Arne

Marheineke

et al. 2019

Applied Mathematical Modelling

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In melt-blowing processes micro-and nanofibers are produced by the extrusion of polymeric jets into a directed, turbulent high-speed airflow. Up to now the physical mechanism for the drastic jet thinning is not fully understood, since in the existing literature the numerically computed/predicted fiber thickness differs several orders of magnitude from those experimentally measured. Recent works suggest that this discrepancy might arise from the neglect of the turbulent aerodynamic fluctuations in the simulations. In this paper we confirm this suggestion numerically. Due to the complexity of the process direct numerical simulations of the multiscalemultiphase problem are not possible. Hence, we develop a numerical framework for a growing fiber in turbulent air that makes the simulation of industrial setups feasible. For this purpose we employ an asymptotic viscoelastic model for the fiber. The turbulent effects are taken into account by a stochastic aerodynamic force model where the underlying velocity fluctuations are reconstructed from a k-turbulence description of the airflow. Our numerical results show the significance of the turbulence on the jet thinning and give fiber diameters of realistic order of magnitude.

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“…The effects of gravity on curved liquid jets was investigated by Lorenz et al (2014). Also, Eggers and Dupont (1994) determined drop formation of Newtonian jets.…”

Section: Introductionmentioning

confidence: 99%

Instability of non-Newtonian liquid jets in centrifugal spinning with surfactants

Alsharif¹

2019

Fluid Dyn. Res.

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Centrifugal spinning process is a novel method used to produce nanofibers. In this process, we focus on the temporal and spatial instability of slender non-Newtonian jets falling under gravity in the presence of centrifugal forces and surfactants. The effects of the surfactants on the trajectory of non-Newtonian jets in the centrifugal spinning have been shown using asymptotic and numerical approaches. Furthermore, the results obtained from the linear theory have been used to estimate the break-up lengths and droplet sizes of this study. Our results also show that surfactants can provide a possibility of further manipulating of the break-up and main droplets.

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On simulations of spinning processes with a stationary one-dimensional upper convected Maxwell model

Cited by 6 publications

References 20 publications

Centrifugal spinning of viscoelastic nanofibres

Centrifugal spinning of viscoelastic nanofibres

Melt-blowing of viscoelastic jets in turbulent airflows: Stochastic modeling and simulation

Instability of non-Newtonian liquid jets in centrifugal spinning with surfactants

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