scholarly journals On an asymptotic upper-convected Maxwell model for a viscoelastic jet

PAMM ◽  
2012 ◽  
Vol 12 (1) ◽  
pp. 601-602 ◽  
Author(s):  
Maike Lorenz ◽  
Nicole Marheineke ◽  
Raimund Wegener
Keyword(s):  
Maxwell Model ◽  
Upper Convected Maxwell Model

scholarly journals Geometric scaling of a purely elastic flow instability in serpentine channels

2012 ◽  
Vol 712 ◽  
pp. 203-218 ◽  
Author(s):  
J. Zilz ◽  
R. J. Poole ◽  
M. A. Alves ◽  
D. Bartolo ◽  
B. Levaché ◽  
...  
Keyword(s):  
Flow Instability ◽  
Three Dimensional ◽  
Maxwell Model ◽  
Azimuthal Direction ◽  
Flexible Polymers ◽  
Good Qualitative Agreement ◽  
Geometric Scaling ◽  
Flow Geometry ◽  
Upper Convected Maxwell Model ◽  
Three Dimensional Simulations

AbstractA combined experimental, numerical and theoretical investigation of the geometric scaling of the onset of a purely elastic flow instability in serpentine channels is presented. Good qualitative agreement is obtained between experiments, using dilute solutions of flexible polymers in microfluidic devices, and three-dimensional numerical simulations using the upper-convected Maxwell model. The results are confirmed by a simple theoretical analysis, based on the dimensionless criterion proposed by Pakdel & McKinley (Phys. Rev. Lett., vol. 77, 1996, pp. 2459–2462) for onset of a purely elastic flow instability. Three-dimensional simulations show that the instability is primarily driven by the curvature of the streamlines induced by the flow geometry and not due to the weak secondary flow in the azimuthal direction. In addition, the simulations also reveal that the instability is time-dependent and that the flow oscillates with a well-defined period and amplitude close to the onset of the supercritical instability.

Corotating or Codeforming Models for Thermoforming: Free Forming

2013 ◽  
Author(s):  
H. M. Baek ◽  
A. J. Giacomin
Keyword(s):  
Differential Equation ◽  
Analytical Solution ◽  
Maxwell Model ◽  
Radius Of Curvature ◽  
Disk Radius ◽  
Differential Model ◽  
Sheet Deformation ◽  
Sheet Curvature ◽  
Upper Convected Maxwell Model

Our previous work [J Pol Eng, 32, 245 (2012)] explores the role of viscoelasticity for the simplest relevant problem in thermoforming, the manufacture of cones. In this previous work, we use a differential model employing the corotational derivative [the corotational Maxwell model (CM)] for which we find an analytical solution for the sheet deformation as a function of time. This previous work also identifies the ordinary nonlinear differential equation corresponding to the upper convected Maxwell model (UCM), for which she finds no analytical solution. In this paper, we explore the role of convected derivative by solving this UCM equation numerically by finite difference. We extend the previous work to include sag by incorporating a finite initial sheet curvature. We treat free forming step in thermoforming and find that the convected derivative makes the free forming time unreasonably sensitive to the initial curvature. Whereas, for the CM model, we get a free forming time that is independent of initial sheet curvature, so long as the sheet is nearly flat to begin with. We cast our results into dimensionless plots of thermoforming times versus disk radius of curvature.

scholarly journals A NEW MODEL FOR SHALLOW VISCOELASTIC FLUIDS

2013 ◽  
Vol 23 (08) ◽  
pp. 1479-1526 ◽  
Author(s):  
FRANÇOIS BOUCHUT ◽  
SÉBASTIEN BOYAVAL
Keyword(s):  
Energy Equation ◽  
Viscoelastic Fluids ◽  
Maxwell Model ◽  
Free Surface Flows ◽  
Layer Depth ◽  
Mathematical Properties ◽  
Finite Volume Discretization ◽  
Gravity Driven ◽  
Upper Convected Maxwell Model ◽  
Intrinsic Energy

We propose a new reduced model for gravity-driven free-surface flows of shallow viscoelastic fluids. It is obtained by an asymptotic expansion of the upper-convected Maxwell model for viscoelastic fluids. The viscosity is assumed small (of order epsilon, the aspect ratio of the thin layer of fluid), but the relaxation time is kept finite. In addition to the classical layer depth and velocity in shallow models, our system describes also the evolution of two components of the stress. It has an intrinsic energy equation. The mathematical properties of the model are established, an important feature being the non-convexity of the physically relevant energy with respect to conservative variables, but the convexity with respect to the physically relevant pseudo-conservative variables. Numerical illustrations are given, based on a suitable well-balanced finite-volume discretization involving an approximate Riemann solver.

scholarly journals On non-Newtonian lubrication with the upper convected Maxwell model

2011 ◽  
Vol 35 (5) ◽  
pp. 2309-2323 ◽  
Author(s):  
Xin Kai Li ◽  
Yingshe Luo ◽  
Yuanwei Qi ◽  
Rong Zhang
Keyword(s):  
Maxwell Model ◽  
Upper Convected Maxwell Model
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