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 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.

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 A Numerical Technique for Solving the Maxwell Model for Free Surface Flows

2004 ◽  
Vol 5 (2) ◽  
Author(s):  
D.M. Carvalho ◽  
M.F. Tomé ◽  
J.A. Cuminato ◽  
A. Castelo ◽  
V.G. Ferreira
Keyword(s):  
Free Surface ◽  
Numerical Technique ◽  
Maxwell Model ◽  
Free Surface Flows ◽  
Surface Flows

scholarly journals Analytical Solution of Mixed Electroosmotic/Pressure Driven Flow of Viscoelastic Fluids between a Parallel Flat Plates Micro-Channel: The Maxwell Model Using the Oldroyd and Jaumann Time Derivatives

Micromachines ◽  
2020 ◽  
Vol 11 (11) ◽  
pp. 986
Author(s):  
Laura Casas ◽  
José A. Ortega ◽  
Aldo Gómez ◽  
Juan Escandón ◽  
René O. Vargas
Keyword(s):  
Flow Behavior ◽  
Viscoelastic Fluids ◽  
Volumetric Flow Rate ◽  
Maxwell Model ◽  
Parallel Plates ◽  
Flat Plates ◽  
Practical Applications ◽  
Low Viscosity ◽  
Pressure Driven Flow ◽  
Pressure Driven

In the present work, an analytical approximate solution of mixed electroosmotic/pressure driven flow of viscoelastic fluids between a parallel plates microchannel is reported. Inserting the Oldroyd, Jaumann, or both time derivatives into the Maxwell model, important differences in the velocity profiles were found. The presence of the shear and normal stresses is only close to the wall. This model can be used as a tool to understand the flow behavior of low viscosity fluids, as most of them experiment on translation, deformation and rotation of the flow. For practical applications, the volumetric flow rate can be controlled with two parameters, namely the gradient pressure and the electrokinetic parameter, once the fluid has been rheologically characterized.

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