Variational principles and entropy production in creeping flow of non-newtonian fluids

1977 ◽  
Vol 2 (4) ◽  
pp. 343-351 ◽  
Author(s):  
Gianni Astarita
Keyword(s):  
Entropy Production ◽  
Variational Principles ◽  
Newtonian Fluids ◽  
Creeping Flow

Variational Principles and Entropy Production

1963 ◽  
Vol 131 (5) ◽  
pp. 2354-2364 ◽  
Author(s):  
Eugene I. Blount
Keyword(s):  
Entropy Production ◽  
Variational Principles

Extrusion of Polymer Melts and Melt Flow Instabilities. III. Theoretical Analysis of Extrusion through a Slit Die

1969 ◽  
Vol 42 (3) ◽  
pp. 691-699 ◽  
Author(s):  
James L. White
Keyword(s):  
Reynolds Number ◽  
Stress Field ◽  
Viscoelastic Fluid ◽  
Polymer Melts ◽  
Second Order ◽  
Secondary Flows ◽  
Newtonian Fluids ◽  
Creeping Flow ◽  
Flow Instabilities ◽  
Field Problem

Abstract In the previous sections of this paper we have discussed our own and other experimental studies of flow instabilities in the extrusion of polymer melts as well as various theories of the mechanism of initiation of the instability. It is our belief that one of the keys to a deeper understanding of this phenomenon is a fuller analytical understanding of the stress and velocity fields in the composite reservoir, capillary, and extrudate system. It is to this problem that we turn our attention here. The velocity, stress-field problem in the entrance region of a conduit being fed from a reservoir has received considerable attention for Newtonian fluids. Most authors have followed Schlichting and Goldstein in using boundary-layer theory to analyze this problem. While there are a number of such solutions for viscous non-Newtonian and viscoelastic fluids, they are of little interest for polymer melts. This is not only because they represent a high Reynolds number, inertia-dominated asymptote but because they neglect all phenomena occurring in the reservoir feeding the conduit. Of more interest are the low Reynolds number creeping flow solutions for Newtonian fluids which are based upon the work of Sampson (see also Roscoe and Weissberg). A decade ago Tomita published a pioneering analysis of the creeping flow of a viscous non-Newtonian (power-law) fluid into a sharp edge entrance of a capillary. More recently LaNieve and Bogue have analyzed the creeping flow of a Coleman-Noll second order into the capillary entrance. A recent study of the entry problem has been made by Metzner, Uebler, and Chan Man Fong. The related problem of creeping flow of a viscoelastic fluid in a converging channel or cone has been analyzed by Adams, Whitehead, and Bogue and Kaloni. While the former authors computed the stress field for a second-order fluid and an integral constitutive equation in a presumed velocity field, Kaloni actually evaluated velocity profiles and predicted the formation of secondary flows. A more intuitive, but far less rigorous approach to extrusion of a viscoelastic fluid has been taken by Dexter and Dienes and Smith. These authors presume a virgin material to enter a capillary die in fully developed flow and utilize the theory of linear viscoelasticity to evaluate the stress field.

scholarly journals Variational Approach for Resolving the Flow of Generalized Newtonian Fluids in Circular Pipes and Plane Slits

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Taha Sochi
Keyword(s):  
Flow Field ◽  
Variational Method ◽  
Variational Approach ◽  
Variational Principles ◽  
Volumetric Flow Rate ◽  
Newtonian Fluids ◽  
New Method ◽  
Optimization Approach ◽  
Generalized Newtonian Fluids ◽  
Circular Pipes

We use a generic and general variational method to obtain solutions to the flow of generalized Newtonian fluids through circular pipes and plane slits. The new method is not based on the use of the Euler-Lagrange variational principle and hence it is totally independent of our previous approach which is based on this principle. Instead, the method applies a very generic and general optimization approach which can be justified by the Dirichlet principle although this is not the only possible theoretical justification. The results that were obtained from the new method using nine types of fluid are in total agreement, within certain restrictions, with the results obtained from the traditional methods of fluid mechanics as well as the results obtained from the previous variational approach. In addition to being a useful method in its own for resolving the flow field in circular pipes and plane slits, the new variational method lends more support to the old variational method as well as for the use of variational principles in general to resolve the flow of generalized Newtonian fluids and obtain all the quantities of the flow field which include shear stress, local viscosity, rate of strain, speed profile, and volumetric flow rate.

Flow of a PTT Fluid Through Planar Contractions: Vortex Inhibition Using Rounded Corners

2010 ◽  
Author(s):  
M. Khodadadi Yazdi ◽  
A. Ramazani S. A. ◽  
H. Hosseini Amoli ◽  
A. Behrang ◽  
A. Kamyabi
Keyword(s):  
Fluid Flow ◽  
Constitutive Equation ◽  
Viscoelastic Fluid ◽  
Constitutive Equations ◽  
Isothermal Condition ◽  
Critical Value ◽  
Newtonian Fluids ◽  
Creeping Flow ◽  
Contraction Flow ◽  
Ptt Fluid

Contraction flow is one of important geometries in fluid flow both in Newtonian and non-Newtonian fluids. In this study, flow of a viscoelastic fluid through a planar 4:1 contraction with rounded corners was investigated. Six different rounding ratios (RR = 0, 0.125, 0.25, 0.375, 0.438, 0.475, 0.488) was examined using the linear PTT constitutive equation at creeping flow and isothermal condition. Then the resulting PDE set including continuity, momentum, and PTT constitutive equations were implemented to the OpenFOAM software. The results clearly show vortex deterioration with increasing rounding diameter, so that when rounding corner exceeds a critical value, the vortex disappears completely. This phenomenon was also observed at different upstream widths. Furthermore, by increasing rounding diameter, the diminishing vortex approaches to the re-entrant corner.

Creeping motion of a sphere through a Bingham plastic

1985 ◽  
Vol 158 ◽  
pp. 219-244 ◽  
Author(s):  
A. N. Beris ◽  
J. A. Tsamopoulos ◽  
R. C. Armstrong ◽  
R. A. Brown
Keyword(s):  
Boundary Layer ◽  
Drag Coefficient ◽  
Yield Stress ◽  
Variational Principles ◽  
Solid Sphere ◽  
Creeping Flow ◽  
Matched Asymptotic Expansion ◽  
Bingham Plastic ◽  
Stagnation Points ◽  
Critical Yield

A solid sphere falling through a Bingham plastic moves in a small envelope of fluid with shape that depends on the yield stress. A finite-element/Newton method is presented for solving the free-boundary problem composed of the velocity and pressure fields and the yield surfaces for creeping flow. Besides the outer surface, solid occurs as caps at the front and back of the sphere because of the stagnation points in the flow. The accuracy of solutions is ascertained by mesh refinement and by calculation of the integrals corresponding to the maximum and minimum variational principles for the problem. Large differences from the Newtonian values in the flow pattern around the sphere and in the drag coefficient are predicted, depending on the dimensionless value of the critical yield stress Yg below which the material acts as a solid. The computed flow fields differ appreciably from Stokes’ solution. The sphere will fall only when Yg is below 0.143 For yield stresses near this value, a plastic boundary layer forms next to the sphere. Boundary-layer scalings give the correct forms of the dependence of the drag coefficient and mass-transfer coefficient on yield stress for values near the critical one. The Stokes limit of zero yield stress is singular in the sense that for any small value of Yg there is a region of the flow away from the sphere where the plastic portion of the viscosity is at least as important as the Newtonian part. Calculations For the approach of the flow field to the Stokes result are in good agreement with the scalings derived from the matched asymptotic expansion valid in this limit.

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