scholarly journals AN EXPLICIT CONSTITUTIVE EQUATION FOR PLANE AND AXISYMMETRIC STEADY FLOWS WITH VISCOELASTIC EFFECTS

2004 ◽  
Vol 3 (2) ◽  
Author(s):  
R. L. Thompson ◽  
P. R. Souza Mendes
Keyword(s):  
Constitutive Equation ◽  
Extensional Flow ◽  
Body Motion ◽  
Simple Shear Flow ◽  
Steady Flows ◽  
Complex Flow ◽  
Dimensionless Numbers ◽  
Dissipative Part ◽  
Viscosity Effects ◽  
Viscoelastic Effects

Non-Newtonian materials respond differently when submitted to shear or extension. A constitutive equation in which the stress is a function of both the rate of deformation and on the type of the flow is proposed and analyzed theoretically. It combines information obtained in shear, extension and rigid body motion in all regions of complex flow. The analysis has shown how to insert some elastic effects in a constitutive equation that depends only on the present time and position. One advantage of the model is that all the steady rheological functions in simple shear flow and in extensional flow are predicted exactly. Another important property that is included is the split of the extensional viscosity in two parts: one dissipative part that is related to the shear viscosity and an elastic part that is related to the first and second normal stress coefficients in shear. A discussion involving the dimensionless numbers that relate elastic and viscosity effects is also given.

scholarly journals AN EXPLICIT CONSTITUTIVE EQUATION FOR PLANE AND AXISYMMETRIC STEADY FLOWS WITH VISCOELASTIC EFFECTS

2004 ◽  
Vol 3 (2) ◽  
pp. 134
Author(s):  
R. L. Thompson ◽  
P. R. Souza Mendes
Keyword(s):  
Constitutive Equation ◽  
Extensional Flow ◽  
Body Motion ◽  
Simple Shear Flow ◽  
Steady Flows ◽  
Complex Flow ◽  
Dimensionless Numbers ◽  
Dissipative Part ◽  
Viscosity Effects ◽  
Viscoelastic Effects

Non-Newtonian materials respond differently when submitted to shear or extension. A constitutive equation in which the stress is a function of both the rate of deformation and on the type of the flow is proposed and analyzed theoretically. It combines information obtained in shear, extension and rigid body motion in all regions of complex flow. The analysis has shown how to insert some elastic effects in a constitutive equation that depends only on the present time and position. One advantage of the model is that all the steady rheological functions in simple shear flow and in extensional flow are predicted exactly. Another important property that is included is the split of the extensional viscosity in two parts: one dissipative part that is related to the shear viscosity and an elastic part that is related to the first and second normal stress coefficients in shear. A discussion involving the dimensionless numbers that relate elastic and viscosity effects is also given.

Viscosity Effects on Mach Reflection in Steady Flows

2008 ◽  
Author(s):  
Yevgeniy Bondar ◽  
Dmitry Khotyanovsky ◽  
Alexey Kudryavtsev ◽  
Georgy Shoev ◽  
Mikhail Ivanov
Keyword(s):  
Mach Reflection ◽  
Steady Flows ◽  
Viscosity Effects

Numerical Simulation of Dynamics on Plant Fibers Suspension in Shear-Planar Extensional Flow

2014 ◽  
Vol 1056 ◽  
pp. 66-69 ◽  
Author(s):  
Zan Huang
Keyword(s):  
Differential Equation ◽  
Numerical Simulation ◽  
Flow Field ◽  
Mathematical Simulation ◽  
Extensional Flow ◽  
Simulation Method ◽  
Complex Flow ◽  
Plant Fibers ◽  
Fibers Orientation ◽  
Planar Extensional Flow

A mathematical simulation method is applied to simulate dynamics on plant fibers suspensions in shear-planar extensional flow. Furthermore, the result of differential equation on plant fibers orientation can be obtained in complex flow field.

scholarly journals Simulations Of Steady Flows Through Cylindrical Geometries With And Without Local Constrictions By Multiparticle Collision Dynamics

2021 ◽  
Author(s):  
Salil K. Bedkihal
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Steady Flows ◽  
Particle Interactions ◽  
Collision Dynamics ◽  
Complex Flow ◽  
Multiparticle Collision Dynamics ◽  
Complex Particle

In this thesis, a recently developed particle-based method called multiparticle collision dynamics (MPC) is used to simulate steady flows through three-dimensional constricted axisymmetric cylinders. The work is motivated by complex particle interactions in blood flow such as aggregation and the need to be able to capture these effects in physiologically relevant complex flow geometries. This is the first time that MPC dynamics has been applied to simulate flows though constrictions. The particle collisions in MPC dynamics are numerically more efficient than other particle-based simulation methods. Particle interactions with the cylinder walls are modeled using bounce-back (BB) and loss in tangential, reversal of normal (LIT) boundary conditions. BB is an analog of the macroscopic no-slip boundary condition, and LIT gives slip. Finally, an averaging procedure is employed to make a connection with the solution to the Navier-Stokes equations. Interesting differences have been found in the velocity profiles obtained using MPC with BB and LIT, compared to Navier-Stokes.

Viscoelastic Effects in Helical Flows of Polymer Fluids

2001 ◽  
Author(s):  
Jae-Hyeuk Jeong ◽  
Arkady I. Leonov
Keyword(s):  
Experimental Data ◽  
Constitutive Equation ◽  
Viscoelastic Properties ◽  
Helical Flow ◽  
Simple Shearing ◽  
Polymer Fluids ◽  
Viscoelastic Effects

Abstract The paper shows that detailed viscoelastic properties of helical flow can be exactly determined from those known for simple shearing as soon as a constitutive equation is specified. This paper also demonstrates the calculated characteristics of helical flow compared with experimental data.

Simple shear flow of a suspension of fibres in a dilute polymer solution at high Deborah number

1993 ◽  
Vol 252 ◽  
pp. 187-207 ◽  
Author(s):  
O. G. Harlen ◽  
Donald L. Koch
Keyword(s):  
Shear Flow ◽  
Extensional Flow ◽  
Normal Stress Difference ◽  
Deborah Number ◽  
Simple Shear Flow ◽  
Stress Difference ◽  
Fluid Analysis ◽  
Dilute Polymer Solutions ◽  
Fibre Suspensions ◽  
The Mean

The behaviour of fibre suspensions in dilute polymer solutions at high Deborah numbers is analysed. In particular, we calculate the change to the extension of the polymers and the orientation of the fibres caused by hydrodynamic interactions between the polymers and the fibres. At a sufficiently high Deborah number the combined effect of the fibre velocity disturbances and the mean shear flow produce a dramatic increase in the extension of the polymers, similar to the coil-stretch transition observed in extensional flow.The non-Newtonian stresses caused by the polymers produce a perturbation to the angular velocity of the fibres, giving rise to a net drift across Jeffery orbits towards the vorticity axis. Unlike the second-order-fluid analysis of Leal (1975), this effect does not depend on the second-normal-stress difference.

The constitutive equation for a dilute emulsion

1970 ◽  
Vol 44 (1) ◽  
pp. 65-78 ◽  
Author(s):  
N. A. Frankel ◽  
Andreas Acrivos
Keyword(s):  
Constitutive Equation ◽  
Numerical Solutions ◽  
Extensional Flow ◽  
Small Deformation ◽  
Order Theory ◽  
Droplet Surface ◽  
Time Dependent ◽  
Deformation Analysis ◽  
First Order Theory ◽  
Freely Suspended

A constitutive equation for dilute emulsions is developed by considering the deformations, assumed infinitesimal, of a small droplet freely suspended in a time-dependent shearing flow. This equation is non-linear in the kinematic variables and gives rise to ‘fluid memory’ effects attributable to the droplet surface dynamics. Furthermore, it has the same form as the corresponding expression for a dilute suspension of Hookean elastic spheres (Goddard & Miller 1967), and reduces to a relation previously proposed by Schowalter, Chaffey & Brenner (1968) when time-dependent effects become small.Numerical solutions are also presented for the case of a small bubble in a steady extensional flow for the purpose of estimating the range of validity of the small deformation analysis. It is shown that, unlike the drag of a bubble which, in creeping motion, is known to be relatively insensitive to its exact shape, the macroscopic stress field in an emulsion is not well described by the present analysis unless the shapes of the deformed bubbles agree closely with those given by the first-order theory. Thus, the present rheological equation should prove of value in a qualitative rather than a quantitative sense.

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