Study on the constitutive equation with fractional derivative for the viscoelastic fluids - Modified Jeffreys model and its application

1998 ◽  
Vol 37 (5) ◽  
pp. 512-517 ◽  
Author(s):  
D. Y. Song ◽  
Ti Qian Jiang
Keyword(s):  
Constitutive Equation ◽  
Fractional Derivative ◽  
Viscoelastic Fluids ◽  
Jeffreys Model

Application of Dynamic Fractional Differentiation to the Study of Oscillating Viscoelastic Medium With Cylindrical Cavity

2002 ◽  
Vol 124 (4) ◽  
pp. 642-645 ◽  
Author(s):  
D. Ingman ◽  
J. Suzdalnitsky
Keyword(s):  
Constitutive Equation ◽  
Fractional Derivative ◽  
Cylindrical Cavity ◽  
Viscoelastic Medium ◽  
Viscoelastic Behavior ◽  
Additional Term ◽  
Variable Order ◽  
Fractional Differentiation ◽  
Order Function ◽  
Damping Effect

Oscillations of a viscoelastic medium with a cylindrical cavity are studied. The viscosity is taken into account in the form of an additional term in the constitutive equation, proportional to a fractional derivative of variable order. In the considered examples the order function corresponds to dependences obtained for real materials. A damping effect is observed in the amplitude behavior. The field which determines the order function demonstrates the viscoelastic behavior of the material under load.

scholarly journals Modeling the initial mechanical response and yielding behavior of gelled crude oil

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 292-301 ◽  
Author(s):  
Chen Lei ◽  
Liu Gang ◽  
Lu Xingguo ◽  
Xu Minghai ◽  
Tang Yuannan
Keyword(s):  
Shear Stress ◽  
Constitutive Equation ◽  
Crude Oil ◽  
Shear Strain ◽  
Mechanical Response ◽  
Shear Rates ◽  
Mechanical Analog ◽  
Constant Shear ◽  
Jeffreys Model ◽  
Yielding Behavior

Abstract The initial mechanical response and yielding behavior of gelled crude oil under constant shear rate conditions were investigated. By putting the Maxwell mechanical analog and a special dashpot in parallel, a quasi-Jeffreys model was obtained. The kinetic equation of the structural parameter in the Houska model was simplified reasonably so that a simplified constitutive equation of the special dashpot was expressed. By introducing a damage factor into the constitutive equation of the special dashpot and the Maxwell mechanical analog, we established a constitutive equation of the quasi-Jeffreys model. Rheological tests of gelled crude oil were conducted by imposing constant shear rates and the relationship between the shear stress and shear strain under different shear rates was plotted. It is found that the constitutive equation can fit the experimental data well under a wide range of shear rates. Based on the fitted parameters in the quasi-Jeffreys model, the shear stress changing rules of the Maxwell mechanical analog and the special dashpot were calculated and analyzed. It is found that the critical yield strain and the corresponding shear strain where shear stress of the Maxwell analog is the maximum change slightly under different shear rates. And then a critical damage softening strain which is irrelevant to the shearing conditions was put forward to describe the yielding behavior of gelled crude oil.

Continuum Theories for the Viscoelasticity of Flexible Homogeneous Polymeric Liquids

2007 ◽  
Author(s):  
Chang Dae Han
Keyword(s):  
Constitutive Equation ◽  
Flow Field ◽  
Polymer Blend ◽  
Constitutive Equations ◽  
Viscoelastic Fluids ◽  
Phenomenological Approach ◽  
The State ◽  
Momentum Balance ◽  
Molecular Approach ◽  
Balance Equations

There are two primary reasons for seeking a precise mathematical description of the constitutive equations for viscoelastic fluids, which relate the state of stress to the state of deformation or deformation history. The first reason is that the constitutive equations are needed to predict the rheological behavior of viscoelastic fluids for a given flow field. The second reason is that constitutive equations are needed to solve the equations of motion (momentum balance equations), energy balance equations, and/or mass balance equations in order to describe the velocity, stress, temperature, and/or concentration profiles in a given flow field that is often encountered in polymer processing operations. There are two approaches to developing constitutive equations for viscoelastic fluids: one is a continuum (phenomenological) approach and the other is a molecular approach. Depending upon the chemical structure of a polymer (e.g., flexible homopolymer, rigid rodlike polymer, microphase-separated block copolymer, segmented multicomponent polymers, highly filled polymer, miscible polymer blend, immiscible polymer blend), one may take a different approach to the formulation of the constitutive equation. In this chapter we present some representative constitutive equations for flexible, homogeneous viscoelastic liquids that have been formulated on the basis of the phenomenological approach. In the next chapter we present the molecular approach to the formulation of constitutive equations for flexible, homogeneous viscoelastic fluids. In the formulation of the constitutive equations using a phenomenological approach, emphasis is placed on the relationship between the components of stress and the components of the rate of deformation (or strain) or deformation (or strain) history, such that the responses of a fluid to a specified flow field or stress can adequately be described. The parameters appearing in a constitutive equation are supposed to represent the characteristics of the fluid under consideration. More often than not, the parameters appearing in a phenomenological constitutive equation are determined by curve fitting to experimental results. Thus phenomenological constitutive equations shed little light on the effect of the molecular parameters of the fluid under investigation to the rheological responses of the fluid.

Selection of kernel functions used in a new constitutive equation for viscoelastic fluids

1986 ◽  
Vol 25 (3) ◽  
pp. 214-224
Author(s):  
B. Tremblay ◽  
J. M. Piau ◽  
P. J. Carreau
Keyword(s):  
Constitutive Equation ◽  
Viscoelastic Fluids ◽  
Kernel Functions ◽  
Selection Of
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