A constitutive equation is a relation between the extra stress (t) and the rate of deformation that a fluid experiences as it flows. Therefore, theoretically, the constitutive equation of a fluid characterises its macroscopic deformation behaviour under different flow conditions. It is reasonable to assume that the macroscopic behaviour of a fluid mainly depends on its microscopic structure. However, it is extremely difficult, if not impossible, to establish exact quantitative [Pg.3]

Phan-Thien, N. and Tanner, R.T., 1977. A new constitutive equation derived from network theory, Non-Newtonian Fluid Mech. 2, 353-365. [Pg.16]

Single-integral constitutive equations for viscoelastic fluids [Pg.13]

Leslie F M 1968 Some constitutive equations for liquid crystals Arch. Ration. Mech. Analysis 28 265-83 [Pg.2569]

The Oldroyd-type differential constitutive equations for incompressible viscoelastic fluids can in general can be written as (Oldroyd, 1950) [Pg.11]

The Maxwell class of viscoelastic constitutive equations are described by a simpler form of Equation (1.22) in which A = 0. For example, the upper-convected Maxwell model (UCM) is expressed as [Pg.11]

Some of the integral or differential constitutive equations presented in this and the previous section have an exact equivalent in the other group. There are, however, equations in both groups that have no equivalent in the other category. [Pg.14]

A frequently used example of Oldroyd-type constitutive equations is the Oldroyd-B model. The Oldroyd-B model can be thought of as a description of the constitutive behaviour of a fluid made by the dissolution of a (UCM) fluid in a Newtonian solvent . Here, the parameter A, called the retardation time is de.fined as A = A (r s/(ri + s), where 7]s is the viscosity of the solvent. Hence the extra stress tensor in the Oldroyd-B model is made up of Maxwell and solvent contributions. The Oldroyd-B constitutive equation is written as [Pg.12]

All of the described differential viscoelastic constitutive equations are implicit relations between the extra stress and the rate of deformation tensors. Therefore, unlike the generalized Newtonian flows, these equations cannot be used to eliminate the extra stress in the equation of motion and should be solved simultaneously with the governing flow equations. [Pg.12]

Model (material) parameters used in viscoelastic constitutive equations [Pg.9]

Doi, M. and Edwards, S.F., 1978. Dynamics of concentrated polymer systems 1. Brownian motion in equilibrium state, 2. Molecular motion under flow, 3. Constitutive equation and 4. Rheological properties. J. Cheni. Soc., Faraday Trans. 2 74, 1789, 1802, 1818-18.32. [Pg.15]

In the decoupled scheme the solution of the constitutive equation is obtained in a separate step from the flow equations. Therefore an iterative cycle is developed in which in each iterative loop the stress fields are computed after the velocity field. The viscous stress R (Equation (3.23)) is calculated by the variational recovery procedure described in Section 1.4. The elastic stress S is then computed using the working equation obtained by application of the Galerkin method to Equation (3.29). The elemental stiffness equation representing the described working equation is shown as Equation (3.32). [Pg.85]

As already discussed, in general, polymer flow models consist of the equations of continuity, motion, constitutive and energy. The constitutive equation in generalized Newtonian models is incorporated into the equation of motion and only in the modelling of viscoelastic flows is a separate scheme for its solution reqixired. [Pg.71]

Other combinations of upper- and lower-convected time derivatives of the stress tensor are also used to construct constitutive equations for viscoelastic fluids. For example, Johnson and Segalman (1977) have proposed the following equation [Pg.12]

In general, the utilization of integral models requires more elaborate algorithms than the differential viscoelastic equations. Furthermore, models based on the differential constitutive equations can be more readily applied under general concUtions. [Pg.80]

See also in sourсe #XX -- [ Pg.695 ]

See also in sourсe #XX -- [ Pg.5 , Pg.6 ]

See also in sourсe #XX -- [ Pg.71 , Pg.84 , Pg.97 ]

See also in sourсe #XX -- [ Pg.544 ]

See also in sourсe #XX -- [ Pg.4 , Pg.97 , Pg.104 , Pg.157 , Pg.169 , Pg.170 , Pg.171 , Pg.172 , Pg.173 ]

See also in sourсe #XX -- [ Pg.21 , Pg.29 , Pg.31 , Pg.107 , Pg.156 ]

See also in sourсe #XX -- [ Pg.140 , Pg.141 , Pg.510 , Pg.703 ]

See also in sourсe #XX -- [ Pg.272 , Pg.281 ]

See also in sourсe #XX -- [ Pg.7 , Pg.543 ]

See also in sourсe #XX -- [ Pg.36 ]

See also in sourсe #XX -- [ Pg.2 , Pg.10 ]

See also in sourсe #XX -- [ Pg.461 ]

See also in sourсe #XX -- [ Pg.111 ]

See also in sourсe #XX -- [ Pg.351 ]

See also in sourсe #XX -- [ Pg.38 , Pg.44 , Pg.47 , Pg.390 ]

See also in sourсe #XX -- [ Pg.74 ]

See also in sourсe #XX -- [ Pg.6 , Pg.8 , Pg.17 , Pg.21 , Pg.24 , Pg.30 , Pg.42 , Pg.77 , Pg.82 , Pg.84 , Pg.95 , Pg.126 , Pg.132 ]

See also in sourсe #XX -- [ Pg.112 , Pg.113 , Pg.114 ]

See also in sourсe #XX -- [ Pg.2 , Pg.16 , Pg.260 , Pg.528 ]

See also in sourсe #XX -- [ Pg.443 , Pg.461 ]

See also in sourсe #XX -- [ Pg.384 , Pg.385 , Pg.386 , Pg.429 , Pg.430 , Pg.431 , Pg.432 , Pg.433 , Pg.434 ]

See also in sourсe #XX -- [ Pg.4 , Pg.6 , Pg.19 , Pg.505 ]

See also in sourсe #XX -- [ Pg.7 , Pg.130 ]

See also in sourсe #XX -- [ Pg.6 ]

See also in sourсe #XX -- [ Pg.341 ]

See also in sourсe #XX -- [ Pg.133 , Pg.142 ]

© 2019 chempedia.info