A Rheological Equation of State which Predicts Non‐Newtonian Viscosity, Normal Stresses, and Dynamic Moduli

1955 ◽  
Vol 26 (7) ◽  
pp. 889-894 ◽  
Author(s):  
T. W. DeWitt
Keyword(s):  
Equation Of State ◽  
Normal Stresses ◽  
Dynamic Moduli ◽  
Newtonian Viscosity ◽  
Rheological Equation ◽  
Rheological Equation Of State

scholarly journals Semi-analytical solution for the problem of extended Pom-Pom fluid flow in a round pipe

2021 ◽  
Vol 2057 (1) ◽  
pp. 012007
Author(s):  
A I Kadyirov ◽  
E K Vachagina
Keyword(s):  
Experimental Data ◽  
Fluid Flow ◽  
Analytical Solution ◽  
Solution Method ◽  
Parametric Method ◽  
Single Equation ◽  
Weissenberg Number ◽  
Normal Stresses ◽  
Rheological Equation ◽  
Rheological Equation Of State

Abstract A semi-analytical solution to the problem of the steady flow of viscoelastic single equation eXended Pom-Pom (XPP) fluid in a round pipe using the four-mode rheological equation of state of XPP is presented. An original parametric method for solving the set problem is used. The resulting method is applicable for solving a similar problem in a flat slit. The developed solution method is tested by comparing it with numerical results and experimental data. Using a polyacrylamide solution as an example, the influence of the Weissenberg number on the axial velocity profiles and the components of normal stresses is studied.

The flow properties of two types of non-Newtonian fluid

1967 ◽  
Vol 302 (1468) ◽  
pp. 1-23 ◽  
Keyword(s):  
Shear Stress ◽  
Equation Of State ◽  
Flow Rate ◽  
Translational Motion ◽  
Flow Behaviour ◽  
Stress Rate ◽  
Newtonian Flow ◽  
Rheological Equation ◽  
Rheological Equation Of State ◽  
Particle Aggregates

The impulse theory of flow has been extended to include the rotational motion of the particles of the minority component of certain types of suspension which exhibit non-Newtonian flow behaviour. Some physical considerations are discussed for the flow of a suspension of identical rigid spheres dispersed in a continuous medium exhibiting Newtonian flow behaviour. Steady translational motion produces a steady state distribution of single spheres and multi-particle aggregates, consisting of two or more spheres, which are generated by shear induced collisions amongst the various species of particle. The present discussion is, however, limited to an ideal system consisting of single spheres and aggregates containing only two individual spheres, a multi-link bond being formed between colliding spheres. The two-particle aggregates are approximated to rigid ellipsoids, the rotational and translational motion of the aggregates and the associated hydrodynamic drag forces being considered in relation to the particle-mobility approximation. By specifying the way in which the bond formed between colliding spheres behaves under tension, an expression for the associated impulse has been developed which in turn yields the rheological equation of state. Two regions of flow are distinguished; with increasing flow rate the strength of the bond increases, ultimately reaching saturation at a particular flow rate. For a saturated bond the rheological equation of state is formally similar to that of an ideal Bingham plastic. An experimental technique has been developed which involves measurement of the whole of the transient flow behaviour of the fluids. The measurements yield the shear stress-rate of flow characteristics corresponding to both the initial and final rheological states of the fluids which exhibit thixotropic flow behaviour. Some experimental results are presented for a non-thixotropic fluid and for two fluids which exhibit thixotropic flow behaviour, the measurements being obtained with a coaxial cylinder viscometer. The rheological equations of state, derived by way of the impulse theory of flow, correlate favourably the shear stress-rate of flow measurements for all three fluids.

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