Viscoplastic systems

The results of the latest research into helical flow of viscoplastic fluids (media characterized by ultimate stress or yield point ) have been systematized and reported most comprehensively in a recent preprint by Z. P. Schulman, V. N. Zad-vornyh, A. I. Litvinov 15). The authors have obtained a closed system of equations independent of a specific type of rheological model of the viscoplastic medium. The equations are represented in a criterion form and permit the calculation of the required characteristics of the helical flow of a specific fluid. For example, calculations have been performed with respect to generalized Schulman s model16) which represents adequately the behavior of various paint compoditions, drilling fluids, pulps, food masses, cement and clay suspensions and a number of other non-Newtonian media characterized by both pseudoplastic and dilatant properties. 

The heat equation (Eq. 29) is coupled to the equations governing the mechanical response through the temperature dependence of the bulk viscoplastic strain rate (Eq. 3), the craze thickening rate (Eq. 22), and the thermal expansion in Eq. 1. The system of differential equations resulting from the finite element discretization of the energy balance in [9] is modified [57] to... 

As the shear stress reaches some value, xSchW(, the region of slow viscoplastic flow, known as Schwedov s region (Fig. IX-24, region II ), is observed in the system with almost undestroyed structure. In this region the shear strain is caused by fluctuational process of fracture and subsequent restoration of coagulation contacts. Due to the action of external pressures this process becomes directed in a certain way. Such mechanism of creep may be described analogously to the mechanisms of fluid flow, the description of which was developed by Ya.B. Frenkel and G. Eiring. 

At higher temperatures the semi-rigid domains become less and less rigid the system becomes viscoplastic, which means that the dynamic moduli become strongly strain dependent (see Fig 129). At 119°C the system behaves like an elastic liquid with less strain dependence. In Fig. 130 the various rheological regions are shown as a kind of phase diagram. 

Fig. 8.7. Mechanical models of viscoelastic and viscoplastic materials, built as systems containing spring and dashpot elements...

When the shear stress reaches a particular value, T chw. the system reveals a viscoplastic flow with an essentially preserved structure and enters the so-called Schwedow creep region (region II in Figures 3.20 and 3.21). In this region, shear is caused by the fluctuation process of the destruction and subsequent restoration of the coagulation contacts. Due to external stresses, this process becomes directional. This mechanism of creep may be considered by the analogy with the mechanism of flow of liquids developed by Frenkel [19]. 

Let us consider the uniform deformation of a unit volume of a disperse system under the condition of a steady-state viscoplastic flow or the slow stage of the elastic aftereffect under the action of a shear stress t. The system consists of flbers of length / and diameter d occupying the volume fraction V. The contact between the crossed flbers can be characterized by the average tangential friction force (which in turn characterizes the mean force of resistance to the shear motion in the contact), Ptg- The number of particles, v, per unit volume of the disperse system is... 

In the case of non-Newtonian behavior and especially in the case of viscoplastic behavior, such as that typical for moderately concentrated colloidal dispersions, Poiseuille s law gradually loses its validity. This happens because in the shear force-free central region close to the capillary axis, the structure of the concentrated colloidal system remains intact, so that the viscous shear exists only in the peripheral regions of the capillary. This process causes serious issues in the pumping of cement slurries or crude oil containing crystallizing phases. In laboratory practice, it is beneflcial to conduct such measurements in combination with other measurements that utilize uniform states. 

In Section 3.1, we examined the mechanical properties of disperse systems that were capable of undergoing viscoplastic flow. In these cases, we considered the stressed state of shear with its characteristic parameters G, ti, and t. The strength of such systems could be characterized by the yield point. When we shift to describing the mechanical behavior of compact and primarily elastic-brittle solids, it is worth using the stressed state of a uniaxial extension in which we replace the shear stress, T, with the extension stress, / the shear modulus G with Young s modulus, E and the resistance to tear, P, with the yield stress, t, as the strength characteristic. 

In order to illustrate the effect that the fittings loss has in laminar viscoplastic flow, a simple system consisting of 10 m of straight 50 mm ID pipe and 5 fittings - the loss coefficient of the above diaphragm valve in laminar flow is kv=946/Re3, and for turbulent flow is constant at kv= 2.5 - is set and analysed. The fluid used for the analysis is a viscoplastic paste (xy = 100 Pa, K = 1 Pas, relative density = 1.5 and n = 1). These values were chosen so as to present a relatively simple viscoplastic rheology which would yield laminar flow in a 50 mm pipe at 3 m/ s. 

The number of parameters to be identified is small energy and activation volume of the viscoplastic flow law based on Arrhenius s law (stress-assisted thermally activated slip). The experimental curves used during parameter adjustment are tensile curves, obtained at different rates. Unlike the Taylor or Sachs models, the previous mean-field homogenization models naturally predict a limited number of systems activated at low amplitude and a large number at high amplitude. Even at equal cumulated... 

Microstructural variations in terms of growth in subgrain size and reduction in dislocation density are shown in Fig. 6.16(a,b). The effect of strain rate is explained by the activation of a larger number of slip systems at low strain rate, due to the slightly higher viscoplastic strain amplitude. 

The contribution of phase heterogeneity (in the regions of I + LC and LC + CS of the phase diagram) to the viscoplastic behavior of LC polymers thus becomes clearer. The phase inhomogeneity of the system intensities the effects... 

A hypothesis was thus advanced concerning the determining role of the system of disclinations in the manifestation of the viscoplastic behavior of liquid crystals, which predicts the presence of a branch of Newtonian flow for very low shear rates or stresses. The schematic flow curve of LC polymers should be supplemented by another segment, illustrated in Fig. 9.13 by the broken line. 

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