Nonlinear viscoplastic flow

FIGURE 8.7 Non-Newtonian flow behavior, a Structural viscosity (for high molecular solution). b Dilatant flow (suspension with high concentration), c Viscoplastic with flow limits 1, ideal plastic 2 or 3, nonlinear plastic flow, d 1, thixotropy flow 2, antithixotropy flow 3, viscoelastic flow e rheopexy flow. 

Fluoropolymers, as well as other thermoplastics, exhibit a complicated nonlinear response when subjected to loads. The behavior is characterized by initial linear viscoelasticity at small deformations, followed by distributed yielding, viscoplastic flow, and material stiffening at large deformations until ultimate failure occurs. The response is further complicated by a strong dependence on strain rate and temperature, as illustrated in Fig. 11.1. It is clear that higher deformation rates and lower temperatures increase the stiffness of the material. 

The motion of plastic fluids with finite yield stress to has some qualitative specific features not possessed by nonlinearly viscous fluids. Let us consider a layer of a viscoplastic fluid on an inclined plane whose slope is gradually varied. It follows from (6.2.5) that, irrespective of the rheological properties of the medium, the tangential stress decreases across the film from its maximum value Tjnax = pgh sin a on the solid wall to zero on the free surface. Therefore, a flow in a film of a viscoplastic fluid can be initiated only when the tangential stress on the wall becomes equal to or larger than the yield stress to ... 

Following [47, 443, 444], let us consider absorption of weakly soluble gases on the surface of a fluid film flowing down an inclined plane. The steady-state velocity distribution inside the film is given by (6.2.8) for nonlinearly viscous fluids and by (6.2.17) for viscoplastic fluids. 

Up to the different notation (APjL -> pg sin a), formula (6.4.15) coincides with the expression (6.2.5) for shear stresses, which was obtained earlier for film flows. Therefore, we can calculate the velocity profile V in a plane channel (in the region 0 < < h), the maximum velocity f/max, and the mean flow rate velocity (V) for nonlinear viscous fluids by formulas (6.2.8)—(6.2.11) and for viscoplastic fluids by formulas (6.2.17)-(6.2.19) if we formally replace pg sin a by AP/L in these formulas. 

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