Maxwell fluids tensile stress

Figure 9.11. Tensile stress divided by SXGye as a function of reduced time for a single mode of a Maxwell fluid. Reprinted with permission from Denn and Marrucci, AIChE /., 17,101 (1971). Copyright American Institute of Chemical Engineers.

Figure 9.12. Tensile stress divided by ye as a function of reduced time for a two-mode Maxwell fluid, rj is the viscosity and X is the mean relaxation time. Reprinted from Denn, in R. S. Rivlin, ed.. The Mechanics of Viscoelastic Fluids, AMD Vol. 22, ASME, New York, 1977, p. 101.

Note that the natural length scale LDe is kvo. The grouping BDeL/do is simply the initial spinline stress divided by the tensile (Young s) modulus, 3G. The initial ratio of the radial to axial extra stress, Xrr )/vzz(S>)> is required. As F oo (B oo) the velocity profile approaches the straight line 1 -I- z/LDe, and there is a maximum achievable draw ratio Dr = vl/vo = 1-1- De. This result is the analog of the infinite force in a Maxwell fluid at a finite rate of extension. 

As shown in Figure 15.4, the sudden application of stress to a Maxwell element causes an instantaneous stretching of the spring to an equilibrium value of xJG (or aJE if a tensile stress is applied), where Xg is the constant applied shear stress (or Og is the constant applied extensional stress). The dashpot extends linearly with time with a slope of xjx] (or Maxwell element is a fluid, because it will continue to deform as long as it is stressed. The creep response of a Maxwell element is therefore... 

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