Tumbling flow/viscosity

Turbulence proprieties. Used to describe an erratic, tumbling flow of liquid elastomer through a mold or cavity during filling. Usually caused by poor mold design, incorrect location of the polyurethane pouring point, obstructions in the mold or cavity, or high polyurethane viscosity. 

The term p, V2u> reveals that vorticity (i.e., the strength of fluid rotation) can diffuse by molecular interactions throughout a flow field, with the viscosity being the diffusion coefficient. Quite often the source of vorticity is the fluid tumbling caused by the shearing action associated with a no-slip condition on a solid wall. This vorticity, once produced, is both convected and diffused throughout the flow. The relative strength of the convective and diffusive processes depends on the flow field and the viscosity. 

A second requirement for this instability to occur is that the two Leslie viscosity coefficients tt2 and Oi are of opposite signs [276,312]. If the ratio between the two viscosities is positive, the director exhibits different dynamics it aligns with respect to the velocity at an angle 6I9 such that tan (6b) = a2/ 3- Note finally that, despite a complex microstructure, the classification in terms of flow-aligning and tumbling nematics, as defined for low molecular weight liquid-crystals, still applied to lyotropic systems. 

If the director is free to rotate there will be either a rotation to a stable orientation (flow alignment, see Fig. 6) or a continuous rotation (tumbling) under the influence of the shear gradient. Which case is observed depends on the signs of 2 and a. Because of thermodynamical arguments (see Sect. 8.1.9) the rotational viscosity coefficient must be positive. 

An alternative to reorientation of the sample or the magnetic field is the application of shear during the NMR measurement [130-134]. For liquid-crystalline samples with high viscosity, such as liquid crystal polymers, the steady-state director orientation is governed by the competition between magnetic and hydrodynamic torques. Deuteron NMR can be used to measure the director orientation as a function of the applied shear rate and to determine two Leslie coefficients, and aj, of nematic polymers [131,134]. With this experiment, flow-aligning and tumbling nematics can be discriminated. Simultaneous measurement of the apparent shear viscosity as a function of the shear rate makes it possible to determine two more independent viscosity parameters [131, 134]. 

Figure 11 demonstrates the application of deuteron NMR spectroscopy on sheared samples with the simultaneous measurement of the viscosity to two different nematic polymer systems. The different behavior of these systems is apparent from the data one system is flow-aligning, the other system is tumbling. The Leslie eoefficients and 3 obtained for the shear-aligning system are both negative, whereas and 3>0 for the tumbling system. Deuteron NMR has also been employed to study the director orientation of lyotropic lamel-... 

The curve for 4-n-pentyloxybenzylidene-4 - -butylaniline (50-4) shows some remarkable deviations from this course [56]. These are caused by pretransitional effects from a smectic phase at low temperatures. Due to these effects the range of flow alignment is limited to a small region below the clearing point. At lower temperatures the director begins to tumble and a viscosity between and % is observed. This leads to the pronounced minimum in the T curve for 50-4. A further deviation is caused by the divergence of rj at the transition to the smeetic phase. 

Equations (4.8)-(4.10) have been solved in simple steady state shear flow using Mathematica software (Leonov and Chen 2010). The stress components are expressed as function of shear rate y with the values of constitutive parameters 00, a,p, r, r2,Xe, and t o. Here Oq and t]o represent relaxation time and zero shear viscosity respectively. The other parameters XgandXv represent the tumbling for elasticity and viscosity. Rest of the characteristic parameters a,p,ri,r2 represent anisotropic properties of liquid crystal polymers. Among the eight parameters, only relaxation time and zero shear viscosity are determined from experimental data. The other six parameters can be obtained from cinve fitting data using the Mathematica software. 

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