Biaxial flow/viscosity

Analyze lubricated squeezing flow to determine biaxial extensional viscosity (T)R), which is calculated from biaxial stress (cB) and biaxial extensional strain rate (eB). 

The sample is subjected to compression by moving the crosshead downwards at a constant speed. The sample is extruded from between the two discs, undergoing elongational or biaxial flow the sample is stretched radially and azimuthally as it flows outwards between the approaching discs. Lubrication ensures that shear flow cannot occur. Elongational viscosity is calculated directly from the measured force-distance data, disc radius and crosshead speed no rheological model is required (Campanella and Peleg, 2002). 

Here uniaxial and biaxial (compression) elongation viscosity of a 1% polyacrylamide in a glycerine-water system is shown. Note that the material shows a reasonably constant resistance to biaxial (compression) elongation, but quite an increase in uniaxial extension with increasing extension rate. This has implications for processing of this fluid using predominantly uniaxial or biaxial flows. 

Furthermore, when this flow is looked upon as biaxial stretching, it is thought of as being generated by a radial, tensile stress rather than an axial, compressive stress. Thus, the biaxial extensional viscosity is defined as... 

The elongation viscosity defined by Equation (1.19) represents a uni-axial extension. Elongational flows based on biaxial extensions can also be considered. In an equi-biaxial extension the rate of deformation tensor is defined as... 

Extensional Viscosity. AH three types of extensional viscosity can be measured (101,103) uniaxial, biaxial, and pure shear. Only a few commercial instmments are available, however, and most measurements are made with improvised equipment. Extensional viscosity of polymer melts can be estimated from converging flow (entrance pressure) or from a melt strength drawdown test (208). 

Compression of a weakly structured food between parallel plates may achieve squeezing flow (Steffe, 1996). When lubricated parallel plates are used, the result is a form of biaxial extension. Biaxial extension may be used to measure biaxial viscosity, which is a reflection of resistance to radial stretching flow in a plane. Lubricated squeezing flow of a semi-solid... 

The fluctuation relations for the viscosities have also been generalised to biaxial nematic liquid crystals. They have been evaluated numerically for a biaxial version of the Gay-Beme fluid consisting of a linear string of oblate Gay-Beme ellipsoids, the axes of which point in the same direction. The flow... 

Hydrodynamic Retardation. Smoluchowski assumed in the derivation of his equations that )pair = Z)1+Z)2, but this is not true if the diffusing particles are relatively close to each other. When two particles come close, the liquid between them has to flow out of the gap, and this means that (a) the local velocity gradient is increased and (b) the flow type becomes biaxial elongation rather than simple shear (see Section 5.1). Both factors cause the effective viscosity to be increased, which means in turn that the mutual diffusion coefficient of the particles is decreased, the more so as the particle separation (h) is smaller. The phenomenon is called the Spielman-Honig effect. 

In the extensional, irrotational field, under steady state conditions, the particles remain oriented in the direction of stress. In uniaxial flow, they align with the main axis in the flow direction, while in biaxial they lie on the stretch plane [Batchelor, 1970, 1971]. For dilute spherical suspensions in Newtonian liquid the extensional viscosity follows the Trouton rule, i.e., = 3q. 

The only way to generate data for this type of unsteady biaxial tensile flow is to instrument a blown film machine. The tensile viscosity, defined by Eq. (5.16), hardly changes with the tensile strain rate. Figure 5.15 shows data for the uniaxial stretching of an LDPE and an HDPE. The apparent tensile viscosity increases with strain rate for the more elastic LDPE, in contrast with the non-Newtonian reduction in viscosity in shear flows. 

Three main types of elongational flow are uniaxial, biaxial, and planar. Although resistance to flow can be referred to loosely as an elongational or extensional viscosity (which further depends upon the type of elongational flow), this parameter generally is not constant. 

Extensive reviews [6-10] and a monograph [11] summarize the literature covering significant aspects of extensional flows in various commercial processes, theoretical treatment for ttie hydrod)mamics of such flows and different methods of determining material functions such as uniaxial, biaxial and planar extensional viscosities. 

If we want to find out how a fluid behaves under extension, we have to somehow grip and stretch it. Experimentally, this is much more difficult than the shear arrangement, especially if the fluid has a low viscosity. Earlier (see Section 5) we saw that it is possible to classify steady extensional flows under the categories of uniaxial, biaxial and planar flows. We will now examine uniaxial testing, since this mode is more commonly employed as a routine characterization tool. Here we encounter two approaches the first seeks to impart a uniform extensional field and back out a true material function, while the second employs a mixed flow field that is rich in its extensional component (e.g. converging flows) and use it to back out a measured property of the fluid which is somehow related to its extensional viscosity. 

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