Shear flow extensional

Flow is generally classified as shear flow and extensional flow [2]. Simple shear flow is further divided into two categories Steady and unsteady shear flow. Extensional flow also could be steady and unsteady however, it is very difficult to measure steady extensional flow. Unsteady flow conditions are quite often measured. Extensional flow differs from both steady and unsteady simple shear flows in that it is a shear free flow. In extensional flow, the volume of a fluid element must remain constant. Extensional flow can be visualized as occurring when a material is longitudinally stretched as, for example, in fibre spinning. When extension occurs in a single direction, the related flow is termed uniaxial extensional flow. Extension of polymers or fibers can occur in two directions simultaneously, and hence the flow is referred as biaxial extensional or planar extensional flow. 

Section B This section is tapered so there will be pressure losses due to both shear and extensional flows. 

Indireet systematie forees transmitted through the hydrodynamie medium by movement or other partieles or externally applied flow fields (e.g. shear or extensional). 

The Giesekus criterion for local flow character, defined as

extensional flow, 0 in simple shear flow and — 1 in solid body rotation [126]. The mapping of J> across the flow domain provides probably the best description of flow field homogeneity current calculations in that direction are being performed in the authors laboratory. 

In simple shear flow where vorticity and extensional rate are equal in magnitude (cf. Eq. (79), Sect. 4), the molecular coil rotates in the transverse velocity gradient and interacts successively for a limited time with the elongational and the compressional flow component during each turn. Because of the finite relaxation time (xz) of the chain, it is believed that the macromolecule can no more follow these alternative deformations and remains in a steady deformed state above some critical shear rate (y ) given by [193] (Fig. 65) ... 

Any rheometric technique involves the simultaneous assessment of force, and deformation and/or rate as a function of temperature. Through the appropriate rheometrical equations, such basic measurements are converted into quantities of rheological interest, for instance, shear or extensional stress and rate in isothermal condition. The rheometrical equations are established by considering the test geometry and type of flow involved, with respect to several hypotheses dealing with the nature of the fluid and the boundary conditions the fluid is generally assumed to be homogeneous and incompressible, and ideal boundaries are considered, for instance, no wall slip. 

It is well known that LCB has a pronounced effect on the flow behavior of polymers under shear and extensional flow. Increasing LCB will increase elasticity and the shear rate sensitivity of the melt viscosity ( ). Environmental stress cracking and low-temperature brittleness can be strongly influenced by the LCB. Thus, the ability to measure long chain branching and its molecular weight distribution is critical in order to tailor product performance. 

This flow field is somewhat idealized, and cannot be exactly reproduced in practice. For example, near the planar surfaces, shear flow is inevitable, and, of course, the range of % and y is consequently finite, leading to boundary effects in which the extensional flow field is perturbed. Such uniaxial flow is inevitably transient because the surfaces either meet or separate to laboratory scale distances. 

Fig. 13. Streamlines and velocity profiles for two-dimensional linear flows with varying vorticity. (a) K = -1 pure rotation, (b) K = 0 simple shear flow, (c) K = 1 hyperbolic extensional flow. 

Flows that produce an exponential increase in length with time are referred to as strong flows, and this behavior results if the symmetric part of the velocity gradient tensor (D) has at least one positive eigenvalue. For example, 2D flows with K > 0 and uniaxial extensional flow are strong flows simple shear flow (K = 0) and all 2D flows with K < 0 are weak flows. 

Oscillatory shear experiments are the preferred method to study the rheological behavior due to particle interactions because they directly probe these interactions without the influence of the external flow field as encountered in steady shear experiments. However, phenomena that arise due to the external flow, such as shear thickening, can only be investigated in steady shear experiments. Additionally, the analysis is complicated by the different response of the material to shear and extensional flow. For example, very strong deviations from Trouton s ratio (extensional viscosity is three times the shear viscosity) were found for suspensions [113]. 

The step-strain experiments discussed above furnish the simplest example of a strong flow. Many other flows are of experimental importance transient and steady shear, transient extensional flow and reversing step strains, to give a few examples. Indeed the development of phenomenological constitutive equations to systematise the wealth of behaviour of polymeric liquids in general flows has been something of an industry over the past 40 years [9]. It is important to note that it is not possible to derive a constitutive equation from the tube model in... 

In industrial applications, emulsions are often obtained by exerting a crude stirring, made of a very complex combination of extensional and shearing flows. To study and understand the fragmentation process, the flow must be simplifled before... 

The mechanism of formation of jets such as that in Fig. 6 is not clear but apparently is associated with swelling of the La or L3 phase (the latter can also exist at very low surfactant concentrations, as shown in Fig. 1). The phenomenon resembles the tip streaming observed in drops of liquids subjected to shear or extensional flows with surfactants present [12,13]. In these cases shear stresses from the flow in the external phase cause the drop to elongate and form a jet with a conical shape similar to that seen in Fig. 6. No such external flow is present here, but perhaps flow inside the drop accompanying the swelling process produces a similar effect. 

J. Plucinski, R.K. Gupta and S. Chakrabarti, Shear and Extensional Rheology of Mayonnaises, presented at the Second International Conference on Extensional and Shear Flow of Polymer Fluids from the Solution to the Melt, St. Andrews, Scotland, June 19-22, 1994. 

Using this concept, Erwin [9] demonstrated that the upper bound for the ideal mixer is found in a mixer that applies a plane strain extensional flow or pure shear flow to the fluid and where the surfaces are maintained ideally oriented during the whole process this occurs when N = 00 and each time an infinitesimal amount of shear is applied. In such a system the growth of the interfacial areas follows the relation given by... 

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