Rheology defined

Incorporation of viscosity variations in non-elastic generalized Newtonian flow models is based on using empirical rheological relationships such as the power law or Carreau equation, described in Chapter 1. In these relationships fluid viscosity is given as a function of shear rate and material parameters. Therefore in the application of finite element schemes to non-Newtonian flow, shear rate at the elemental level should be calculated and used to update the fluid viscosity. The shear rale is defined as the second invariant of the rate of deformation tensor as (Bird et at.., 1977)... 

Molecular Weight. The range of molecular weights of commercial LLDPE resias is relatively narrow, usually from 50,000 to 200,000. One accepted parameter that relates to the resin molecular weight is the melt index, a rheological parameter which, broadly defined, is inversely proportional to molecular weight. A typical melt index range for LLDPE resias is from 0.1 to 5.0, but can reach over 30 for some appHcations. 

Extensional Viscosity. In addition to the shear viscosity Tj, two other rheological constants can be defined for fluids the bulk viscosity, iC, and the extensional or elongational viscosity, Tj (34,49,100—107). The bulk viscosity relates the hydrostatic pressure to the rate of deformation of volume, whereas the extensional viscosity relates the tensile stress to the rate of extensional deformation of the fluid. Extensional viscosity is important in a number of industrial processes and problems (34,100,108—110). Shear properties alone are insufficient for the characterization of many fluids, particularly polymer melts (101,107,111,112). 

Fillers may be broadly defined as solid particulates or fibrous materials, substantially inert chemically, incorporated in polymer compositions to modify the properties and/or to reduce cost. Cost reduction is not the primary reason to incorporate fillers in adhesives but they are used to impart specific properties such as flow, improved adhesion, mechanical, thermal, electrical and optical properties, chemical and weather resistance, and rheological behaviour. 

The rheology, for a polymer system with a melt index of 1.0, was defined by Equations 9 to 11. 

In shear studies, the most commonly used type of device for the generation of well-defined flow fields is the rotational viscometer. The use of these devices for the rheological characterization of liquids is well established [137]. Compared with the capillary and jet devices (Sects. 5.1 and 5.2), rotational viscometers allow the investigation of the effects of continuous rather than intermittent shearing. 

The drawback with the use of the Gillmore needle is that it is not a test of any well-defined rheological property, but of resistance to indentation. 

Compatibility is a difficult property to define. It will include effects on colour and rheology, but lack of this property may manifest as coagulation, loss of corrosion inhibition, deactivation of defoamers, etc. 

To characterize rheological behavior of materials, some basic terms need to be defined. Consider a liquid material that is subjected to a shearing force as illustrated in Fig. 2. The liquid is assumed to consist of a series of parallel layers with the surface area A, the bottom layer being fixed. When a force is applied on the top layer, the top plane moves at a constant velocity, whereas each lower layer moves with a velocity directly proportional to its distance from the stationary bottom layer. The velocity gradient (dv/dr, the difference in velocity, dv, between the top and bottom planes of liquid separated by the distance, dr) is also called the rate of shear, G ... 

Newtonian flow, and their viscosity is not constant but changes as a function of shear rate and/or time. The rheological properties of such systems cannot be defined simply in terms of one value. These non-Newtonian phenomena are either time-independent or time-dependent. In the first case, the systems can be classified as pseudoplastic, plastic, or dilatant, in the second case as thixotropic or rheopective. 

Rheological studies explore the flow of a material as an external force acts upon it. This flow depends not only on the magnitude and directionality of the external force, but also on the molecular composition and structure of the material that experiences the force. In this chapter, we will focus on the flow behavior of molten polymers, as it relates to their molecular structure. It is important to note that the molecular characteristics that determine a molten polymer s behavior also define the polymer s solid state behavior. Therefore, many of the concepts introduced in this chapter will reappear in Chapter 8, Solid State Properties of Polymers., ... 

The dissipation factor of a polymer (which we also refer to as tan 5) is the ratio of energy lost to the energy stored when it is placed in an alternating field. The dissipation factor is analogous to a mechanical tan 8 describing rheological behavior. The dissipation factor at a specific frequency is defined according to Eq. 8.14. 

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