Giesekus expression

This result is referred to as the Giesekus expression [62,86] and can be used to develop the form of the stress tensor for the rigid dumbbell model. Equation (7.63) for the rate of change of the second-moment tensor for this model is used to give the following result ... 

The simplest model for dilute polymer solutions is to idealize the polymer molecule as an elastic dumbbell consisting of two beads connected by a Hookean spring immersed in a viscous fluid (Fig. 2.1). The spring has an elastic constant Hq. Each bead is associated with a frictional factor C and a negligible mass. If the instantaneous locations of the two beads in space are riand r2, respectively, then the end-to-end vector, R = ri — ri, describes the overall orientation and the internal conformation of the polymer molecule. The polymer-contributed stress tensor can be related to the second-order moment of R. There are two expressions namely the Kramers expression and the Giesekus expression, respectively (Bird et al. 1987b) ... 

MIXED FLOW. Other flows with extensional components also have coil-stretch transitions. The smaller the extensional component is relative to the overall strain rate, the higher the overall strain rate at which the transition takes place (Giesekus 1962, 1966) A steady planar flow, for example, can be considered to be a mixture of a shearing and an extensional flow in such a mixed flow, the velocity gradient tensor, Vv, can be expressed as (Fuller and Leal 1980, 1981)... 

Sepehr et al. [2008] are investigating the viscoelastic Giesekus model [Giesekus, 1982, 1983 Bird et al., 1987] coupled with Eq. (16.41), with Dr described by Doi [1981]. The interactions between polymer and particles were incorporated following suggestions by Fan [1992] and Azaiez [1996]. These authors used Eq. (16.42) with the contribution to stress tensor caused by clay platelets [Eq. (16.43)] and viscoelastic Giesekus matrix expressed as [Fan, 1992]... 

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