Steady shear behavior

The experimental [44, 64, 651, and computer simulation [661 results suggest that the shear stress t of an ER fluid can be well expressed with the Bingham equation  

Tjccy of the apparent viseosity t) on the strain rate A increases from 0.68 at 400 V/mm to 0.93 at 1000 V/mm [75J. This shear thinning phenomenon can be explained qualitatively with the model that the roughly prolate spheroidal droplets are assumed to form in the condensed FR phase [761- The shear flow will rotate the ellipsoidal droplets and thus the long axis will deviate from the direction of the electric field, leading to the weak 

The infinite shear-rate viscosity, was measured as 0.45 Pa. Reproduced with permission from T. C. Halsey, J.E. Martin, and D. Adolf Phys. Rev. Lett., 68(1992)1519. 

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Holden et al. (47) first noted the peculiar characteristics in the steady shear behavior of the SBS block copolymer melts. For a certain composition of styrene and butadiene, no limiting Newtonian viscosity was found at low shear rates. For some of the others, there exist two distinct viscosity vs. shear rate relationships (Figure 10). Arnold and Meier (73) carried out the experiments in oscillatory shear and found the same... 

Linear viscoelastic measurements can provide surprising insight into the steady shear behavior of many polymer melts through an empiricism known as the Cox-Merz rule. According to this relation, a plot of t] = [( ) + versus fre-... 

Goldstein C (1974) Transient and steady shear behavior of SBR polymers. Trans Soc Rheol 18 357-369... 

The two normal stress functions, Niiy) and N2iy), are referred to as the first and second normal stress differences, respectively. The former is positive and increases with increasing shear rate, as shown in Figure 19 (177,178), which describes the steady-shear behavior of the polymer melt in Figure 18. The stress... 

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]. 

Consistent with the Newtonian flow of concentrated PAMAM solutions, it was found that all three types of dendrimers [40, 41, 50] under steady-shear conditions, and both PAMAMs [40] and PPIs [50] under creep [16,50] showed typical viscous behavior at all applied stress levels and testing temperatures. For example, as illustrated in Figure 14.9 [40], all of the first seven generations of PAMAMs showed constant viscosities over the entire ranges of shear rates investigated, and in addition to this, there was no hysteresis between the forward and the reverse stress sweeps in steady shearing, indicating the absence of thixotropy. 

Fernandez et al. (2007) have characterized the rheological behavior of the mashed potatoes with added biopolymers using steady shear measurements. Fresh and frozen/thawed mashed potatoes present shear thinning with yield stress (Canet et al., 2005a), and dynamic shear data reveal weak gel-like behavior in potato purees (Alvarez et al., 2004). The effects are strongly... 

The Weissenbeig Rheogoniometer (49) is a complex dynamic viscometer that can measure elastic behavior as well as viscosity. It was the first rheometer designed to measure both shear and normal stresses and can be used for complete characterization of viscoelastic materials. Its capabilities include measurement of steady-state rotational shear within a viscosity range of 10-1 —13 mPa-s at shear rates of 10-4 — 104 s-1, of normal forces (elastic effect) exhibited by the material being sheared, and of an oscillatory shear range of 5 x 10-6 to 50 Hz, from which the elastic modulus and dynamic viscosity can be determined. A unique feature is its ability to superimpose oscillation on steady shear to provide dynamic measurements under flow conditions all measurements can be made over a wide range of temperatures (—50 to 400°C). 

The response of simple fluids to certain classes of deformation history can be analyzed. That is, a limited number of material functions can be identified which contain all the information necessary to describe the behavior of a substance in any member of that class of deformations. Examples are the viscometric or steady shear flows which require, at most, three independent functions of the shear rate (79), and linear viscoelastic behavior (80,81) which requires only a single function, in this case a relaxation function. The functions themselves must be determined experimentally for each substance. 

Such behavior is qualitatively understandable in terms of partial disentanglement in steady shear flow. In highly entangled systems (cM>gM )Je0 is of the form (Section 5) ... 

Studies have been made of the stresses produced in several non-steady flow histories. These include the buildup to steady state of a and pu — p22 at the onset of steady shearing flow (355-35 ) relaxation of stresses from their steady state values when the flow is suddenly stopped (356-360) stress relaxation after suddenly imposed large deformations (361) recoil behavior when the shear stress is suddenly removed after a steady state in the non-linear region has been reached (362) and parallel or transverse oscillations superimposed on steady shearing flow (363-367). Experimental problems caused by the inertia and compliance of the experimental apparatus are much more severe than in steady state measurements (368,369). Quantitative interpretations must therefore still be somewhat tentative. Nevertheless, the pattern of behavior emerging is suggestive with respect to possible molecular flow mechanisms. 

Graessley,W.W., Segal,L. Flow behavior of polystyrene systems in steady shearing flow. Macromolecules 2,49-57 (1969). 

Einaga,Y., Osaki,K., Kurata,M, Tamura,M. Creep behavior of polymer solutions. II. Steady-shear compliance of concentrated polystyrene solutions. Macromolecules 4, 87-92 (1971). 

The use of a rotating vane has become very popular as a simple to use technique that allows slip to be overcome (33,34). Alderman et al (35) used the vane method to determine the yield stress, yield strain and shear modulus of bentonite gels. In the latter work it is interesting to note that a typical toique/time plot exhibits a maximum torque (related to yield stress of the sample) after which the torque is observed to decrease with time. The fall in torque beyond the maximum point was described loosely as being a transition from a gel-like to a fluid-like behavior. However, it may also be caused by the development of a slip surface within the bulk material. Indeed, by the use of the marker line technique, Plucinski et al (15) found that in parallel plate fixtures and in slow steady shear motion, the onset of slip in mayonnaises coincided with the onset of decrease in torque (Fig. 8). These authors found slip to be present for... 

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