Shear stress response

The transition strongly affects the molecular mobility, which leads to large changes in rheology. For a direct observation of the relaxation pattern, one may, for instance, impose a small step shear strain y0 on samples near LST while measuring the shear stress response T12(t) as a function of time. The result is the shear stress relaxation function G(t) = T12(t)/ < >, also called relaxation modulus. Since the concept of a relaxation modulus applies to liquids as well as to solids, it is well suited for describing the LST. 

Typical for the spectroscopic character of the measurement is the rapid development of a quasi-steady state stress. In the actual experiment, the sample is at rest (equilibrated) until, at t = 0, oscillatory shear flow is started. The shear stress response may be calculated with the general equation of linear viscoelasticity [10] (introducing Eqs. 4-3 and 4-9 into Eq. 3-2)... 

Sample changes during the measurement might cause severe problems. The shear stress response of a crosslinking system exemplifies this nicely ... 

Khachigian LM, Resnick N, Gimbrone MA Jr, Collins T. Nuclear factor-KB interacts functionally with the platelet-derived growth factor B-chain shear-stress response element in vascular endothelial cells exposed to fluid shear stress. / Clin Invest. 1995 96 1169-1175. 

Resnick N, Collins T, Atkinson W, Bonthron DT, Dewey CF Jr, Gimbron MA. Platelet-derived growth factor B chain promoter contains cis-acting fluid shear-stress responsive element. Proc Natl Acad Sci USA. 1993 90 7908. 

Let us assume that a sinusoidal shear strain z t) = Sq sin cot is imposed on a viscoelastic solid, where 8q and co are, respectively, the amplitude and frequency of the perturbing strain. A dynamic shear strain is illustrated in Figure 6.1. Experimentally one observes that the shear stress (response) is... 

P450 8A1 is constitutively expressed in human endothelial cells . The human CYP8A1 gene (chromosome 20) has 10 exons and has consensus sequences for Spl, AP-2, an interferon--/ response element, GATA NF, B, a CACCC box, glucocorticoid receptor, and a shear stress responsive element (GAGACC) . Whether or not all of these are functional and how they interact to maintain constitutive expression is not well understood yet. 

NOS III is found to be constitutively expressed in endothelial cells and some other cell types (see below). Some mechanisms that also regulate the expression of the NOS III gene have been described. Shear stress produced by the flowing blood not only increases endothelial NO release acutely (Lamontagne etal., 1992) but also up-regulates NOS III expression (Nishida et al., 1992). A putative shear stress-responsive element has been described... 

Resnick, N., Collins, T., Atkinson, W., Bonthron, D. T., Dewey, C. F., Jr., and Gimbrone, M. A., Jr. (1993). Platelet-derived growth factor (3 chain promoter contains a cis-acting fluid shear-stress-responsive element. Proc. Natl. Acad. Sci. U.S.A. 90, 4591-4595. 

In a dynamic experiment, a small-amplitude oscillatory shear is imposed to a molten polymer confined in the rheometer. The shear stress response of the polymeric system can be expressed as in Equation 22.14. In this equation, G and G" are dynamic moduli related to the elastic storage energy and dissipated energy of the system, respectively. For a viscoelastic fluid, two independent normal stress differences, namely, first and second normal stress differences can be defined. These quantities are calculated in terms of the differences of the components of the stress tensor, as indicated in Equation 22.15a and 22.15b, and can be obtained, for instance, from the radial pressure distribution in a cone-and-plate rheometer [5]. Some other experiments used in the determination of the normal stress differences can be found elsewhere [9, 22] ... 

Constantinou A, Mehta R, Runyan C, Rao K, Vaughan A, Moon R (1995) Flavonoids as DNA topoisomerase antagonists and poisons structure-activity relationships. J Nat Prod 58 217—225 Corder R, Warburton RC, Khan NQ, Brown RE, Wood EG, Lees DM (2004) The procyanidin-induced pseudo laminar shear stress response a new concept for the reversal of endothelial dysfunction. Clin Sci (Lond) 107 513-517... 

The Stress relaxation experiment consists of applying a constant relative strain. Yii. and recording the shear. stress response, as shown in Fig. 12. Typical relaxation curves for elastic solids, viscoelastic solids or liquids, and Newtonian liquids are shown in the latter figure. The clastic solid is able to store energy and, in consequence, can maintain deformation and does not relax under the applied strain. The other extreme is the Newtonian flow that relaxes completely and flows. 

The shear stress growth on the inception of shear flow may reflect the orientation of the liquid crystalline domains. Orientation seems to occur within less than 2 strain units in shear flow. This primary normal stress difference can exhibit different phenomena from the shear stress response. In particular for the 60 mole % PHB/PET system, values of N are positive and rise gradually to the equilibrium values whereas the 80 mole % PHB/PET system can exhibit negative values of N. Ericksen s transversely isotropic fluid theory can qualitatively handle some of the observed phenomena. Further studies which couple the transient flow behavior to the orientation and morphology need to be carried out. 

Figure 3. Model predictions in response to a complex history of intermittent shear rates. (a) Shear rate program, with Y = 15 sec periods alternating with y = 0 periods of variable duration. (b) The structure function P(t) characterizes the density of chain entanglements at t = 0 the equilibrium level is taken to be P = 1, and subsequent rest periods after shearing show structure recovery which is never allowed to equilibrate. (c) Shear stress response, normalized to the steady-state level for y = 15 sec . Stress overshoot upon start-up is a manifestation of structural breakdown. Overshoot is progressively smaller following shorter rest periods, as structure then has less time to recover. Model parameters are the same as used for curve-fitting in Figs. 1 and 2.

Fig. 40. Comparison of the half-step shear stress response predicted by the K-BKZ theory (open circles) with the experimental data (filled circles) for a pol3dsobutylene solution. After Zapas (118), with permission.

Step-Up. Figure 49 shows the response for a two-step history in which the second step is approximately the same magnitude as the first step, ie, K2 = 2y i. The results are from Osaki s work (138) on polystyrene solutions and illustrate that both the shear stress response and the normal stress response are well represented with the DE independent alignment approximation (ie, the K-BKZ equations). This result is similar to what was found previously for the K-BKZ model (Fig. 34) (138). 

Half-Step Deformation. In the discussion of the K-BKZ model, the half-step deformation was covered. Here two sets of data that go beyond what was described above are discussed. First, in the Osaki data shown in Figure 52, it is seen that the DE model with independent alignment fits the shear stress response, but not the normal stress response. Also, the theory without the independent alignment assumption does not fit the shear data. The normal stress deviation from the model prediction is interesting, as this was a special history for which the K-BKZ and... 

Fig. 52. Shear stress a (O) and normal stress vz (o) responses to a two-step half-step type of deformation history with yi = 2.89 and Y2 = 1-45 for a concentrated polystyrene solution. Duration of the first step was = 20 s. The solid lines are the predictions for the K-BKZ or DE-IA equations and the dashed lines are for the DE-NIA equations. Dashed-dotted line is the single-step shear stress response for y = 1.45. After Osaki et al. (138), with permission.

Fig. 53. Shear stress response to half-step type of deformation history for a concentrated polystyrene solution and for different values of the first step duration t. Dotted line (i = 1 s dashed line = 4 s solid line = 16 s. After Brown and Burghardt (134), with...

Fig. 62. Normal force response in step to zero type of deformation history for a PMMA polymer glass, showing the comparison between the experimental data (filled squares), the K-BKZ model predictions (crosses), and the predictions (filled circles) from the Zapas strain-clock model (118). Note that the clock terms for the normal force response were determined by fitting the shear stress response in the same experiment. After McKenna and Zapas (112).

Fig. 64. Half-step shear stress response for a PMMA glass. Circles represent single-step stress relaxation response at y = 0.05 crosses, K-BKZ prediction and open squares, experimental data for second step of y = 0.05 after a first step of y = 0.10 having a duration = 419 s. After McKenna (114).

Fig. 27 (a) Shear stress response obtained from a flow reversal experiment in CPCl/Hex nematic wormUke micelles at total concentration c = 37 wt. % and molar ratio [Hex]/[CPa]=0.49 [302]. In the flow reversal, the shear rate is changed stepwise from -1-1 (after sample loading) to -1 s and then to -1-1 s. (b) Variation of the normalized shear stress Flow reversal experiments were carried out at 7= 0.5 (close circles) and 1 s (open circles) and were found to be superimposed... 

Yoshisue H, Suzuki K, Kawabata A, et al. Large scale isolation of non-uniform shear stress-responsive genes from cultured human endothelial cells through the preparation of a subtracted cDNA library. Atherosclerosis 2002 162 323-334. 

Groenendijk, B. C., B. P. Hierck, A. C. Gittenberger-De Groot, and R. E. Poelmann. 2004. Development-related changes in the expression of shear stress responsive genes KLF-2, ET-1, and NOS-3 in the developing cardiovascular system of chicken embryos. DevDyn 230(l) 57-68. 

Fig. 2 Schematic depiction of the procedure for conducting LAOS experiments and analysis using FT-rheology. a Measurement of the oscillatory shear strain and shear stress response in the time domain, b Normalized frequency spectra after the Fourier transformation of the shear stress exhibit the fundamental peak at the angular frequency (d. Higher harmonics / /i with n being a positive odd integer are detected for a periodic nonlinear shear stress, c By variation of yo the transition from linear to nonlinear mechanical behavior can be observed in the increase of/ /i...

The data shown thus far describing the success of the K-BKZ theory were, generally, such that the stress never changed sign. However, it turns out that in stress-reversing flows, the K-BKZ theory seems not to work as well (62,82,107, 112,114,116,118). Figure 40 shows the shear stress response for a poljnsobutylene... 

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