Creeping profile

Rhee, H.-K., and Amundson, N. R., Equilibrium theory of creeping profiles in fixed-bed catalytic reactors. Ind. Eng. Chem. Funda. 13, 1-4 (1974). 

Rossi, S., Bonferoni, M.C., Caramella, C., Ironi, L., and Tentoni, S., Model-based interpretation of creep profiles for the assessment of polymer-mucin interaction, Pharm. Res., 16 1456-1463 (1999). 

The reaction mixture is able to react, ignition occurs at the reactor exit and a reaction front moves toward reactor inlet. The resulting steady state is at the reactor inlet and a strong preheating of the inlet gas occurs. The transient operation is referred to as "creeping profiles" and was extensively studied by Amundson [4-6]. Experimentally observed in [1, 15]. 

Creep tests with UP mat laminates with various glass fiber-reinforcements subsequent to several months of loading exhibit linear creep profiles for almost 15 years. Figure 6.1 to Figure 6.3. The straight line approximations were performed according to the four-parameter method or Burgers equation. 

Figure 6.1 Creep profiles for UP-GF mat laminate, linear plot of measurement values P4 moderately reactive standard resin P7 highly reactive, heat-resistant resin...

Figure 6.3 Creep profiles for UP-GF mat laminate (highly reactive, tough resin [P8]), test temperature 23 °C and 40 °C, respectively...

Numerous creep tests with test times no longer than 105 hours determined that for GFP pipe the creep profiles do not exhibit a sharp downturn. When plotted on a double-logarithmic scale, they are linear instead. Therefore, linear extrapolation up to 1.5 decades is regarded permissible. 

With disk diameters above 5.25 in., all parameters, eg, water absorption and thermal expansion, become more critical which aggravates the expansion or warp of disks. If in the future disk rotation speeds have to be increased significantly to boost data transfer rates, higher demands will be placed on warp (tilt angle) and modulus to avoid creeping (ie, irreversible elongation in radial direction). A survey of the requirement profile for the substrate material of optical disks is given in Table 5 (182,186,187,189). 

Fig. 2-22 Viscoelastic creep behavior typical of many TPs under long-term stress to rupture (a) input stress vs. time profile and (b) output strain vs. time profile.

Bunimovich et al. (1984) point out that if the period of flow reversal, t, is very small relative to the time required for the temperature front to creep through the bed and the high-temperature zone occupies most of the bed a relaxed steady state is achieved in which the temperature profile is constant through most of the bed. This profile can be calculated and leads to a steady-state model for this extreme variant of flow reversal. 

Sheet molding compounds (SMCs) and bulk molding compounds (BMCs) are the dominant materials used in automotive applications. These composites of unsaturated polyester resin, fillers and fiberglass have advantages of high stiffness, heat resistance and low coefficient of expansion. Coupled with low creep resistance, which is a distinct advantage over thermoplastic competition, and low-profile additives, which can yield Class A surfaces, these materials are well suited for applications from exterior body panels to under the hood components. 

For increased flow rates, however, the CFD simulations show more and more deviations from an ideal SAR multi-lamination pattern [7]. Since inertial forces come into play, a secondary flow pattern is superposed on the SAR velocity profile of the creeping flow regime. Streamlines seeded at the initial lamellae interface in top view for various Reynolds numbers. The lamellae pattern right at the outlet for the same set of Reynolds numbers were also given. Further simulations showed that for Re above -15 the center lamellae are thinned out until they detach from the top and bottom walls for Re 30 (see center image of Figure 1.128). 

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