The flow past a cylinder in a channel with the aspect ratio of 2: 1 for the upper convected Maxwell (UCM) fluid and the Oldroyd-B fluid with the viscosity ratio of 0.59is studied by using the Galerkin/Least-square finite element method and a p-adaptive refinement algorithm. A posteriori error estimation indicates that the stress-gradient error dominates the total error. As the Deborah number, De, approaches 0.8 for the UCM fluid and 0.9 for the Oldroyd-B fluid, strong stress boundary layers near the rear stagnation point are forming, which are characterized by jumps of the stress-profiles on the cylinder wall and plane of symmetry, huge stress gradients and rapid decay of the gradients across narrow thicknesses. The origin of the huge stress-gradients can be traced to the purely elongational flow behind the rear stagnation point, where the position at which the elongation rate is of 1/2De approaches the rear stagnation point as the Deborah number approaches the critical values. These observations imply that the cylinder problem for the UCM and Oldroyd-B fluids may have physical limiting Deborah numbers of 0.8 and 0.9, respectively.
The isothermal crystallizations of three kinds of commercial isotactic polypropylene have been studied by DSC and rheometric experiments, in a range of temperatures where the rate of crystallization is moderate. As the crystallization proceeds, volume contraction induces tensile force upon the parallel plates. The tensile force relaxed quickly in liquid states,but after a critical amount of the relative crystallinity, it starts to accumulate in the static test, that is, with the motionless parallel plates. A new method to determine the liquid-solid transition by the static tensile force is proposed and compared with two dynamic methods of detecting liquid-solid transition, that is, the power-law modulus theory and the yield modulus model. The tensile force method predicted considerably earlier transition than the dynamic methods, and the corresponding DSC data indicate relative crystallinity of larger than 0.2 at the transition times. The limitation of dynamic methods and other possible errors have been analyzed. While the dynamic methods are suitable for slow crystallization, the tensile force method is more appropriate for the crystallization of moderate rates. Moreover, it has the advantage of almost not disturbing the crystallizing materials before the transition.
