A PURELY ELASTIC INSTABILITY IN TAYLOR-COUETTE FLOW
A PURELY ELASTIC INSTABILITY IN TAYLOR-COUETTE FLOW
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DOI：
10.1017/s0022112090001124
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发表时间：
1990-09-01
影响因子：
3.7
通讯作者：
MULLER, SJ
中科院分区：
文献类型：
--
作者：
LARSON, RG;SHAQFEH, ESG;MULLER, SJ
稀聚合物溶液的泰勒-库埃特流动发现了非惯性（零泰勒数）粘弹性不稳定性。 Oldroyd-B 流体无惯性流的线性稳定性分析（使用近似伽辽金分析和相关小间隙特征值问题的数值解）表明，当 Deborah 数超过 f(S) ε−1/2 时，过稳定（振荡）模式会增长，其中 ε 是间隙与内圆柱半径的比率，f(S) 是溶剂与聚合物对溶液粘度的贡献之比的函数。使用 1000 p.p.m. 溶液进行实验当德博拉数 De 达到 20（ε 为 0.14，泰勒数为 10−6）时，粘性溶剂中的高分子量聚异丁烯显示出次级环形细胞的开始，与理论值 21 非常一致。观察到临界 De 随着 ε 减小而增加，与理论一致。在不稳定发生后很长一段时间内，与惯性不稳定中发生的细胞相比，细胞的波长变得更小，这再次与我们的线性分析一致。对于这种流体，锥板流中也会出现类似的不稳定性，如先前报道的那样。这些不稳定性的驱动力是速度波动与基态第一法向应力差之间的相互作用。我们在此报告的这种不稳定性很可能发生在粘弹性流体的许多旋转剪切流中。
A non-inertial (zero Taylor number) viscoelastic instability is discovered for Taylor–Couette flow of dilute polymer solutions. A linear stability analysis of the inertialess flow of an Oldroyd-B fluid (using both approximate Galerkin analysis and numerical solution of the relevant small-gap eigenvalue problem) show the growth of an overstable (oscillating) mode when the Deborah number exceeds f(S) ε−½, where ε is the ratio of the gap to the inner cylinder radius, and f(S) is a function of the ratio of solvent to polymer contributions to the solution viscosity. Experiments with a solution of 1000 p.p.m. high-molecular-weight polyisobutylene in a viscous solvent show an onset of secondary toroidal cells when the Deborah number De reaches 20, for ε of 0.14, and a Taylor number of 10−6, in excellent agreement with the theoretical value of 21. The critical De was observed to increase as ε decreases, in agreement with the theory. At long times after onset of the instability, the cells become small in wavelength compared to those that occur in the inertial instability, again in agreement with our linear analysis. For this fluid, a similar instability occurs in cone-and-plate flow, as reported earlier. The driving force for these instabilities is the interaction between a velocity fluctuation and the first normal stress difference in the base state. Instabilities of the kind that we report here are likely to occur in many rotational shearing flows of viscoelastic fluids.