振动剪切流场的等效稳态剪切速率

Equivalent Steady Shear Rate for Oscillatory Shear Flow

根据瞬态网络结构理论,建立了振动剪切流场中聚合物熔体缠结密度的动态速率微分方程。计算结果表明,当振动剪切达到动态平衡时,缠结密度在平衡位置处周期性地波动,其时均值等于稳态剪切速率下的缠结密度。因此,在时均意义上,振动剪切流的时均网络结构状态可等效为稳态剪切流的缠结平衡状态。通过计算发现:当应变振幅小于1.7时,等效稳态剪切速率可取振动剪切速率的周期平均值,由此产生的均方根误差随着应变振幅增加而增大,但小于0.017;而当应变振幅大于1.7时,则取峰-峰均值作为等效剪切速率,其均方根误差随着应变振幅增加而减小。

In this paper, equivalent steady shear rate for oscillatory shear flow was proposed. Based on kinetic network structural theory, a kinetic rate equation of entanglement density was established for oscillatory flow. Numerical solution shows the entanglement density depends on time varying sinusoidally about a cycle-averaged value that is regarded as a consequence of an equivalent steady shear rate. It is found that, the equivalent steady shear rate may be equal to the cycle mean of the oscillatory shear rate when strain amplitude is less than 1.7 with root-meansquare-error less than 0. 017, and the peak-peak mean preferred when more than 1.7.