液晶高分子哑铃模型中的瞬态剪切带
Transient shear banding in the nematic dumbbell model of liquid crystalline polymers
摘要：
在液晶聚合物（LCP）的剪切流动中，对于某些材料，液晶指向矢取向可以与流动方向对齐，但在其他材料中连续翻转。哑铃型流变模型最初是用来描述流动取向型半柔性液晶聚合物的流变特性，本文主要研究流动取向型液晶聚合物。在单畴LCP的剪切流中，通常假定速度的空间分布是均匀的。这与聚合物溶液相反，在实验中观察到高度不均匀的空间速度分布。我们分析的ND模型，在本构模型中的附加梯度项，使用线性稳定性分析。我们研究了恒定施加剪切应力和恒定施加剪切速率的不同情况。我们发现，ND模型有一个瞬态流动不稳定性的空间不均匀的流速的形成为某些起始方向的导演。我们计算的空间分辨的流动剖面恒定施加的应力和恒定施加的剪切速率在启动从休息，使用一个空间维度的模型来说明流体的流动行为。对于低剪切速率，流动逆转可以被看作是导向器与流动方向重新对准，而对于高剪切速率，导向器重新取向同时发生在间隙上。实验上，这种不均匀的流动被预测在LCP的流动反转实验中观察到。
英文摘要：
In the shear flow of liquid crystalline polymers (LCPs) the nematic director orientation can align with the flow direction for some materials, but continuously tumble in others. The nematic dumbbell (ND) model was originally developed to describe the rheology of flow-aligning semi-flexible LCPs, and flow-aligning LCPs are the focus in this paper. In the shear flow of monodomain LCPs it is usually assumed that the spatial distribution of the velocity is uniform. This is in contrast to polymer solutions, where highly non-uniform spatial velocity profiles have been observed in experiments. We analyse the ND model, with an additional gradient term in the constitutive model, using a linear stability analysis. We investigate the separate cases of constant applied shear stress, and constant applied shear rate. We find that the ND model has a transient flow instability to the formation of a spatially inhomogeneous flow velocity for certain starting orientations of the director. We calculate the spatially resolved flow profile in both constant applied stress and constant applied shear rate in start up from rest, using a model with one spatial dimension to illustrate the flow behaviour of the fluid. For low shear rates flow reversal can be seen as the director realigns with the flow direction, whereas for high shear rates the director reorientation occurs simultaneously across the gap. Experimentally, this inhomogeneous flow is predicted to be observed in flow reversal experiments in LCPs.
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