Chemical Engineering, University of Delaware, Newark, Delaware 19716, USA.
Langmuir. 2010 Sep 7;26(17):14284-93. doi: 10.1021/la102314r.
A very important morphological parameter in two-phase fluids is the interface anisotropy, which can be quantified using the interface tensor, q(ij). However, the computation of this tensor for complex interfaces is not straightforward. A novel method (the local cross product method, LCPM) to compute the interface tensor of two-phase fluids using 3D imaging coupled with differential geometry is presented here. The method was used to evaluate the degree of anisotropy of phase separated systems with bicontinuous morphologies subjected to uniaxial and shear deformation fields. A model bicontinuous structure (i.e., the gyroid surface) was used to assess the accuracy and precision of the method. The method was then used to track the anisotropy changes of an immiscible polymer blend with cocontinuous morphology, during uniaxial deformation and subsequent retraction. It was found that the dependence of the anisotropy on the Hencky strain of both the gyroid surface and the cocontinuous blend follow the same trend. The retraction of the blend after uniaxial extension is accompanied by an exponential decay of the second invariant of q(ij), which obeys the relation: |II(q)|/Q(2) approximately e(-0.129t).
在二相流体中，一个非常重要的形态参数是界面各向异性，可以使用界面张量 q(ij) 来量化。然而，对于复杂的界面，计算这个张量并不简单。本文提出了一种使用 3D 成像结合微分几何计算二相流体界面张量的新方法（局部叉积法，LCPM）。该方法用于评估具有双连续形态的相分离体系在单轴和剪切变形场下的各向异性程度。使用模型双连续结构（即，gyroid 表面）来评估该方法的准确性和精度。然后，该方法用于跟踪具有共连续形态的不混溶聚合物共混物在单轴变形和随后的回缩过程中的各向异性变化。结果发现，gyroid 表面和共连续共混物的各向异性对 Hencky 应变的依赖性遵循相同的趋势。共混物在单轴拉伸后的回缩伴随着 q(ij) 的第二不变量的指数衰减，遵循以下关系：|II(q)|/Q(2) approximately e(-0.129t)。
