Collaborative Research: Time-Dependent and Inhomogeneous Flows of Entangled Polymeric and Micellar Networks

在这个合作项目中，研究人员和同事研究了复杂流体的运动，特别是蠕虫状胶束流体和单分散聚合物溶液在各种几何形状和各种作用力下的流动。表面活性剂体系由两亲分子组成，头亲水，尾疏水。在合适的化学条件下，这些分子可以在水溶液中自组装成长长的聚集体，称为蠕虫状胶束。这些长而柔韧的结构缠绕在一起形成了一个网络，并导致了类似于聚合物熔体和浓缩溶液的粘弹性特性，但增加了蠕虫不断破坏和重组的复杂性（即它们是“活聚合物”）。外部变形可以提高局部胶束断裂速率，从而宏观流动影响微观结构，进而进一步改变整体速度场。由于这些多尺度的相互作用，这些流体即使在简单的几何形状中也表现出流动的不均匀性。新的本构模型的发展和分析以及与实验结果的比较，正在对这些流动的多尺度性质以及微观结构的演变对宏观可测量物的影响产生新的见解和理解。控制数学是描述质量守恒和线性动量的非线性偏微分方程系统，加上控制纠缠分子数量密度的方程和每个物种的本构（应力）方程。具体来说，研究人员研究了他们最近提出的一对两种网络模型：一种是具有链断裂和重整效应的两种模型（VCM模型），物理上适用于虫状胶束溶液，另一种是简化的非相互作用模型（PEC+M模型），适用于单分散纠缠聚合物溶液。本文采用渐近、计算和实验相结合的方法研究了强扩展流和快速时变流解的时间演化问题。生成近似封闭形式的解决方案，以便理解流动和急剧的空间转变（微观结构和边界层）。研究人员研究了复合流体的材料特性，如构成洗发水、液体洗涤剂、熔融塑料和用于提高采收率的流体的材料特性。在微观尺度上，这些聚合物流体由大聚集体或大分子组成，这些分子的形状和方向控制着流体的性质及其在预期应用中的表现。用实验来描述这些流体是非常困难的，因为它们的流动特性，不像牛顿流体，如水，即使在简单的几何形状中也变得不均匀。这意味着通常的测量类型（在流动边界处测量流体特性）不足以理解和表征材料响应。研究人员已经制定了一个新的状态方程——一个数学模型——更全面地描述了这些流体的微观结构特性以及它们是如何流动的。他们现在研究了该模型在各种复杂流动中的预测，并将其与实验结果进行比较。这反过来又使他们能够开发新的方法来探测和表征流体的性质。上面列出的复杂流体在商业上用于各种几何形状，可能涉及拉伸流动（例如射流的运动，从喷嘴流出）以及剪切流动（例如泵送管道中的流体）。为了确保他们的分析和实验结果与工业研究人员相关，研究人员调查了两种类型的流动条件的稳定和时间相关的例子。

CookDMS-0807395McKinleyDMS-0807330 In this collaborative project, the investigators and acolleague study the motion of complex fluids, especially flows ofwormlike micellar fluids and of monodisperse polymer solutions ina variety of geometries and under a variety of forcings. Surfactant systems consist of amphiphilic molecules withhydrophilic heads and hydrophobic tails. Under suitable chemicalconditions these molecules can self-assemble in aqueous solutioninto long aggregates known as worm-like micelles. These longflexible structures entangle to form a network and lead toviscoelastic properties similar to those of polymer melts andconcentrated solutions, but with the added complexity that theworms continuously break and reform (i.e. they are "livingpolymers"). External deformations can enhance the local rate ofmicellar breakage, thus the macroscopic flow affects themicroscopic structure which in turn further modifies the globalvelocity field. Due to these multi-scale interactions thesefluids exhibit flow inhomogeneities even in simple geometries. Development and analysis of new constitutive models andcomparison with experimental results is generating new insightand understanding into the multi-scale nature of these flows andof the influence of the evolution in the microscopic structure onthe macroscopic measurables. The governing mathematics is thatof a nonlinear system of partial differential equationsdescribing conservation of mass and linear momentum, coupled toequations governing the number densities of the entangledmolecules and constitutive (stress) equations for each species. Specifically, the investigators study a pair of two-speciesnetwork models that they recently proposed: a two species modelwith chain scission and reforming effects (the VCM model)physically appropriate for wormlike micellar solutions, and asimplified non-interacting model (PEC+M model) appropriate tomonodisperse entangled polymer solutions. The investigatorsstudy the time evolution of the solutions in strong extensionalflow and in rapidly time-varying flow using a combination ofasymptotics and computation as well as experiments. Approximateclosed form solutions are generated to enable an understanding ofthe flows and of sharp spatial transitions (microstructuralboundary layers). The investigators study the material properties of complexfluids such as those constituting shampoos, liquid detergents,molten plastics, and fluids utilized in enhanced oil recovery. On the microscopic scale these polymeric fluids consist of largeaggregates or macromolecules and the shape and orientation ofthese molecules control the properties of the fluid and how itperforms in the desired application. It is very difficult tocharacterize these fluids experimentally because their flowproperties, unlike those of Newtonian fluids such as water,become inhomogeneous even in simple geometries. This means thatthe usual types of measurements (in which the fluid propertiesare measured at the flow boundaries) are not sufficient tounderstand and characterize the material response. Theinvestigators have formulated a new equation of state -- amathematical model -- that more fully describes themicrostructural properties of these fluids and how they flow. They now investigate the predictions of this model in variouscomplex flows and compare this with experimental findings. Thisin turn enables them to develop new means to probe andcharacterize the properties of the fluids. The complex fluidslisted above are used commercially in a variety of geometriesthat may involve both stretching flows (such as the motion of ajet, flow out of a nozzle) as well as shearing flows (for examplepumping of the fluids in a pipe). To ensure that theiranalytical and experimental results are relevant to researchersin industry, the investigators investigate both steady andtime-dependent examples of both types of flow conditions.