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

CookDMS-0807395 McKinley DMS-0807330在这个合作项目中，研究人员和一个团队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受力下的流动。表面活性剂体系由具有亲水头部和疏水尾部的两亲性分子组成。在适当的化学条件下，这些分子可以在水溶液中自组装成被称为蠕虫状胶束的长聚集体。这些长而灵活的结构缠绕在一起形成网络，并导致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裂和改造的复杂性(即它们是“活的聚合物”)。外部变形可以提高胶束的局部破碎率，从而宏观流动影响微观结构，而微观结构又进一步改变了全局速度场。由于这些多尺度的相互作用，即使在简单的几何结构中，这些流体也表现出流动的不均质性。新本构模型的发展和分析以及与实验结果的比较，使人们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的影响有了新的见解和理解。主要的数学是描述质量守恒和线动量守恒的非线性偏微分方程组，耦合到控制纠缠分子数密度的方程和每个物种的本构(应力)方程。具体地说，研究人员研究了他们最近提出的两种物种网络模型：物理上适用于蠕虫状胶束溶液的具有链断裂和重整效应的两种物种模型(VCM模型)和适用于单分散纠缠聚合物溶液的简化的非相互作用模型(PEC+M模型)。研究人员采用渐近性、计算和实验相结合的方法，研究了强可拓流动和快速时变流动中解的时间演化。生成了近似的闭合形式的解，以便能够理解流动和剧烈的空间转变(微结构边界层)。研究人员研究复杂流体的材料特性，如组成洗发水、液体洗涤剂、熔融塑料和用于提高石油采收率的流体。在微观尺度上，这些聚合物流体由大的聚集体或大分子组成，这些分子的形状和取向控制着流体的性质以及它在所需应用中的表现。对这些流体进行实验表征是非常困难的，因为它们的流动特性与水等牛顿流体不同，即使在简单的几何结构中也会变得不均匀。这意味着通常类型的测量(在流动边界测量流体性质)不足以理解和表征材料的响应。研究人员已经建立了一个新的状态方程--一个数学模型--它更全面地描述了这些流体的微观结构特性以及它们的流动方式。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了比较。这反过来又使他们能够开发新的方法来探索和表征流体的性质。以上所示的复杂流体在商业上可用于各种几何形状，可能既包括拉伸流动(如喷嘴的运动，从喷嘴中流出)，也包括剪切流动(例如管道中的流体泵送)。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流动条件的稳态和随时间变化的例子。

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.