A new computational method for the solution of flow problems of microstructured fluids. Part 2. Inhomogeneous shear flow of a suspension

A numerical investigation is conducted into the flow of a dilute suspension of rigid rod-like particles between parallel flat plates, driven by a uniform pressure gradient. The particles are assumed to be small relative to lengthscales of the flow with the effect that particle orientations evolve according to the local velocity gradient; the particles are also assumed to be small in an absolute sense, with the consequence that Brownian motions are of consequence. The calculations are performed using a novel approach, with a theoretical basis that has been developed previously in a companion paper (Szeri & Leal 1992). The new approach permits one to solve flow problems of microstructured fluids (such as suspensions, liquid crystals, polymer solutions and melts) without ‘pre-averaging’ or closure approximations. In the present work, the new approach is used to expose previously unknown pathological, non-physical predictions in various constitutive models derived using closure approximations. This appears to have passed unnoticed in prior work. In addition, the new approach is shown to possess several computational advantages. The determination of the orientation distribution of particles is self-adaptive; this leads, in effect, to a very efficient solution of the associated Smoluchowski (or Fokker–Planck) equation. Moreover, the new approach is highly suited to parallel (and vector) implementation on modern computers. These issues are explored in detail in the context of the example flow.

Cryo-TEM of amphiphilic polymer and amphiphile/polymer solutions

To achieve complete microstructural characterization of self-aggregating systems, one needs direct images in addition to quantitative information from non-imaging, e.g., scattering or Theological measurements, techniques. Cryo-TEM enables us to image fluid microstructures at better than one nanometer resolution, with minimal specimen preparation artifacts. Direct images are used to determine the “building blocks” of the fluid microstructure; these are used to build reliable physical models with which quantitative information from techniques such as small-angle x-ray or neutron scattering can be analyzed.To prepare vitrified specimens of microstructured fluids, we have developed the Controlled Environment Vitrification System (CEVS), that enables us to prepare samples under controlled temperature and humidity conditions, thus minimizing microstructural rearrangement due to volatile evaporation or temperature changes. The CEVS may be used to trigger on-the-grid processes to induce formation of new phases, or to study intermediate, transient structures during change of phase (“time-resolved cryo-TEM”). Recently we have developed a new CEVS, where temperature and humidity are controlled by continuous flow of a mixture of humidified and dry air streams.

Cryo-TEM study of novel morphology in mixed surfactant-lipid systems

Microstructured fluids arise in a number of biological, chemical, and physical systems as interfaces, films, emulsions, membranes, gels, and liquid crystals. We have recently discovered a wealth of new types of microstructure formed by mixed surfactant systems in water, including the first system of spontaneous, equilibrium vesicles formed by simple cationic and anionic surfactant mixtures. Many of these systems present unusual rheological or phase behavior, and accompanying technological opportunities. However, these systems do not lend themselves to simple characterization by conventional light, X-ray, or neutron scattering, NMR, etc. This is due to the indirect nature of these probes; structural information is inferred from these measurements, and a model is often necessary to infer structural information. For mixed surfactant systems, the microstructure is often so unexpected as to make it impossible to construct a model; or worse, a model built on simple structural concepts leads to erroneous interpretation. Cryo-electron microscopy is a necessary alternative to these techniques as the structural information provided is much more direct and model independent.

A new computational method for the solution of flow problems of microstructured fluids. Part 1. Theory

The theoretical basis for a new computational method is presented for the solution of flow problems of microstructured fluids: examples include suspensions of rigid particles and polymeric liquids ranging from liquid crystals to concentrated solutions or melts of flexible chains. The method is based on a Lagrangian conservation statement for the distribution function of the conformation of the local structure, which can be derived from the conventional, Eulerian conservation statement and is exactly equivalent. The major difference, which is reflected in the numerical technique, is that the Lagrangian representation of the distribution function allows for computation of the Brownian contribution and of moments of distribution functions in ways that do not require explicit knowledge of the distribution function, and involve no approximation whatsoever. This suggests a new type of efficient, self-adaptive numerical scheme that is suitable for the solution of flow problems of microstructured fluids, in which macroscopic properties depend on the state of the microstructure.