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2012 | Buch

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Dissipative Ordered Fluids

Theories for Liquid Crystals

verfasst von: Andre M. Sonnet, Epifanio G. Virga

Verlag: Springer US

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik"

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Über dieses Buch

This is a book on the dissipative dynamics of ordered fluids,
with a particular focus on liquid crystals. It covers a whole
range of different theories, mainly concerned with nematic liquid
crystals in both their chiral and nonchiral variants. The authors
begin by giving a detailed account of the molecular origins of
orientational order in fluids. They then go on to develop a general
framework in which continuum theories for ordered fluids can be phrased.
Within this unified setting, they cover both well-established classical theories and new ones with aspects that are not yet completely settled. The book treats a wide range of hydrodynamic theories for liquid crystals, from the original 1960s works by Ericksen and Leslie to new, fast-developing ideas of liquid crystal science. The final chapter is devoted to nematoacoustics and its applications. Old experiments on the propagation of ultrasound waves in nematic liquid crystals are interpreted and explained
in the light of a new theory developed within the general theoretical infrastructure proposed in the body of the book.

This book is intended both for graduate students and professional
scholars in mathematics, physics, and engineering of advanced
materials. It delivers a solid framework for liquid crystal
hydrodynamics and shows the unifying concepts at the basis of the
classical theories. It illustrates how these concepts can also be
applied to a wide variety of modern topics.

Andre M. Sonnet is in the Department of Mathematics and Statistics at the University of Strathclyde, Glasgow (Scotland) and Epifanio G.
Virga is in the Department of Mathematics at the University of Pavia (Italy). They have a long history of working together in liquid crystal science and have contributed, in particular, to the theories of
defects and biaxial nematics.

Inhaltsverzeichnis

Frontmatter

1. Molecular Theories

Abstract

Any expository account of liquid crystals would invariably commence by saying that they constitute a state of matter that is intermediate between crystals and liquids. Their apparently contradictory appellation conveys well their being mesophases, that is, their participating in properties of two worlds. Macroscopically, they exhibit optical birefringence, a property typical of crystals, while retaining their ability to flow, which characterizes fluids. Microscopically, the tendency of liquid crystals to mediate between diversities is ascribed to the anisotropy of their molecules. In this introductory chapter, we present the microscopic basis for our development, which will mostly be macroscopic. We explore the microscopic origin of the ordering transition that gives rise to nematic liquid crystals. This discussion will ultimately serve to identify the most appropriate macroscopic order parameters for nematic liquid crystals, both in the uniaxial and biaxial phases.

André M. Sonnet, Epifanio G. Virga

2. Dynamics of Dissipative Fluids

Abstract

In the first chapter we explored the microscopic origins of orientational order. We now turn to macroscopic continuum theories. These are phenomenological theories that attempt to model real materials. They do not attempt to explain material properties by resorting to the molecular structure of matter, but they can draw inspiration from molecular theories—and the best of modern theories actually do so, in the spirit of a true multiscale approach to materials science. The same continuum theory can describe different materials by means of specific constitutive laws, which being first formulated in accordance with general invariance and symmetry principles, are then corroborated by matching experimental evidence with theoretical predictions, a comparison that eventually determines the phenomenological coefficients of the continuum theory. Often, it is also possible to link microscopic and macroscopic theories by estimating directly on molecular grounds the values of the phenomenological coefficients—for example, through a mean field theory. Whenever this happens, we extract the best from both worlds.

André M. Sonnet, Epifanio G. Virga

3. Director Theories

Abstract

We have seen in Chapter 1 that the nematic phase is most naturally described by two order parameter tensors Q and B that can be obtained as macroscopic averages of molecular tensors. However, different phenomenological theories were first developed motivated by the unique optical properties of the nematic phase. We postpone to Chapter 4 the investigation of continuum theories based on the order tensors and begin here by looking at director theories that are motivated by the observation that a nematic, although liquid, behaves like a crystal in that it exhibits optically distinguished local directions. These directions are the main protagonists of director theories.

André M. Sonnet, Epifanio G. Virga

4. Order Tensor Theories

Abstract

The history of order tensor theories is a long and winding one. Since DE GENNES introduced what he called the tensor order parameter in [57, 58] to phrase a LANDAU- GINZBURG-type theory for the nematic order, many steps have been taken toward a general continuum theory of nematics with tensorial order. Using standard methods of nonequilibrium thermodynamics, HESS [142, 143] and later OLMSTED and GOLDBART [254, 255] obtained constitutive theories for homogeneous alignments, later generalized by HESS and PARDOWITZ to include also spatial variations [145]. All these attempts were impaired by not yielding the full anisotropy of viscosities predicted by the ERICKSEN-LESLIE director theory. An extension using a codeformational model was proposed in [144], and while it recovered the complete anisotropy of viscosities, it failed to be otherwise fully consistent with the phenomenological ERICKSEN-LESLIE theory [267].

André M. Sonnet, Epifanio G. Virga

5. Nematoacoustics

Abstract

At this stage of our development we apply our general theory to a field that is still somewhat controversial. Though the orienting effect of an ultrasonic wave on the nematic texture has long been known,1 its interpretation in terms of a coherent dynamical theory, widely if not universally accepted, has not yet been achieved. In this chapter, following [354] and [67], we phrase such a theory within the setting of this book; hopefully, this will serve as a further illustration of the generality of our method. Below, we first summarize the diverse theoretical approaches attempted in the past to describe the interaction between sound and molecular orientation in nematic liquid crystals. We then revive a theory for second-grade fluids, which we believe provides the most appropriate theoretical background to posit our nematoacoustic theory that elaborates on a proposal not new in its intuitive phrasing, but which has only recently found both a more precise theoretical formulation and its first experimental validation.We shall actually depart from the latest theoretical formulation in an effort to draw from it all its consequences. A closing explicit application to a simple computable case will also show some predictions of our theory, which are both qualitatively and quantitatively confirmed by a number of experimental results.

André M. Sonnet, Epifanio G. Virga

Backmatter

Titel: Dissipative Ordered Fluids
verfasst von: Andre M. Sonnet
Epifanio G. Virga
Verlag: Springer US
Electronic ISBN: 978-0-387-87815-7
Print ISBN: 978-0-387-87814-0
DOI: https://doi.org/10.1007/978-0-387-87815-7

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