Publications by authors named "Peter D Howell"

4 Publications

  • Page 1 of 1

Colloidal liquid crystals in rectangular confinement: theory and experiment.

Soft Matter 2014 Oct 26;10(39):7865-73. Epub 2014 Aug 26.

Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK.

We theoretically and experimentally study nematic liquid crystal equilibria within shallow rectangular wells. We model the wells within a two-dimensional Oseen-Frank framework, with strong tangent anchoring, and obtain explicit analytical expressions for the director fields and energies of the 'diagonal' and 'rotated' solutions reported in the literature. These expressions separate the leading-order defect energies from the bulk distortion energy for both families of solutions. The continuum Oseen-Frank study is complemented by a microscopic mean-field approach. We numerically minimize the mean-field functional, including the effects of weak anchoring, variable order and random initial conditions. In particular, these simulations suggest the existence of higher-energy metastable states with internal defects. We compare our theoretical results to experimental director profiles, obtained using two types of filamentous virus particles, wild-type fd-virus and a modified stiffer variant (Y21M), which display nematic ordering in rectangular chambers, as found by confocal scanning laser microscopy. We combine our analytical energy expressions with experimentally recorded frequencies of the different equilibrium states to obtain explicit estimates for the extrapolation length, defined to be the ratio of the nematic elastic constant to the anchoring coefficient, of the fd-virus.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1039/c4sm01123fDOI Listing
October 2014

A theoretical analysis of the surface tension profiles of strongly interacting polymer-surfactant systems.

J Colloid Interface Sci 2010 Oct 16;350(2):486-93. Epub 2010 Jul 16.

Mathematical Institute, University of Oxford, 24-29 St. Giles', Oxford OX1 3LB, UK.

Measurements of the surface tension of static polymer-surfactant mixtures as the concentrations of polymer and surfactant are varied produce interesting and surprising profiles. It is well known how the critical points in the surface tension profile of a weakly interacting system relate to the formation of complexes in the bulk. However the critical points in the profiles of strongly interacting systems are much less well understood, and an important open question is what conditions are required for the formation of a peak. Here, using a model for the surface tension developed in a previous article (Bell et al., Langmuir 23 (2007) 6042), we apply asymptotic techniques to show explicitly how the structure of the surface tension profile and the critical concentrations depend on the relative stability of the underlying polymer-surfactant complexes. We derive the interesting result that none of the critical concentrations is at the critical aggregation concentration (CAC). We also identify a criterion for the appearance of a peak in the surface tension profile, expressed in terms of the physical and chemical parameters of the system.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1016/j.jcis.2010.07.020DOI Listing
October 2010

Macroscopic modeling of the surface tension of polymer-surfactant systems.

Langmuir 2007 May 28;23(11):6042-52. Epub 2007 Apr 28.

Mathematical Institute, University of Oxford, 24-29 St. Giles', Oxford, OX1 3LB, UK.

Polymer-surfactant mixtures are increasingly being used in a wide range of applications. Weakly interacting systems, such as SDS/PEO and SDS/PVP, comprise ionic surfactants and neutral polymers, while strongly interacting systems, such as SDS/POLYDMDAAC and C12TAB/NaPSS, comprise ionic surfactants and oppositely charged ionic polymers. The complex nature of interactions in the mixtures leads to interesting and surprising surface tension profiles as the concentrations of polymer and surfactant are varied. The purpose of our research has been to develop a model to explain these surface tension profiles and to understand how they relate to the formation of different complexes in the bulk solution. In this paper we show how an existing model based on the law of mass action can be extended to model the surface tension of weakly interacting systems, and we also extend it further to produce a model for the surface tension of strongly interacting systems. Applying the model to a variety of strongly interacting systems gives remarkable agreement with the experimental results. The model provides a sound theoretical basis for comparing and contrasting the behavior of different systems and greatly enhances our understanding of the features observed.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1021/la063714hDOI Listing
May 2007

Model for the breakup of a tuft of fibers.

Phys Rev E Stat Nonlin Soft Matter Phys 2006 Oct 10;74(4 Pt 1):041806. Epub 2006 Oct 10.

BP Institute for Multiphase Flow, University of Cambridge, Madingley Road, Cambridge, CB3 0EZ, United Kingdom.

A simple model for the forces acting on a single fiber as it is withdrawn from a tangled fiber assembly is proposed. Particular emphasis is placed on understanding the dynamics of the reptating fiber with respect to the entanglement of fibers within the tuft. The resulting two-parameter model captures the qualitative features of experimental simulation. The model is extended to describe the breakup of a tuft. The results show good agreement with experiment and indicate where a tuft is most likely to fracture based on the density of fiber endpoints.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1103/PhysRevE.74.041806DOI Listing
October 2006