Now showing 1 - 4 of 4
  • Publication
    Travelling-wave spatially periodic forcing of asymmetric binary mixtures
    (Elsevier, 2019-06)
    We study travelling-wave spatially periodic solutions of a forced Cahn–Hilliard equation. This is a model for phase separation of a binary mixture, subject to external forcing. We look at arbitrary values of the mean mixture concentration, corresponding to asymmetric mixtures (previous studies have only considered the symmetric case). We characterize in depth one particular solution which consists of an oscillation around the mean concentration level, using a range of techniques, both numerical and analytical. We determine the stability of this solution to small-amplitude perturbations. Next, we use methods developed elsewhere in the context of shallow-water waves to uncover a (possibly infinite) family of multiple-spike solutions for the concentration profile, which linear stability analysis demonstrates to be unstable. Throughout the work, we perform thorough parametric studies to outline for which parameter values the different solution types occur.
      415Scopus© Citations 1
  • Publication
    Liquid Wicking in Hierarchical Microstructures
    (European Study Group with Industry, 2018-06-29) ; ;
    The aim of this work is to model the flow of liquid as it spreads through a structured cavity (‘wicking’), as described schematically in Figure 1. The problem was posed by Analog Devices in the context of the 118th European Study Group with Industry, which was held in UCD in July 2018. The aim of the modelling exercise is to find the optimum structure morphology/size/porosity/materials for wicking/routing of liquid inside a cavity under various temperature and environment conditions? Wicking of surfaces has many applications in the fields of biology, sensing and integrated chip cooling. As such, the existing literature on the subject is extensive. Therefore, the first objective of this report is to carry out a detailed literature review (Section 2), wherein we outline how the answers to many of the questions posed by Analog Devices can be answered by methods from the existing literature. Further refinements of this approach could be carried out, if any of the questions are not answered in this report. In this existing literature, the fluid that permeates the substrate is assumed to come from an infinite reservoir. Therefore, in section 3 we examine how including the finite volume of the liquid drop that permeates into the substrate affects the spreading dynamics. Additionally, we have also examined lubrication theory as a way of providing a very detailed and mathematically consistent description of wetting on rough surfaces, which we describe below in Section 4. Finally, our conclusions are presented in Section 5.
  • Publication
    A Geometric Diffuse-Interface Method for Droplet Spreading
    This paper exploits the theory of geometric gradient flows to introduce an alternative regularization of the thin-film equation valid in the case of large-scale droplet spreading-the geometric diffuse-interface method. The method possesses some advantages when compared with the existing models of droplet spreading, namely the slip model, the precursor-film method and the diffuse-interface model. These advantages are discussed and a case is made for using the geometric diffuse-interface method for the purpose of numerical simulations. The mathematical solutions of the geometric diffuse interface method are explored via such numerical simulations for the simple and well-studied case of large-scale droplet spreading for a perfectly wetting fluid-we demonstrate that the new method reproduces Tanner's Law of droplet spreading via a simple and robust computational method, at a low computational cost. We discuss potential avenues for extending the method beyond the simple case of perfectly wetting fluids.
      260Scopus© Citations 1
  • Publication
    A Review of Applied Mathematics
    (Irish Applied Mathematics Teachers Association, 2015-12) ;
    Applied Mahtematics is a subject which deals with problmes arising inthe physical, life, and social sciences as well as in engineering and provides a broad body of knowledge for use in a wide spectrum of research and insdustry. Applied Mathematics is an important school subject which builds students' mathematical and problem solving skills. The subject has remained on the periphery of school time-tables and, without the commitment and enthusiasm of Applied Maths teachers, would likely be omitted from most school curricula.