The role of advection in phase-separating binary liquids
arXiv:0805.1242
Abstract
Using the advective Cahn-Hilliard equation as a model, we illuminate the role of advection in phase-separating binary liquids. The advecting velocity is either prescribed, or is determined by an evolution equation that accounts for the feedback of concentration gradients into the flow. Here, we focus on passive advection by a chaotic flow, and coupled Navier-Stokes Cahn-Hilliard flow in a thin geometry. Our approach is based on a combination of functional-analytic techniques, and numerical analysis. Additionally, we compare and contrast the Cahn-Hilliard equation with other models of aggregation; this leads us to investigate the orientational Holm-Putkaradze model. We demonstrate the emergence of singular solutions in this system, which we interpret as the formation of magnetic particles. Using elementary dynamical systems arguments, we classify the interactions of these particles.
Ph.D. Thesis, Imperial College London, February 2008
References in corpus (12)
- Formation of clumps and patches in self-aggregation of finite size particles
- Turbulence and coarsening in active and passive binary mixtures
- Lifshitz-Slyozov Scaling For Late-Stage Coarsening With An Order-Parameter-Dependent Mobility
- Stirring up trouble: Multi-scale mixing measures for steady scalar sources
- Optimizing the Source Distribution in Fluid Mixing
- Bubbles and Filaments: Stirring a Cahn-Hilliard Fluid
- Geometric gradient-flow dynamics with singular solutions
- Phase separation of bacterial colonies in a limit of high degradation. Analogy with Jupiter's great red spot
- Formation and Evolution of Singularities in Anisotropic Geometric Continua
- Geometric dissipation in kinetic equations
- Bounds on the mixing enhancement for a stirred binary fluid
- Emergent singular solutions of non-local density-magnetization equations in one dimension