Bounds on the mixing enhancement for a stirred binary fluid
arXiv:0709.1747 · doi:10.1016/j.physd.2008.04.012
Abstract
The Cahn-Hilliard equation describes phase separation in binary liquids. Here we study this equation with spatially-varying sources and stirring, or advection. We specialize to symmetric mixtures and time-independent sources and discuss stirring strategies that homogenize the binary fluid. By measuring fluctuations of the composition away from its mean value, we quantify the amount of homogenization achievable. We find upper and lower bounds on our measure of homogenization using only the Cahn-Hilliard equation and the incompressibility of the advecting flow. We compare these theoretical bounds with numerical simulations for two model flows: the constant flow, and the random-phase sine flow. Using the sine flow as an example, we show how our bounds on composition fluctuations provide a measure of the effectiveness of a given stirring protocol in homogenizing a phase-separating binary fluid.
20 pages, 16 figures. RevTex4 class
References in corpus (9)
- Walls Inhibit Chaotic Mixing
- Turbulence and coarsening in active and passive binary mixtures
- A Bound on Mixing Efficiency for the Advection-Diffusion Equation
- Multiscale Mixing Efficiencies for Steady Sources
- Statistics of transition times, phase diffusion and synchronization in periodically driven bistable systems
- 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
- Dynamical Effects and Phase Separation in Thin Films
Cited by in corpus (6)
- Using multiscale norms to quantify mixing and transport
- Phase separation in the advective Cahn-Hilliard equation
- Suppression of epitaxial thin film growth by mixing
- The Mixing efficiency of open flows
- Travelling-wave spatially periodic forcing of asymmetric binary mixtures
- The role of advection in phase-separating binary liquids