Phase separation in the advective Cahn-Hilliard equation
arXiv:1912.12714 · doi:10.1007/s00332-020-09637-6
Abstract
The Cahn--Hilliard equation is a classic model of phase separation in binary mixtures that exhibits spontaneous coarsening of the phases. We study the Cahn--Hilliard equation with an imposed advection term in order to model the stirring and eventual mixing of the phases. The main result is that if the imposed advection is sufficiently mixing then no phase separation occurs, and the solution instead converges exponentially to a homogeneous mixed state. The mixing effectiveness of the imposed drift is quantified in terms of the dissipation time of the associated advection-hyperdiffusion equation, and we produce examples of velocity fields with a small dissipation time. We also study the relationship between this quantity and the dissipation time of the standard advection-diffusion equation.
arXiv comment21 pages, 8 figures. v2: changes following referee reports
References in corpus (9)
- Using multiscale norms to quantify mixing and transport
- Suppression of chemotactic explosion by mixing
- Optimal stirring strategies for passive scalar mixing
- Dissipation Enhancement by Mixing
- Phase separation in an homogeneous shear flow: Morphology, growth laws and dynamic scaling
- Diffusion-limited mixing by incompressible flows
- Bubbles and Filaments: Stirring a Cahn-Hilliard Fluid
- Dynamical Effects and Phase Separation in Thin Films
- Bounds on the mixing enhancement for a stirred binary fluid