Diffusion properties of gradient-based lattice Boltzmann models of immiscible fluids

We study the diffusion and phase separation properties of a gradient-based lattice Boltzmann model of immiscible fluids. We quantify problems of lattice pinning associated with the model, and suggest a scheme that removes these artifacts. The interface width is controlled by a single parameter that acts as an inverse diffusion length. We derive an analytic expression of a fully developed interfacial curve and show that interfaces evolve towards this stable distribution if no fluid is trapped. Fluid can become trapped inside a competing phase if no connecting path to the bulk phase exists. Such trapped bubbles also evolve towards the fully developed interfacial curve but constraints on mass conservation limit this development. We also show how small numerical errors lead to spontaneous phase separation for all values of the diffusion length.