Phase-separation fronts leave in their wakes morphologies that are substantially different from the morphologies formed in homogeneous phase separation. In this paper we focus on fronts in binary mixtures that are enslaved phase-separation fronts, i.e., fronts that follow in the wake of a control-parameter front. In the one-dimensional case, which is the focus of this paper, the formed morphology is deceptively simple: alternating domains of a regular size. However, determining the size of these domains as a function of the front speed and other system parameters is a nontrivial problem. We present an analytical solution for the case where no material is deposited ahead of the front and numerical solutions and scaling arguments for more general cases. Through these enslaved phase-separation fronts large domains can be formed that are practically unattainable in homogeneous one-dimensional phase separation.

A phase-separation front will leave in its wake a phase-separated morphology that differs markedly from homogeneous phase-separation morphologies. For a purely diffusive system such a front, moving with constant velocity, will generate very regular, nonequilibrium structures. We present here a numerical study of these fronts using a lattice Boltzmann method. In two dimensions these structures are regular stripes or droplet arrays. In general the kind and orientation of the selected morphology and the size of the domains depends on the speed of the front as well as the composition of the material overtaken by the phase-separation front. We present a survey of morphologies as a function of these two parameters. We show that the resulting morphologies are initial condition dependent. We then examine which of the potential morphologies is the most stable. An analytical analysis for symmetrical compositions predicts the transition point from orthogonal to parallel stripes.

We show that an enslaved phase-separation front moving with diffusive speeds U = C/ √ T can leave alternating domains of increasing size in their wake. We find the size and spacing of these domains is identical to Liesegang patterns. For equal composition of the components we are able to predict the exact form of the pattern analytically. We also show that there is a critical value for C below which only two domains are formed. Our analytical predictions are verified by numerical simulations using a lattice Boltzmann method.

Abstract. The effects of elasticity on the break-up of liquid threads in microfluidic cross-junctions is investigated using numerical simulations based on the "lattice Boltzmann models" (LBM). Working at small Capillary numbers, we investigate the effects of non-Newtonian phases in the transition from droplet formation at the cross-junction (DCJ) and droplet formation downstream of the cross-junction (DC) (Liu & Zhang, Phys. Fluids. 23, 082101 (2011)). Viscoelasticity is found to influence the break-up point of the threads, which moves closer to the cross-junction and stabilizes. This is attributed to an increase of the polymer feedback stress forming in the corner flows, where the side channels of the device meet the main channel.