Fig. 1: Phase separation and dynamic asymmetry.
From: Power-law coarsening in network-forming phase separation governed by mechanical relaxation
a Three classical coarsening mechanisms for phase separation and the corresponding growth exponents ν. b The left panel shows a typical phase diagram of colloidal suspensions. For a shallow quench, the two phases have similar relaxation time τα because of the similar colloid volume fraction, ϕ, between the two phases (see the upper right panel ‘shallow quench’, where we can see similar particle mobilities between the two phases; each particle trajectory is coloured differently). Since the domain deformation rate induced by phase separation is much slower than 1/τα, both phases behave as viscous liquids. In this case, the growth exponents are those known for classical coarsening mechanisms17,18,20. Such behaviours are observed only for a very shallow quench condition (see the green-shaded region; see also Fig. 2). For a deeper quench, on the other hand, the phase with higher ϕ has a much slower relaxation time than the one with lower ϕ (see the lower right panel ‘deep quench’, where we can see very different particle trajectories between the two phases), and the phase separation proceeds with an average speed between them. As a result, the higher ϕ (slower) phase cannot catch up with the domain deformation speed and thus behaves as an elastic body transiently. Thus, the viscoelastic response of the higher ϕ phase plays a dominant role in the domain coarsening dynamics, which cannot be described in the conventional theory of phase separation of fluid mixtures. Here we emphasise that this effect is essential in a broad region of the phase diagram in various dynamically asymmetric systems (see Fig. 2).
