Abstract
Phase separation can drive spatial organization of multicomponent mixtures. For instance in developing animal embryos, effective phase separation descriptions have been used to account for the spatial organization of different tissue types. Similarly, separation of different tissue types is also observed in stem cell aggregates, where the emergence of a polar organization can mimic early embryonic axis formation. Here, we describe such aggregates as deformable two-phase fluid droplets, which are suspended in a fluid environment (third phase). Using hybrid finite-volume Lattice-Boltzmann simulations, we numerically explore the out-of-equilibrium routes that can lead to the polar equilibrium state of such a droplet. We focus on the interplay between spinodal decomposition and advection with hydrodynamic flows driven by interface tensions, which we characterize by a Peclet number Pe. Consistent with previous work, for large Pe the coarsening process is generally accelerated. However, for intermediate Pe we observe long-lived, strongly elongated droplets, where both phases form an alternating stripe pattern. We show that these "croissant" states are close to mechanical equilibrium and coarsen only slowly through diffusive fluxes in an Ostwald-ripening-like process. Finally, we show that a surface tension asymmetry between both droplet phases leads to transient, rotationally symmetric states whose resolution leads to flows reminiscent of Marangoni flows. Our work highlights the importance of advection for the phase separation process in finite, deformable systems.
Highlights
Systems composed of two or more components can undergo phase separation. 1–3 During this process, phase domains of different composition first emerge either through spinodal decomposition or nucleation, before these domains coarsen through diffusive processes such as Ostwald ripening
Coarsening is associated with a power-law growth of typical domain size λ, which scales as λ ∼ t1/3 with time t. 1 In the case of fluid-fluid phase separation, coarsening can occur through advection with hydrodynamic flows that are driven by the interface tension between adjacent domains
While the thermodynamic equilibrium state for such a system is well known, we studied the route to reach equilibrium
Summary
Systems composed of two or more components can undergo phase separation. 1–3 During this process, phase domains of different composition first emerge either through spinodal decomposition or nucleation, before these domains coarsen through diffusive processes such as Ostwald ripening. 1 In the case of fluid-fluid phase separation, coarsening can occur through advection with hydrodynamic flows that are driven by the interface tension between adjacent domains. Such hydrodynamic flows can speed up domain coarsening, which can lead to e.g. a linear scaling λ ∼ t. We find that while increasing P e generally speeds up the phase separation process, intermediate P e give rise to longlived “croissant” states that slow down the relaxation to the final polarized state These results are not fundamentally changed by including an asymmetry between the surface tensions σ13 and σ23. Our work demonstrates the importance of hydrodynamic flows in deformable multi-phase droplets
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