Phase-field theory of multicomponent incompressible Cahn-Hilliard liquids

Modeling, simulation, and optimization of electrowetting-on-dielectric (EWOD) devices

With widespread research studies on electrowetting-on-dielectric (EWOD) for droplet manipulation in the field of lab-on-a-chip, how to improve the driving capability of droplets has increasingly attracted enormous interest. Aiming to decrease driving voltages and improve driving effectiveness, this paper studies the modeling, simulation, and optimization of EWOD devices. The theoretical model is refined mainly in consideration of the saturation effect of the contact angle and then verified by both simulation and experiments. As a design guide to decrease the driving voltage, a theoretical criterion of droplet splitting, the most difficult one among four basic droplet manipulations, is developed and then verified by experimental results. Moreover, a novel sigmoid electrode shape is found by the optimization method based on finite element analysis and achieves better driving effectiveness and consistent bidirectional driving capability, compared with the existing electrode shapes. Taken together, this paper provides an EWOD analysis and optimization method featuring a lower voltage and a better effectiveness and opens up opportunities for optimization designs in various EWOD-based applications.

Kinetics of coarsening have dramatic effects on the microstructure: Self-similarity breakdown induced by viscosity contrast

The viscous coarsening of a phase separated mixture is studied and the effects of the viscosity contrast between the phases are investigated. From an analysis of the microstructure, it appears that for moderate departure from the perfectly symmetric regime the self-similar bicontinuous regime is robust. However, the connectivity of one phase decreases when its volume fraction decreases or when it is becoming less viscous than the complementary phase. Eventually self-similarity breakdown is observed and characterized.

Experimental investigations and phase-field simulations of triple-phase-separation kinetics within liquid ternary Co-Cu-Pb immiscible alloys

The phase-separation kinetics and microstructure evolution mechanisms of liquid ternary Co_{43}Cu_{40}Pb_{17} immiscible alloys are investigated by both the drop tube technique and phase-field method. Two successive phase separations take place during droplet falling and lead to the formation of a three-phase three-layer core-shell structure composed of a Co-rich core, a Cu-rich middle layer, and a Pb-rich shell. The Pb-rich shell becomes more and more conspicuous as droplet diameter decreases. Meanwhile, the Co-rich core center gradually moves away from the core-shell center. Theoretical analyses show that a larger temperature gradient inside a smaller alloy droplet induces the accelerated growth of the surface segregation shell during triple-phase separation. The residual Stokes motion and the asymmetric Marangoni convection result in the appearance of an eccentric Co-rich core and the core deviation degree is closely related to the droplet size and initial velocity. A three-dimensional phase-field model of ternary immiscible alloys, which considers the successive phase separations under the combined effects of Marangoni convection and surface segregation, is proposed to explore the formation mechanisms of three-phase core-shell structures. The simulated core-shell morphologies are consistent with the experimental observations, which verifies the model's validity in reproducing the core-shell dynamic evolution. Numerical results reveal that the development of three-phase three-layer core-shell structures can be attributed to the primary and then secondary phase separations dominated simultaneously by Marangoni convection and surface segregation. Furthermore, the effects of droplet temperature gradient on the growth kinetics of the surface segregation shell are analyzed in the light of phase-field theory.

A multi-fluid model for microstructure formation in polymer membranes

We develop a multi-fluid model for a ternary polymer solution using the Rayleighian formalism of Doi and Onuki, and give an efficient pseudo-spectral method for solving both the diffusion and momentum equations that result. Subsequently, we find that the numerical simulation is capable of describing systems at the micron length-scale and easily reaches millisecond time-scales. In addition, we characterize the model thermodynamics and kinetics including the (i) phase behavior, (ii) structure of the interfaces, (iii) mutual diffusion coefficients, (iv) bulk spinodal decomposition kinetics with and without hydrodynamics and (v) spinodal decomposition in the presence of an interface with a non-solvent bath. We obtain good qualitative agreement with the expected thermodynamic and kinetic behavior. We also show that a linear stability analysis of the diffusion equation quantitatively predicts the fastest growing mode obtained from simulation and gives insight into the phase separation process relevant for the evolution of microstructure in phase-separating ternary polymer solutions.

Phase-field modeling of isothermal quasi-incompressible multicomponent liquids

In this paper general dynamic equations describing the time evolution of isothermal quasi-incompressible multicomponent liquids are derived in the framework of the classical Ginzburg-Landau theory of first order phase transformations. Based on the fundamental equations of continuum mechanics, a general convection-diffusion dynamics is set up first for compressible liquids. The constitutive relations for the diffusion fluxes and the capillary stress are determined in the framework of gradient theories. Next the general definition of incompressibility is given, which is taken into account in the derivation by using the Lagrange multiplier method. To validate the theory, the dynamic equations are solved numerically for the quaternary quasi-incompressible Cahn-Hilliard system. It is demonstrated that variable density (i) has no effect on equilibrium (in case of a suitably constructed free energy functional) and (ii) can influence nonequilibrium pattern formation significantly.