Phase Separation
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Index   Experiments   Theory   Simulation   Drops   Conclusions
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Results of Simulation

Using the model H, we have derived a theoretical model to describe 2D phase separating systems. The ratio between convective and diffusive fluxes is proportional to a convection parameter alpha expressing the ratio between thermal and viscous forces. In a typical case of liquid mixture, the convection parameter is of the order of 105. In the following pictures, we see how morphology changes at different times (vertical axis) as the convection parameter is equal to 0, 102, 103, and 104 (horizontal axis).

Table of Images
alpha = 0
movie
(1.5M mpeg)
alpha = 102
movie
(0.9M mpeg)
alpha = 103
movie
(0.6M mpeg)
alpha = 104
movie
(0.5M mpeg)

Note that at very short times, as the system evolves only by diffusion, the morphology is bicontinuous and does not depend on alpha as we see below.

alpha = 0 alpha = 104
solid liquid

Now, when we analyze these simulations, we conclude that they are in excellent agreement with the experimental results.

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Separation Depth

Separation Depth Plot
Separation depth as function of time for phi = 0.50

First, we analyze the separation depth,

Separation Depth Definition
that is the distance of the system from local equilibrium, where concentrations in and out of the drops are equal to their equilibrium value. As we can see, when the convection parameter is small, first drops form, and then they grow. On the other hand, when the convection parameter is large enough, drops formation and growth occur at the same time.

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Growth Rate

Domain Size Plot
Average domain size as function of time for phi = 0.45

Measuring the typical size of the microdomains, we see below that there are two stages, corresponding to those observed for the separation depth. First, during the drop-formation stage, microdomains grow linearly in time, while later, during the drop-growth stage, they grow as t1/3, in agreement with experimental results. Corresponding plot for the separation depth is shown below.

Separation Depth Plot
Separation depth as function of time for phi = 0.45

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Index   Experiments   Theory   Simulation   Drops   Conclusions
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By: Roberto Mauri, Andrea Malagoli, Natalia Vladimirova,
Last modified: 10 January 1999