Theory of Early Stage Spinodal Decomposition in Fluids Near the Critical Point. I

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Abstract
Early stage spinodal decomposition in fluids is studied on the basis of the stochastic equation for the probability distribution functional of the local order parameter. The difficulty of appearance of an arbitrary upper cutoff wave number in the naive treatment of the problem is resolved by introducing the time-depencent upper cutoff. This results in an effective growth rate of fluctuations of unstable modes which increases as t1/3 in time t until the time of the order of a second, after which the growth rate remains constant. This latter value is favorably compared with the experimental value for the growth rate. The spinodal decomposition in the nonlinear regime is compared with the hydrodynamic turbulence, and the average wave number of fluctuations is shown never to increase with time.

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