Phase Separation Kinetics of Binary Systems: Effects of Hydrodynamic Interaction And Surfactants
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PHASE SEPARATION KINETICS OF BINARY SYSTEMS: EFFECTS OF HYDRODYNAMIC INTERACTION AND SURFACTANTS KYOZI KAWASAKI, TSUYOSHI KOGA AND TOSHIHIRO KAWAKATSU Kyushu University 33, Dept. of Physics, Fukuoka 812, Japan
ABSTRACT Cell dynamics computer simulation method is used to investigate effects of hydrodynamic interaction as well as effects of added surfactants on phase separation kinetics. In the former the obtained scattering structure function for 3-dimensional system reproduces the experimental results for polymer blends remarkably well. In the latter we display self-assembling process in two-dimensional system on computer.
INTRODUCTION Dynamics of ordering processes in which initially disordered phase is transformed into regular ordered phase has attracted continued attention[l]. Although this problem originated in phase separation of binary alloys (spinodal decomposition), the phenomenon is quite common in any situation involving phase transition. A recent surprising development is a proposal to relate this problem to that of the early Universe[2], where the order parameter is much more complex than that of binary systems. Here our aim is much more modest. We describe our recent works on the two aspects of phase separation kinetics in binary fluid systems:effects of hydrodynamic interaction between order parameter fluctuations and effects of adding surfactants.
HYDRODYNAMIC INTERACTION Importance of the effects of hydrodynamic interactions on spinodal decomposition in binary fluids was noted by one of us many years ago[3]. This was exhaustively examined by Siggia[4] but still on a qualitative level. In view of complex and highly nonlinear character of the governing equation, an approximate treatment[3] is not satisfactory especially at the late stage when the nonlinearity comes in with full strength. At this time the only quantitatively reliable analysis of the problem depends on computer simulations of the governing equation. First we derive the governing equation. We start from the following macroscopic continuity equation for the local concentration S(r, t) which is normalized to zero at the critical point :
S(r, ( t)
=
-V j(r, t),
(1)
where j(r, t) is the concentration current density. There are two contributions to j(r, t) in binary fluids, that is, the diffusion current and the convection current represented, respectively, by the two terms in the following equation :
j(rIt) = -LVs(r,,t) + S(r, t)v(r,t), Mat. Res. Soc. Symp. Proc. Vol. 237. 01992 Materials Research Society
(2)
88
where L and v are the Onsager kinetic coefficient and the local convective velocity, respectively. p is the local chemical potential that can be expressed as (the time arguments in various functions will often be suppressed for simplicity)
y(r) = HjlS}lSS(r),
(3)
where H{S} is the Ginzburg-Landau free energy functional given by
H{S}
+ 1 gS(= 2T{-LV 6(r
-
r') + [VS(r)]. T(r
-
r') . [V'S(r')]}6(t - t'). (12)
T being the Boltzmann constant times the absolute temperature. This kind of closed stochastic equation for
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