ON THE ULTIMATE FINENESS OF A DISPERSION

Abstract

Equilibrium composition and pressure profiles are determined for spherical drops within a binary, Landau-Ginzburg fluid that has undergone phase separation. There is a smallest possible drop size, below which a drop would redissolve to form a homogeneous system. This minimum drop size has a radius of

R_i = √k/-gⁿ(ã)

where κ is the gradient energy parameter and g(ã) is the Gibbs free energy of mixing evaluated at the system average concentration. The minimum drop size at equilibrium is approximately equal to the minimum size for growth by spinodal decomposition as predicted from linearized Cahn-Hilliard theory. It represents a practical limit on the ultimate fineness of polymer-in-polymer microdisper-sions. The minimum drop radius will be on the order of 0.02 microns for typical, high molecular weight polymers.

The surface tension is calculated for systems of finite extent in both radial and spherical coordinates. It vanishes when the size of the system is less than the minimum size needed for bifurcation into two phases. The pressure distribution within spherical drops is calculated using a differential form of the Young-Laplace equation. The classical result,

ΔP = 2σ/R

overpredicts the internal pressure for small drop sizes although this is partially due to the ambiguity in specifying the radius of small drops.

KEYWORDS:

• Dispersion
• Phase separation
• Phase equilibrium
• Landau-Ginzburg
• Spinodal decomposition
• Drop size

Notes

Present address: Department of Equipment Design for Process Industries, Czech Technical University, Suchbatarova 4, 116 07 Prague, Czechoslovakia.