BINARY NUCLEATION KINETICS .2. NUMERICAL-SOLUTION OF THE BIRTH-DEATH EQUATIONS

We numerically solve the complete set of coupled differential equation s describing transient binary nucleation kinetics for vapor-to-liquid phase transitions. We investigate binary systems displaying both posit ive and negative deviations from ideality in the liquid phase and obta in numerical solutions over a wide range of relative rates of monomer impingement. We emphasize systems and conditions that either have been or can be investigated experimentally. In almost every case, we find behavior consistent with Stauffer's idea that the major particle flux passes through the saddle point with an orientation angle that depends on the rates of monomer impingement. When this is true, the exact num erical steady state nucleation rates are within 10%-20% of the predict ions of Stauffer's analytical theory. The predictions of Reiss' saddle point theory also agree with the numerical results over a wide range of relative monomer impingement rates as long as the equilibrium vapor pressures of the two pure components are similar, but Stauffer's theo ry is more generally valid. For systems with strong positive deviation s from ideality, we find that the saddle point approximation can occas ionally fail for vapor compositions that put the system on the verge o f partial liquid phase miscibility. When this situation occurs for com parable monomer impingement rates, we show that the saddle point appro ximation can be rescued by evaluating an appropriately modified nuclea tion rate expression. When the two impingement rates differ significan tly, however, the major particle flux may bypass the saddle point and cross a low ridge on the free energy surface. Even in these rare cases , the analytical saddle point result underpredicts the numerical resul t by less than a factor of 10. Finally, we study the transition from b inary to unary nucleation by progressively lowering the vapor concentr ation of one component. Both Reiss' and Stauffer's rate expressions fa il under these conditions, but our modified rate prescription remains within 10%-20% of the exact numerical rate. (C) 1995 American Institut e of Physics.