Kinetics of growth process controlled by convective fluctuations

Area of Science:

• Physical Chemistry
• Materials Science
• Statistical Mechanics

Background:

• Crystal growth is fundamental in materials science.
• Understanding growth kinetics under fluctuating conditions is crucial.
• Convective velocity fields significantly impact particle dynamics.

Purpose of the Study:

• To introduce a model for spherical crystal growth controlled by fluctuating fluid particle velocities.
• To analyze the impact of different velocity fluctuation correlations on growth kinetics.
• To identify conditions leading to universal versus anomalous growth behavior.

Main Methods:

• Development of a mathematical model for compact growth.
• Analysis of noisy, Gaussian, zero-mean velocity fluctuations with Dirac delta, exponential, and algebraic correlations.
• Investigation of long-time asymptotics and power-law time dependencies.

Main Results:

• Universal power-law growth kinetics with a 1/2 exponent, similar to diffusion-limited growth, is found for many fluctuation types.
• Anomalous kinetics arise with slow algebraic decay (t^-gamma, 0
• Averaged radius exhibits ~ t^(1-gamma/2) for 0 ~ (t ln t)^1/2 for gamma=1.

Conclusions:

• The study reveals universal growth behavior under broad fluctuation conditions.
• Anomalous kinetics are strongly dependent on the decay rate of algebraic correlations.
• The findings provide insights into controlling crystal growth dynamics in complex fluid environments.