A mathematical model of crystallization in an emulsion

Area of Science:

• Physical Chemistry
• Materials Science
• Chemical Engineering

Background:

• Emulsion crystallization involves complex processes like nucleation, precipitation, and monomer transport.
• Existing models often simplify or omit key physical effects, limiting their predictive power.

Purpose of the Study:

• To develop a comprehensive mathematical model for emulsion crystallization.
• To explicitly conserve particle numbers and incorporate monomer transport between emulsion domains.
• To analyze the influence of various physical processes on crystal formation and growth.

Main Methods:

• Formulation of an autonomous system of nonlinear, coupled ordinary differential equations.
• Application of Becker-Döring equations for nucleation and precipitation.
• Stage-wise analysis of the model to understand individual process roles.
• Numerical calculations and linear stability analysis for different scenarios.

Main Results:

• The model accurately describes nucleation, precipitation, monomer transport, and crystal growth in emulsions.
• Numerical results are consistent with experimental observations, particularly when crystals act as monomer sinks.
• Analysis reveals the impact of monomer transport on crystallization dynamics.
• Bifurcation diagrams illustrate the behavior of stationary solutions.

Conclusions:

• The developed mathematical model provides a robust framework for studying emulsion crystallization.
• Explicit conservation of particles and detailed monomer transport are crucial for accurate modeling.
• The model's predictions align with experimental data, validating its approach.