Published Online:August 2024
Product Name:The IUP Journal of Mechanical Engineering
Product Type:Article
Product Code:
Author Name:Basu Rahul
Availability:YES
Subject/Domain:Engineering
Download Format:PDF
Pages:10
The Cahn-Hilliard equation is a fundamental model in the study of phase separation and coarsening phenomena in binary mixtures. The paper investigates the perturbative solutions of the one-dimensional Cahn-Hilliard equation for small spatial and temporal variables. Starting with a uniform state, a small perturbation was introduced and first-order perturbation expansion was derived. Utilizing Fourier transforms, the linearized form of Cahn-Hilliard equation was solved to obtain the general solution. The dispersion relation revealed the growth rates of perturbation modes, providing insight into the early-time dynamics of phase separation. The analytical approach lays the groundwork for understanding the evolution of small perturbations and their impact on the phase separation process in binary systems. This work has potential applications in materials science, particularly in understanding the microstructural development of alloys and polymer blends.
The Cahn-Hilliard equation is a cornerstone in the theoretical study of phase separation and coarsening phenomena. This paper delves into the perturbative solutions of onedimensional Cahn-Hilliard equation, particularly focusing on small spatial and temporal variables. A small perturbation is introduced and the first-order perturbation expansion is derived. By employing series, the linearized form of the Cahn-Hilliard equation is solved, yielding the general solution. The dispersion relation obtained from this analysis elucidates the growth rates of perturbation modes, thereby shedding light on the early-time dynamics of phase separation. This analytical framework provides a deeper understanding of the evolution of small perturbations and their significance in the phase separation process within binary systems. The findings have promising implications for materials science, especially in elucidating the microstructural development of alloys and polymer blends.