| Pub. Date | : Nov, 2023 |
|---|---|
| Product Name | : The IUP Journal of Marketing Management |
| Product Type | : Article |
| Product Code | : IJMM031123 |
| Author Name | : Rahul Basu |
| Availability | : YES |
| Subject/Domain | : Marketing |
| Download Format | : PDF Format |
| No. of Pages | : 18 |
The paper illustrates the effect of additional terms in diffusion equations, particularly spinodal equations. The spinodal mechanism is described by secondorder diffusion with additional terms of 4th order coupled with a constant. Solutions are seldom found in a simple manner. These materials can yield nanostructures and alloys with advanced properties. In this study, a perturbation for small values of x and t was applied. Similarity variables with x and t are employed along with the separation of variable solutions that can produce an exact series solution. The results illustrate how growth proceeds and the effect of material parameters on growth, along with the important combinations of physical properties. The solutions vary depending on the transcendental equations for the moving boundaries. The rate dependencies changed from the square root of t to the 4th root of t at the small-parameter level. For example, a Cu-Ni alloy has been simulated. This study is primarily hypothetical, and focuses on the analysis of mathematical models. Important findings have recently appeared, showing the applicability of these transformations in the design of energy-storage cells, solar energy, nanocomposites, and other areas.
Traditional wisdom concerning phase nucleation states that heterogeneous or
homogeneous nucleation depends on the critical growth size. Growth depends on
the balance between free energy and surface tension. The diffusion and moving
interface balances were neglected. The alternative mechanism involves the 'spinodal
decomposition', where the transformation occurs throughout the original solution,
relying on an inflection in the free-energy curves. This requires a miscibility region,
in which a range of solubilities occurs.
The equations describing the process are diffusion equations modified by a coupled
4th order term, which is a double Laplacian. Normally, such term is of smaller order;
however, under certain parameter combinations, it can dominate. However, no
equation dictates the presence of two or more components.
Moving boundary problem, Nucleation, Spinodal mechanism