Date of Thesis

Spring 2025

Description

Coarsening describes the phase-separation dynamics that follows after a temperature quench from a stable to unstable region of the phase diagram in binary systems. Whereas binary systems with an isotropic surface tension have been thoroughly examined and modeled, the case of an anisotropic surface tension lacks the same degree of analysis and development. In this thesis, we demonstrate the self-consistency of the scaling hypothesis with an anisotropic surface tension in the dilute limit. We begin by assuming weak anisotropy in the surface tension and working only to first order in perturbation theory. Following a similar approach laid out in the isotropic theory, we derive an equation of motion in terms of a scaled parameter x ≡ R0/L(t) , where R0 is the isotropic radius of the droplet and L(t) is the characteristic length scale of the system, and t is time. We then solve this equation of motion to observe how the anisotropy in the surface tension influences the drop shape and drop size distribution. We find that the drop size distribution, though different from the isotropic case, may be consistently expressed in terms of the scaled parameter x, thus achieving a self-consistent theory of scaling in the anisotropic case. Furthermore, we find that the characteristic length scale of the system remains the same as the isotropic theory L ∼ t^{1/3}, but we also find that the domain structures are governed by the scaled parameter x rather than assuming their equilibrium shapes (Wulff shapes), in direct opposition to previous expectations.

Keywords

physics, phase, kinetics, anisotropic, surface tension

Access Type

Honors Thesis

Degree Type

Bachelor of Arts

Major

Physics

Minor, Emphasis, or Concentration

Mathematics

First Advisor

Ben Vollmayr-Lee

Second Advisor

Deepak Iyer

Third Advisor

Sanjay Dharmavaram

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