Document Type

Dissertation

Date of Award

8-31-2021

Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)

Department

Mathematical Sciences

First Advisor

Lou Kondic

Second Advisor

Linda Jane Cummings

Third Advisor

Shahriar Afkhami

Fourth Advisor

Richard O. Moore

Fifth Advisor

Miguel Fuentes-Cabrera

Abstract

Thin film dynamics, particularly on the nanoscale, is a topic of extensive interest. The process by which thin liquids evolve is far from trivial and can lead to dewetting and drop formation. Understanding this process involves not only resolving the fluid mechanical aspects of the problem, but also requires the coupling of other physical processes, including liquid-solid interactions, thermal transport, and dependence of material parameters on temperature and material composition. The focus of this dissertation is on the mathematical modeling and simulation of nanoscale liquid metal films, which are deposited on thermally conductive substrates, liquefied by laser heating, and subsequently dewet into nanoparticles, before cooling and resolidifying. Both single- and multi-metal configurations are considered.

In the former case, continuum theory is used to describe the thermohydrodynamics. Separation of length scales (in-plane length scales are larger than those in the out-of-plane direction) allows for formulation of asymptotic theory that reduces the fluid dynamics problem, involving Navier-Stokes equations in evolving domains, to a fourth order nonlinear partial differential equation for the fluid thickness. Similarly, a leading order thermal model is developed that is novel, computationally efficient, and accurate. The resulting coupled fluid dynamics and thermal transport model is then used to simulate metal film evolution in both two and three dimensional domains, and to investigate the role of various material parameters. Thermal effects are found to play an important role; in particular it is found that the inclusion of temperature dependence in the metal viscosity modifies the time scale of the evolution significantly. On the other hand, in the considered setup the Marangoni (thermocapillary) effect turns out to be insignificant. The rate of heat lost in the substrate, measured by a Biot number (Bi) is found to influence peak metal film temperatures and liquid lifetimes (time from film melting to resolidification) more strongly than substrate thickness (H s ). Nevertheless, changes in both Bi and H s can lead to films that freeze in place prior to full dewetting due to the strong dependence of viscosity on temperature.

n the case of multi-metal configurations, molecular dynamics simulations are used to investigate the competition between chemical instabilities and Rayleigh-Plateau type dewetting behavior in NiAg alloys of various geometries. Phase separation occurs for decreasing temperatures and results in Ag@Ni core-shell particles. During the breakup, phase separation and the Rayleigh-Plateau instability either compete or cooperate depending on the relative positioning of Ag and Ni. When the phase separation length scale is sufficiently large, axial migration of Ag onto Ni can result in both Ag@Ni core-shell and pure Ag nanoparticles. Chemical instabilities, therefore, can strongly affect the dewetting mechanism.

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