title: Spectral investigation of thermal conductance at solid/fluid interfaces
Creators: name: El-Rifai, Abdullah
Publisher: name: The University of Edinburgh
Year: 2025
Subjects: subject: Interfacial Thermal Conductance
subject: Kapitza Conductance
subject: Interfacial Thermal Resistance
subject: Kapitza Resistance
subject: Solid/Fluid Interface
subject: Solid/Liquid Interface
subject: Solid/Liquid/Vapour Interface
subject: Three-phase Contact Line
subject: Spectral Decomposition of Heat Flux
subject: Vibrational Density of States
subject: Interfacial Energy Transport

description: Rising transistor densities and on-chip clock speeds have yielded increasing thermal loads on modern integrated circuits (ICs), leading to a severe degradation in their performance. As IC cooling is primarily limited by modern single-phase thermal management technologies, this has spurred interest in two-phase cooling devices, which exploit the latent heat of vaporisation of the working fluid to extract significantly greater amount of heat from ICs. Traditionally, the efficiency of heat transfer across the solid/liquid (SL) interface has been disregarded in such processes, given the greater importance of conduction, evaporation, and diffusion in the bulk liquid. However, in emerging micro- and nano-engineered systems, the efficiency of SL energy transport is much more likely to be the bottleneck to performance improvements compared to bulk processes. The SL energy transport is dictated by the interfacial thermal conductance (G), which manifests as a temperature discontinuity across any interface comprising dissimilar materials, hypothesised to be caused by the difference in their vibrational properties. Given its growing relevance to the thermal management of ICs, the nanoscale origins of G must be understood. There is an extensive literature on the role of structural parameters (work of adhesion, peak density, structuring, etc) on G, but limited insight has been produced. In contrast, the study of spectral parameters (i.e. the vibrational interactions between SL atoms) have recently shown promise and forms the focus of this thesis. A set of new metrics based on the spectral decomposition of heat flux (SDHF) are developed in this work to track how energy is sent and received across the SL interface. Using these metrics, the mechanisms underlying G are investigated for a range of systems in increasing complexity: a) simple Lennard-Jones SL interface; b) a Lennard-Jones SL interface containing a liquid meniscus; and c) a set of realistic metal/water SL interfaces. For a simple Lennard-Jones interface, G has been shown to exhibit an exponential-tolinear cross-over with increasing SL interaction strength, previously attributed to the relative strength of SL to liquid/liquid interactions. Instead, this thesis reveals that the cross-over in G occurs due to the onset of solidification in the interfacial liquid at high SL interaction strengths. This solidification subsequently influences interfacial SDHF, leading to the cross-over. The overlap between the spectrally decomposed heat fluxes of the interfacial solid and liquid is used to pinpoint when “solid-like energy transport” within the interfacial liquid emerges. A novel decomposition of G is also proposed, separating it into: (i) the conductance right at the SL interface and (ii) the conductance of the nanoscale interfacial liquid region. It is demonstrated that the rise of solid-like energy transport within the interfacial liquid influences the relative magnitude of these conductances, which in turn dictates when the cross-over occurs. Next, the thesis focuses on the demonstrated enhancement in solid/liquid energy transport at a nanoconfined SL interface in the presence of a meniscus. The SL interaction strength at Lennard-Jones interfaces is varied for both confined SL and solid/liquid/vapour systems, finding that the presence of a meniscus yields an enhancement in the interfacial thermal conductance across wettabilities. However, the magnitude of the enhancement is found to depend on the surface wettability, initially rising monotonously for low to moderate wettabilities, followed by a sharp rise between moderate and high wettabilities. By computing the in-plane and out-of-plane components of the spectrally decomposed heat fluxes within both the interfacial solid and liquid, it is shown that the initial monotonous rise in conductance enhancement predominantly stems from a rise in the coupling of out-of-plane vibrations within both the solid and the liquid. In contrast, the subsequent sharp rise at more wetting interfaces is linked to sharp increases in the utilisation of the in-plane modes of the solid and liquid. These observations result from the interplay between the SL adhesive forces and the liquid/vapour interfacial tension. Finally, the thesis studies the enhancement that G experiences with increasing surface wettability at realistic metal/water interfaces, previously attributed to an increase in the similarity of the permissible vibrations within the interfacial solid and liquid, as quantified by the vibrational density of states (VDOS) Overlap. Instead, it is shown for the first time that the VDOS Overlap is unable to explain increases in G for certain interfaces, and that the change in the magnitude of the VDOS Overlap instead only depends on the position of the VDOS distribution of the solid relative to that of the liquid. By computing the spectrally decomposed heat fluxes within the interfacial solid and liquid, it is shown that variations in G for a given metal/water interface with increasing surface wettability stem from an increase in the utilisation of the inplane modes of both the interfacial solid and liquid. Meanwhile, variations in G across metal/water interfaces for the same wettability are shown to stem from a change in the degree to which the interfacial solid and liquid utilise their available modes. The results presented in this thesis provide novel insights into the role of interfacial solid and liquid vibrations in various phenomena, such as: (i) the nonlinearity that G experiences with increasing interaction strength, (ii) the enhancement in G in confined systems brought about by a liquid meniscus, and (iii) the increase in G with increasing surface wettability at realistic interfaces. Additionally, the metrics developed throughout this work demonstrably outperform currently widespread metrics used to investigate G. It is hoped that these results can aid engineers in optimising G at interfaces of interest that are critical to designing effective cooling solutions for electronics. These results have broad application in other areas, such as for improving the heat transfer across plasmonic nanoparticles in various applications such as drug delivery, medical imaging, and thermal therapies.