## 1 Introduction  
Interfacial thermal conductance (ITC) is an important parameter for various technologies, as it affects the transfer of heat from one material to another [1]. ITC is of great importance for the development of the electronics industry, as it affects the cooling capabilities of electronic components [2]. ITC can determine the rate of fast melting and solidification of metal microdroplets during industrial laser-based processes. Thus, ITC is significant in laser welding [3] and laser additive manufacturing [4]. ITC affects the solidification rate, microstructure, and mechanical properties of the resulting materials [3, 5, 6, 7]. Actually, various nanostructures can be created by controlled crystallization in many applications, such as additive manufacturing [5, 8, 9]. Advances in laser and additive manufacturing can be achieved through the proper development and modification of commercial base powders to optimize heat transfer in the system [10]. Thus, a deep understanding of the influence of different contributions to the ITC at the solid-solid and liquid-solid interfaces during phase transitions in microparticles can be useful for optimizing various technological processes. In this article, we will focus on the mesoscopic effects that affect the ITC during the fast melting and solidification of metal microparticles in contact with a solid. We will consider the interfacial thermal conductance \(G\), defined by Equation (1)  
\[G=q/S\Delta T, \tag{1}\]  
where \(q\) is the heat flow across the interface, \(S\) is the area of the interface, and \(\Delta T\) is the temperature jump at the interface [1; 11]. Heat transfer experiments in heterostructures and epitaxial interfaces (when the interfaces are atomically smooth and clean) show that ITC can be on the order of \(10^{8}\)-\(10^{9}\) W/m\({}^{2}\)K at temperatures of about 300 K [12; 13]. Acoustic phonons are the dominant heat carriers through such interfaces [1; 13; 14]. However, most interfaces are not so perfect in the case of melting and solidification of microparticles in contact with a solid. The surface roughness of the contacting bodies leads to the appearance of an interfacial gap. The magnitude of the various contributions to ITC is highly dependent on the size of this gap. The effective distance \(d\) between contacting materials is a key parameter for determining ITC. This distance can change significantly during melting and solidification. In fact, for liquid-solid interfaces, the influence of the substrate surface roughness on the ITC is strongly suppressed since liquids can spread over the surface roughness. Remarkably, liquids can spread very efficiently over surface roughness even in the absence of good wetting, as evidenced by experiments with mercury-silicon interfaces [15], as well as interfaces between water and hydrophobic surfaces [16]. Dispersion forces [17], which are always present and play an important role in interfacial adhesion during the melting of metal particles on a solid, can lead to the spreading of the sample over the surface roughness during melting. As a result, the thickness \(d\) can be significantly reduced during the sample melting. Near-field photon tunneling plays an important role in ITC for liquid-solid interfaces, see below. Actually, ITC can vary over a wide range of \(10^{3}\)-\(10^{7}\) W/m\({}^{2}\)K and depends on the influence of various mesoscopic effects affecting the interfacial heat transfer. Interfacial adhesion is the most important factor affecting ITC. For example, interfacial adhesion between nanoparticles and an organic matrix is due to the covalent chemical bonds [18; 19]. This chemical adhesion is relatively strong compared to the dispersive adhesion that occurs when metal particles are melted on a solid. Chemical forces act at very short sub-nanometer distances [17]. In this case, acoustic phonons can be the dominant heat carriers at interfaces at sub-nanometer distances [14].