  Existing theoretical models of the interfacial thermal conductance, i.e.,
Kapitza conductance, of insulating solid-fluid interfaces only consider bulk
properties, e.g., acoustic mismatch model and diffuse mismatch model. In this
work, we propose a classical lattice dynamical model calculation of the Kapitza
conductance, thereby incorporating interfacial structural details. In our
model, we assume that heat is mostly carried by phonons in the solid, and that
sound waves carry diffusive heat from the interface into the bulk of the
liquid, where both longitudinal and transverse sound waves are considered.
Sound wave dispersion is calculated from the fluid pair distribution function,
evaluated using approximate integral equation theories (i.e., Percus-Yevick,
Hypernetted-chain approximation). The Kapitza conductance of the solid-fluid
interface is obtained from the phonon transmission coefficient at the
interface. We determine the interfacial phonon transmission coefficient by
solving the coupled equations of motion for the interfacial solid and fluid
atoms. As an illustrative example, we derive the Kapitza conductance of solid
argon-fluid neon interface, with pair-wise Lennard-Jones interactions.
