When phonon transport is in the hydrodynamic regime, the thermal conductivity exhibits peculiar dependences on temperatures (T) and sample widths (W). These features were used in the past to experimentally confirm the hydrodynamic phonon transport in three-dimensional bulk materials. Suspended graphene was recently predicted to exhibit strong hydrodynamic features in thermal transport at much higher temperature than the three-dimensional bulk materials, but its experimental confirmation requires quantitative guidance by theory and simulation. Here we quantitatively predict those peculiar dependences using the Monte Carlo solution of the Peierls-Boltzmann equation with an ab initio full three-phonon scattering matrix. Thermal conductivity is found to increase as T α where α ranges from 1.89 to 2.49 depending on a sample width at low temperatures, much larger than 1.68 of the ballistic case. The thermal conductivity has a width dependence of 1.17 W at 100 K, clearly distinguished from the sublinear dependence of the ballistic-diffusive regime. These peculiar features are explained with a phonon viscous damping effect of the hydrodynamic regime. We derive an expression for the phonon hydrodynamic viscosity from the Peierls-Boltzmann equation, and discuss that the phonon viscous damping explains well those peculiar dependences of thermal conductivity at 100 K. The phonon viscous damping still causes significant thermal resistance when a temperature is 300 K and a sample width is around 1 μm, even though the hydrodynamic regime is not dominant over other regimes at this condition.

Hydrodynamic phonon transport was recently predicted as an important regime for phonon transport in graphitic materials. Many of past studies on hydrodynamic phonon transport have focused on the cases where the hydrodynamic regime is significantly stronger than other regimes such that hydrodynamic features can be clearly observed. However, this often requires stringent conditions of temperature and sample size. In many cases, the transport cannot be characterized by a single regime, but the features of all three regimes -ballistic, hydrodynamic, and diffusive regimes -exist to some extent. Here we assess the extent of three regimes by comparing momentum destruction rates by three different mechanisms, each of which represents a different regime: diffuse boundary scattering without internal phonon scattering (ballistic regime), diffuse boundary scattering combined with normal scattering (hydrodynamic regime), and umklapp scattering (diffusive regime). We solve the Peierls-Boltzmann equation with an ab initio full scattering matrix using a deviational Monte Carlo method. We sample distribution functions of ballistic and scattered particles separately, and thereby compare the momentum destruction rates by the three different mechanisms. Using this framework, we discuss a well-known phenomenon of ballistic-to-hydrodynamic crossover, called phonon Knudsen minimum.

The hydrodynamic phonon transport was studied several decades ago for verifying the quantum theory of lattice thermal transport. Recent prediction of significant hydrodynamic phonon transport in graphitic materials shows its practical importance for high thermal conductivity materials and brought a renewed attention. As the study on this topic has been inactive to some extent for several decades, we aim at providing a brief overview of the past studies as well as very recent studies. The topics we discuss in this chapter include the collective motion of phonons, several approaches to solve the Peierls-Boltzmann transport equation for hydrodynamic phonon transport, the role of normal scattering for thermal resistance, and the propagation of second sound. Then, we close this chapter with our perspectives for the future studies and the practical implication of hydrodynamic phonon transport.

Using a neutron scattering technique that measures a statistically-averaged density correlation function in real space rather than the conventional reciprocal-space structure factor, we have measured correlations between poly(methyl-methacrylate) (PMMA) colloidal particles of several sizes suspended in decalin. The new method, called Spin Echo Small Angle Neutron Scattering (SESANS) provides accurate information about particle composition, including the degree of solvent penetration into the polymer brush grafted on to the PMMA spheres to prevent aggregation. It confirms for particles, between 85 nm and 150 nm in radius that inter-particle correlations closely follow the Percus-Yevick hard-sphere model when the colloidal volume-fraction is between 30% and 50% provided the volume-fraction is used as a fitted parameter. No particle aggregation occurs in these systems. When small amounts of polystyrene are added as a depletant to a concentrated suspension of PMMA particles, short-range clustering of the particles occurs and there is an increase in the frequency of near-neighbor contacts. Within a small range of depletant concentration, near-neighbor correlations saturate and large aggregates with power law density correlations are formed. SESANS clearly separates the short- and long-range correlations and shows that, in this case, the power-law correlations are visible for inter-particle distances larger than roughly two particle diameters. In some cases, aggregate sizes are within our measurement window, which can extend out to 16 microns in favorable cases. We discuss the advantages of SESANS for measurements of the structure of concentrated colloidal systems and conclude that the method offers several important advantages.