Interactions and Dynamics at the Nanoscale Solid-Liquid Interface

At the solid-liquid interface the fluid interacts with both the phonons an the electrons of the solid. These interactions, called respectively phonon drag and Coulomb drag, can only be explained properly using a quantum formalism. While the collisions (generating the phonon drag) are at the origin of the “classical” friction, the coupling between the collective modes of the fluid and the electronic excitations at the surface of the solid (generating the Coulomb drag) are the source of a new kind of friction which is dominant in certain conditions of nanofluidics. In particular, this provides an understanding of the surprising friction in carbon nanotube where the friction drops as the radius is reduced. When imposing a flow, the solid reaches a quasi-equilibrium state where its different quantum particles fulfil a modified fluctuation-dissipation theorem which includes a frequency shift. In particular, we predict the generation of an electric current which has been measured and studied experimentally. The form of the current is tunnable by choosing the internal structure of the solid: this is a quantum effect. Such an flow-induced electric current may have crucial applications if the solid is well engineered: this opens the door to sensing and controlling the flow velocity at the nanoscales and energy production at larger scales. Physically, the liquid exchanges momentum to the phonons and the electrons through respectively the phonon drag and Coulomb drag: this is like a wind blowing on the Fermi sea. In most situations the former is dominant while the latter is negative: this means that the momentum path is from the flow to the phonons, then the electrons and then back to the flow. In pratice this phenomenon reduces the total friction. This opens the door quantum engeenering the friction by controling the internal structure of the solid. Moreover, everything may be affected by confinement, paving the way to new experimental discoveries.

Geometric Theory of Mechanics and Thermodynamics

The standard formalism to study dynamics is the Hamiltonian mechanics which is founded on a symplectic form (or Poisson bracket) and a dynamical funtion: the Hamiltonian. Such a formalism is powerful to study the dynamics of point objects and fluids in many physical situations and is well suited for numerial integration. However, Hamiltonian dynamics does not include dissipation and then can only study systems at the thermodynamic equilibrium. Yet, some dissipative models can be written in a Hamiltonian structure using non-standard formulations of the theory. This is, in particular, the case with b-symplectic geometry which allows singularities in the phase space. These situations are fascinating for numerical and mathematical studies of dynamics and applies to basic dissipative systems. Another approach is the metriplectic (or GENERIC) framework, which has been developed to adress the limitations of the standard Hamiltonian methods. In this formalism the symplectic form is completed by a pseudo-Riemannian metric and the free energy is used as the dynamical function. Under reasonable assumptions, the two principles of thermodynamics arise from the geometric structure. Such a formalism is well-suited to study close-to-the-equilibrium systems where the thermodynamics is described by Onsager’s linear response. This applies in particular for the majority of models of fluid dynamics, like Naver-Stokes equations. In these models, the metric (or dissipative bracket) contains the microscopic physics and is the geometric realisation of the Onsager’s transport tensor. It can also be derived as a emerging property form grand deviation theory and kinetic theory.