Mario Liu

Granular solid hydrodynamics

A complete continuum mechanical theory for granular media, including explicit expressions for the energy current and the entropy production, is derived and explained. Its underlying notion is: granular media are elastic when at rest, but turn transiently elastic when the grains are agitated—such as by tapping or shearing. The theory includes the true temperature as a variable, and employs in addition a granular temperature to quantify the extent of agitation. A free energy expression is provided that contains the full jamming phase diagram, in the space spanned by pressure, shear stress, density and granular temperature. We refer to the theory as GSH, for granular solid hydrodynamics. In the static limit, it reduces to granular elasticity, shown previously to yield realistic static stress distributions. For steady-state deformations, it is equivalent to hypoplasticity, a state-of-the-art engineering model.

Convective Nonlinearity in Non-Newtonian Fluids

In the limit of infinite yield time for stresses, the hydrodynamic equations for viscoelastic, non-Newtonian liquids such as polymer melts must reduce to that for solids. This piece of information suffices to uniquely determine the nonlinear convective derivative, an ongoing point of contention in the rheology literature.

Granular elasticity without the Coulomb condition

A self-contained elastic theory is derived which accounts both for mechanical yield and shear-induced volume dilatancy. Its two essential ingredients are thermodynamic instability and the dependence of the elastic moduli on compression.

Rotating Superconductors and the Frame-Independent London Equation

A frame-independent, thermodynamically exact, London equation is presented, which is especially valid for rotating superconductors. A direct result is the unexpectedly high accuracy (

Invalidation of the Kelvin Force in Ferrofluids

\ensuremath{\sim}{10}^{\ensuremath{-}10}

Fluid pumped by magnetic stress

) for the usual expression of the London moment.

The effects of boundary curvature on hydrodynamic fluid flow; Calculation of slip lengths

Direct and unambiguous experimental evidence for the magnetic force density being of the form MnablaB in a certain geometry-rather than being the Kelvin force MnablaH--is provided for the first time. ( M is the magnetization, H is the field, and B is the flux density.)

Rotating superconductors and the London moment: Thermodynamics versus microscopics

A magnetic field rotating on the free surface of a ferrofluid layer is shown to induce considerable fluid motion toward the direction the field is rolling. The measured flow velocity (i) increases with the square of the magnetic field amplitude, (ii) is proportional to the thickness of the fluid layer, and (iii) has a maximum at a driving frequency of about 3kHz. The pumping speed can be estimated with a two-dimensional flow model.

Causality and stability of the relativistic diffusion equation

The slip description of fluid flow past solid boundaries is reconsidered. We find that the traditional picture of fluid slip as a mean free path correction to hydrodynamics has to be revised whenever the particle scattering becomes close to specular. Then the microscopic slip length may diverge and it is the boundary’s curvature which is decisive for the momentum transfer between fluid and wall. By explicitly considering surface roughness we can explain discrepancies between experimentally observed data and traditional slip theory.

Inconsistency of a dissipative contribution to the mass flux in hydrodynamics

Comparing various microscopic theories of rotating superconductors to the conclusions of thermodynamic considerations, we traced their marked difference to the question of how some thermodynamic quantities (the electrostatic and chemical potentials) are related to more microscopic ones: The electrons the work function, mean-field potential and Fermi energy -- certainly a question of general import. After the correct identification is established, the relativistic correction for the London Moment is shown to vanish, with the obvious contribution from the Fermi velocity being compensated by other contributions such as electrostatics and interactions.