番茄社区

Research Areas

• Non-equilibrium Thermodynamics
• Kinetic Theory of Gases
• Microscale Transport
• Aerosol coagulation

Research Description

The emphasis of Henning Struchtrup's research lies on the kinetic theory of gases, in particular in the development of continuum models for rarefied gas flow in the transition regime, where the relevant length scales are of the order of magnitude of the mean free path of the gas particles, and the usual continuum models - Navier-Stokes and Fourier equations - are not applicable. Typical problems are the reentry problem of space craft or the flow around very small objects, i.e. micro mechanical devices (MEMS). Applications for quantum gases include the transport of electrons in semiconductor devices, radiative transfer in thin atmospheres, and energy transport through phonons in small solid objects.

The rational derivation of transport models for microscale gasflows is based on the Boltzmann equation, which describes the gas as a set of statistical particles. Equations for macroscopic quantities like temperature or velocity, follow by proper averaging of the Boltzmann equation, and a careful discussion of the order of magnitude of quantities involved.

Only recently, Struchtrup developed a new approach to derive transport equations for rarefied gases from the Boltzmann equation within higher orders of the Knudsen number. The new method yields the Euler equations at zeroth order, the Navier-Stokes-Fourier equations at second order, Grad's 13 moment equations (with omission of a non-linear term) at second order, and a regularization of these at third order. An important feature of the method presented is that the equations of any order are stable, other than in the traditional Chapman-Enskog method, where the second and third approximation - Burnett and super-Burnett equations - are unstable.

The third order equations - termed as regularized 13 moment equations (R13) - were developed and investigated together with M. Torrilhon (ETH Zurich). The R13 equations contain the Burnett and Super-Burnett equations when expanded in a series in the Knudsen number, but, other than the Burnett and Super-Burnett equations, they are linearly stable for all wavelengths and frequencies. Dispersion relation and damping for the new equations agree better with experimental data than those for the Navier-Stokes-Fourier equations, or the original Grad 13 moment system. The new equations allow the description of Knudsen boundary layers, and yield smooth shock structures for all Mach numbers in good agreement with experiments and DSMC simulations.

An important issue is to provide proper boundary conditions for the higher order models, and this is one of the main topics under research in Struchtrup's group. Other current topics include the development of improved BGK models for the Boltzmann collision term, evaporation and condensation in strong non-equilibria, and transport models for fuel cell membranes.