ONE-DAY WORKSHOP ON APPLIED MATHEMATICS 2024

SPEAKER

Silvia Lorenzani (Politecnico di Milano)

SCHEDULE

11:00 - 12:00

TITLE

On the linearized Boltzmann equation with Cercignani-Lampis boundary conditions: well-posedness and microfluidic applications

ABSTRACT

An accurate modeling of gas-surface interaction is crucial for the study of rarefied gas flows in microdevices. This issue can be addressed by choosing suitable boundary conditions for the Boltzmann equation. Unfortunately, over the years, research in this direction has not made much progress and most studies in kinetic theory use Maxwell boundary conditions proposed in 1879. However, recent experiments have revealed that this model of gas-surface interaction fails to explain several results related to temperature-driven mass flow rates in microchannels. Therefore, in this talk, we will address the well-posedness of the Boltzmann equation with Cercignani-Lampis boundary conditions (which guarantee a more reliable description of the gas-surface interaction) and we will present recent applications to microfluidics.