Exploitation of continuum and kinetic theory approaches for the simulation of particle beam experiments; 1st ed. 2026

X-ray free-electron lasers (XFELs) promise to allow for atomically resolved imaging of isolated nanoparticles through single-particle diffractive imaging (SPI). Achieving this requires nanoparticle beams with controlled dimensions, typically generated using aerosol injectors operating under varying gas-flow conditions. Numerical simulations play a vital role in understanding and optimizing these injection systems. We present a multi-scale simulation framework that models gas dynamics across continuum-, transition-, and free-molecular-flow regimes as well as particle translation. Leveraging computational fluid dynamics (CFD), direct simulation Monte Carlo (DSMC), and corresponding hybrid methods, the framework provides a foundation for improving aerosol-injection techniques. It was validated against experiments over wide temperature (4–300 K) and size (10–300nm) ranges.