Application of a Kinetic Model to Time-Dependent Density Correlations in Fluids

The kinetic model of Bhatnagar, Gross, and Krook is used to study the double Fourier transform of the time-dependent density correlation function $G(r, t)$. The results are appropriate to a dilute fluid for arbitrary ratio of wavelength to mean free path. The results of the model calculations are compared to those derived from the linearized hydrodynamic equations. Since neutron and light-scattering experiments can be analyzed in terms of $G(r, t)$, this comparison indicates that the hydrodynamic description should be applicable for momentum transfers less than ($\frac{\hslash }{2\lambda }$), where $\lambda$ is the collision mean free path in the fluid.