## Abstract

This work proposes a fully continuum stochastic model of a multicomponent fluid. It is shown that the way to this model leads to a generalized-kinetics (GK) theory. Subsequently, the model is developed as a corresponding extension of this theory. The obtained model presents the overall generalized distribution function. It is described with a nonlinear nonlocal (or "mean-field") system of two scalar equations, no matter how many components are in the fluid, and a special prescription. The system comprises (i) the generalized kinetic equation for the conditional distribution function conditioned with the values of the particle-property stochastic process, and (ii) the McKean-Kolmogorov forward equation for the probability density of this process. The aforementioned prescription determines the number of the fluid components as the number of the modes of this density. The work also includes a theorem that provides an estimation from below for this number in the generic stationary case of the corresponding multidimensional Kolmogorov equation and points out how the modes manifest themselves in the drift and diffusion functions (more specifically, in the Fichera drift function). The discussion on the model and a few directions for future research concludes the work.

Original language | English |
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Pages (from-to) | 637-659 |

Number of pages | 23 |

Journal | Mathematical and Computer Modelling |

Volume | 38 |

Issue number | 5-6 |

DOIs | |

State | Published - Oct 10 2003 |

Externally published | Yes |

## Keywords

- Distribution function
- Generalized kinetic equation
- McKean-Kolmogorov forward equation
- Multimodal probability density
- Real-life multicomponent fluid