Mathematical Model for the Evaporation of a Liquid Fuel Droplet, Subject to Nonlinear Constraints

TL;DR

This paper presents a mathematical model for liquid fuel droplet evaporation, analyzing radius evolution under nonlinear constraints, proving solution existence, and validating with numerical simulations aligned with physical experiments.

Contribution

It introduces a coupled hyperbolic system model with nonlinear constraints and proves the existence of bounded solutions for the droplet's mass fraction.

Findings

Existence of bounded solutions for the mass fraction under nonlinear constraints.

Numerical simulations agree with physical experiments.

Model captures the evolution of droplet radius over time.

Abstract

We study the mathematical evolution of a liquid fuel droplet inside a vessel. In particular, we analyze the evolution of the droplet radius on a finite time interval. The model problem involves an hyperbolic system coupled with the pressure and velocity of the surrounding gas. Existence of bounded solutions for the mass fraction of the liquid, submitted to nonlinear constraints, is shown. Numerical simulations are given, in agreement with known physical experiments.