Thermal rupture of a free liquid sheet

TL;DR

This paper analyzes how temperature-dependent surface tension influences the breakup of a free liquid sheet, revealing exponential thinning driven by temperature gradients and providing universal similarity solutions validated by simulations.

Contribution

It introduces a new analytical framework for the thermal rupture of liquid sheets considering temperature-dependent surface tension and viscosity effects.

Findings

Exponential thinning of the sheet due to temperature gradients.

Universal similarity solutions for the pinch region profiles.

Quantitative agreement between analytical models and numerical simulations.

Abstract

We consider a free liquid sheet, taking into account the dependence of surface tension on temperature, or concentration of some pollutant. The sheet dynamics are described within a long-wavelength description. In the presence of viscosity, local thinning of the sheet is driven by a strong temperature gradient across the pinch region, resembling a shock. As a result, for long times the sheet thins exponentially, leading to breakup. We describe the quasi one-dimensional thickness, velocity, and temperature profiles in the pinch region in terms of similarity solutions, which posses a universal structure. Our analytical description agrees quantitatively with numerical simulations.