Thermal rupture of a free liquid sheet

<jats:p>We consider a free liquid sheet, taking into account the dependence of surface tension on the 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 possess a universal structure. Our analytical description agrees quantitatively with numerical simulations.</jats:p>