A nonlinear analysis of the effect of heat transfer on capillary jet instability

Abstract

Breakup of slender liquid jets under isothermal conditions has been studied extensively. In this work, we investigate the breakup of a viscous jet emanating from an orifice in the presence of convective heat transfer. We study the case where heat is transferred from the jet to the ambient fluid. The temperature varies axially and both viscosity and surface tension are taken to be temperature dependent. Marangoni stresses caused by a thermally induced surface tension gradient are included here. A numerical model based on a one-dimensional slender jet approximation of the equations of motion and heat transfer is used. This results in three coupled nonlinear partial differential equations, which are solved using the method of lines. The advantages of using this approximation lie in (i) its computational elegance and (ii) the physical insight that it provides. We compare the model predictions of both spatial and temporal stability analysis with experiments of a jet of molten Woods metal in water. Molten Woods metal emanating from various orifice diameters (1-10 mm) into water under the action of gravity is analysed for drop sizes and these are compared with the numerical predictions. The presence of heat transfer is found to shorten the breakup length of the jet. This is attributed to the increase in surface tension induced by the heat loss from jet to the ambient. It is found that including the effect of temperature dependence of viscosity and surface tension, however, does not affect the drop size. A critical dimensionless number (Π1 ∼ 10) is found to exist beyond which the breakup is dominated by Marangoni stresses. Below this critical number, the jet breaks up due to the combined effects of the capillary force and the Marangoni stresses. It is shown that including the effect of gravity is necessary to predict the drop size accurately. The results of this work have implications in evaluating safety strategies in the event of a core disruptive accident in a nuclear reactor. A wider application of this analysis is in improving the efficiency of thermally modulated inkjet printing.