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.

Electrohydrodynamic Jet Printing: Introductory Concepts and Considerations

“…This could lead to a point where the surface tension of the material being printed is altered, thus throwing off the balance between the surface and electrostatic force (see Figure 2a). [ 52 ] The likely outcome of this would be a higher‐order jetting mode or excessive material being printed at any one time. This could be rectified with a feedback system which considers the changes in jetting rate.…”

Active control of jet breakup and droplet formation using temperature modulation

“…This expression is also obtained and used in the studies by Pillai et al [26], Furlani et al [28], and several others concerning nonisothermal melt spinning processes [50,51]. This time the physical explanation is related to the thermal boundary layer, namely, if the cooling to the ambient is too large (Bi 1), then a thermal boundary layer would arise within the jet, and the slender-jet approach would be unable to capture the radial variation of the temperature near the jet edge.…”

“…conservation, so the relaxation time of the variations of surface tension cannot be captured. Pillai et al [26] were the first to come up with the nonisothermal slender-jet equations. They studied velocity modulations on a slender jet with temperature-dependent surface tension and viscosity, and subject to cooling.…”

Controlling the breakup of spiralling jets: results from experiments, nonlinear simulations and linear stability analysis

“…The method proved useful also in non-isothermal cases with the additional presence of thermo-capillary (Marangoni) effects (Pillai et al. 2012; Kamis, Eral & Breugem 2021).…”