The role of surfactants in Jet break-up for inkjet printing

Surfactants are often present in fluids used in inkjet printing technology. There is therefore a need to develop a better understanding of the mechanisms underlying the surfactant transport and their effect on the drop formation and jet break-up, in the inkjet printing timescales, which are usually less than a microsecond. The effects of surfactants are modelled by introducing a surface tension force in the boundary condition at the free surface that depends upon the surfactant concentration, which in turn requires an additional equation for the surfactant transport at the surface. This transport equation is coupled with a surface tension isotherm, which captures the dependence of the surface tension on the surfactant concentration. The diffusion of the surfactants on the interface is relatively slow compared to new surface generation and the advection of surfactants by surface flows. As a consequence, surfactants become localised to the front of the ejected fluid with low concentration in the trailing ligament. This non-uniformity of the surfactants along the droplet interface gives rise to surface tension gradients and therefore strong Marangoni forces which have big impact on the jet break-up and drop behaviour. The strength of the surfactant is defined by how much the surface tension can be reduced depending on the concentration. Our results show that a stronger surfactant can prevent satellite formation for viscous fluids. This is a consequence of the effect the surfactants have on the thinning rate of the jet neck. We investigate the scaling laws for the jet break-up for different surfactant strengths and our results show that the break-off time of the neck increases with an increasing surfactant strength. All these results are validated with experiments. We use high-speed video experimental observations to capture the subtle changes to the jetting behaviour at the sub-millisecond timescale of the jet break-up. We also use our model for the surfactant distribution and the surface tension computation to study the effect of surfactants on the oscillation of the drop after break-off. The frequency and decay of these oscillations provide a method for measuring dynamic surface tension. We find an important effect of surfactants on the attenuation of oscillations of droplets, due to the rigidification of the surface. This requires careful interpretation of oscillation results in determining bulk viscosity and surface tension.