Temporal analysis of power law liquid jets

In this paper we investigate the breakup mechanisms of power law liquid jets. The viscosity of the liquid is represented the Carreau–Yasuda model, and the surface tension of the liquid jet has a variation (gradient) along the jet axial direction. The surface tension gradient may be introduced by the thermal disturbance of the jet surface as it comes of out an orifice. The Carreau–Yasuda fluid has a power law viscosity bounded by two plateaus, the higher plateau at zero strain rate, μ0, and the lower plateau at the infinite strain rate, μ∞. The governing equation for the surface profile of the liquid jet is derived in the forms of a partial differential equation (PDE), as well as an ordinary differential equation (ODE). The PDE and ODE are solved for various cases of Carreau–Yasuda fluid to study the effect of fluid properties on jet breakup. The effects of various parameters on the instability behavior are studied in comparison with two Newtonian jets with upper and lower bound viscosities, μ0 and μ∞. A number of quantitative conclusions and sensitivities on the instability behavior of non-Newtonian jets are investigated. It is found that the jet breakup mechanism depends on the properties of the fluid as well as the wave number of the thermal disturbance that causes the surface tension gradient. In contrast to the Newtonian liquid where the jet surface profile has the same frequency as the surface tension gradient, the nonlinear nature of the Carreau–Yasuda constitutive behavior may enable the jet surface profile at frequencies higher than that of the surface tension gradient. This leads to significant surface profile oscillation within one wavelength of the surface tension gradient and the generation of small satellite drops. It is worth noting that at a small wave number the breakup time for the Carreau–Yasuda fluid maybe shorter than that of the Newtonian jet with μ∞, although the Newtonian jet has a lower viscosity.