A theoretical and experimental investigation of the capillary breakup of surfactant-laden non-newtonian laminar jets

The present study focuses on the breakup of surfactant-laden non-Newtonian laminar jets. The combined effect of polymers and soluble surfactants on the dynamics of jet breakup, and especially on satellite drop formation, was experimentally and theoretically investigated. Xanthan gum, Carbopol® 934 NF, Carboxymethyl cellulose 7MF and Carboxymethyl cellulose 7HOF were dissolved in water with Sodium Dodecyl Sulfate or Sylgard® 309 as the surfactant. Sinusoidal controlled disturbances were imposed at the laminar jet interface using a piezoelectric vibrating nozzle with breakup dynamics recorded using a high-speed camera and drop sizes measured using fiber Phase Doppler Anemometry. Emphasis was placed on how bulk and interfacial properties of the prepared liquids influenced ligament and drop evolution. It was found experimentally that if the proper concentration of surfactant was selected (close to the critical micelle concentration), and if the surfactant adsorption/desorption was fast enough, Marangoni interfacial stresses developed and led to an increase in satellite drop size (as was observed by previous researchers for breakup simulations of shear-thinning jets covered with insoluble surfactant). In addition to experiments, a one-dimensional theoretical investigation based on Taylor expansions of liquid velocity, bulk surfactant concentration and pressure in the ligament, as proposed by Eggers and Dupont (1994), was carried out at low Reynolds number. The effect on jet dynamics of a soluble surfactant combined with either a generalized Newtonian liquid (Carreau fluid) or an elastic liquid (Johnson-Segalman) was analyzed. Using the model developed, the adsorption and desorption kinetics in the case of a generalized Newtonian liquid jet were shown to rely on the initial interfacial concentration of surfactant: if the surfactant at the jet exit plane was initially at the thermodynamic equilibrium value, a slowly adsorbed/desorbed surfactant could lead to a jump in satellite drop size (Mac, the critical Marangoni number, ∼1), while if the thermodynamic equilibrium concentration was not originally reached a the jet exit plane a slowly adsorbed/desorbed surfactant rarely led to a jump in satellite drop size (Mac \u3e 2). It was also shown that a soluble surfactant (low solubility number S) with fast adsorption (large adsorption number Kd) did not favor the formation of satellite drops and that the dynamics of jet breakup were not altered when changing the initial interfacial surfactant concentration (at thermodynamic equilibrium concentrations or not) for a surfactant with fast adsorption. Finally, elasticity was shown to significantly increase satellite drop size when combined with surfactant; elastic and Marangoni stresses were found to act synergistically and subsequently lead to a low value of the critical Marangoni number (Mac ∼0.5)