Liquid Jet Instability and Dynamic Surface Tension Effect on Breakup

We studied the instability of a liquid jet by confocal microscopy, a non-invasive three-dimensional imaging technique. The amplitude of jet oscillation can be measured from its early stage to the vicinity of the jet breakup with a radial resolution of 80 nm. A continuous jet with a diameter of 100 μm and mean velocity of 5.6 ms was perturbed at a frequency of 11.8 kHz. The growth rate of the sinusoidal instability was used to determine the dynamic surface tension of water and of surfactant solutions at a surface age of ≤ 1 ms, using an established linear, axisymmetric, constant property model. A commercial aqueous non-ionic Gemini surfactant Surfynol 465 reduced the dynamic surface tension more efficiently than an anionic surfactant sodium dodecyl sulphate (SDS). The effect of surfactant on the jet breakup length has also been studied. We applied the confocal imaging system to study the temporal evolution of a ligament which starts from a concave neck and eventually develops into a satellite drop. The pinch-off process has been studied in detail. It is found that the final stages of ligament rupture are the same for water and surfactant solutions. The time taken for the satellite drop to be engulfed by the following drop depends on the surfactant concentration. Introduction Surfactants (a contraction of surface active agents) can reduce the surface tension of liquids even at low bulk concentrations. They are widely used in many industrial, agricultural and biological processes. For example, surfactants are commonly added to inkjet inks as wetting, emulsifying and dispersing agents. By lowering the surface tension of inks, surfactants can improve the wettability or printability of the inks. The reduction of the surface tension by surfactant is a dynamic process where molecules must first diffuse to the surface from the bulk and then orient themselves at the interface. Many experimental techniques have been developed over the past decades to measure dynamic surface tension (DST) and study the adsorption mechanism, including the maximum-bubble-pressure, oscillating-jet, overflowing-cylinder and drop shape analysis methods [1]. However these techniques can only provide us DST with surface age older than 1 ms. In fact, efficient surfactants can lower the surface tension to its equilibrium value within 1 ms at concentrations of <1%. Take an anionic surfactant sodium dodecyl sulphate (SDS) as an example. It has a critical micelle concentration (cmc) of 8 mM in water, i.e. 0.23% by wt, and the equilibrium value of the surface excess at this concentration is Γcmc ≈ 4 × 10 mol m. Given that SDS adsorption is diffusion controlled, the diffusion time τd is defined as the mean time taken by a surfactant molecule to diffuse a distance given by the depletion length Γ/c, where c is the bulk surfactant concentration. [2]: 2 2 1 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = c Γ D d τ . (1) The diffusion coefficient of SDS is ~ 5 × 10 m s which gives τd ~ 0.25 ms at its cmc. The time taken for a freshly formed surface to reach equilibrium is ~ 5τd ≈ 1 ms. Hence to measure the DST in sub-millisecond or shorter timescale will be of great interest for scientific research and industrial application. In this paper, we present our experimental study on the instability of a continuous liquid jet. The growth rate of the liquid jet in the presence of two types of surfactants has been measured by confocal imaging. The DST of the liquid at a surface age of ≤ 1 ms can be determined via growth rate measurement. The surfactant effect on the jet breakup and satellite drop formation has also been studied in detail. Experiments The experimental apparatus is shown in Figure 1: the details will be presented elsewhere [3]. The pressurised liquid is guided from a reservoir into a dispenser head. A pressure control unit and a liquid pump are adjusted to keep the reservoir liquid volume constant so as to guarantee a constant liquid flow rate. A laminar jet emerges from the dispenser head through a funnel-shaped glass nozzle with an exit diameter of 100 μm into free air at a room temperature of 22 °C. The jet is mounted in a three-dimensional motorised translation stage with an actuator travel range of 12.5 mm and an accuracy of 0.2 μm. A TTL signal generator is applied to the valve control. The flow rate for the partially closed microvalve inside the disperser head is about 98% of that for an open valve. The amplitude of the applied periodic perturbation on the jet is therefore small. Figure 1. Experimental setup. SLD: superluminescent diode; BS: beamsplitter; PMT: photomultiplier tube; Amp: amplifier. S/I: signal-in; S/O: signal-out; T/I: trigger-in; G/O: gate-out. We used UHQ water from Millipore water purification system (Millipore Corporation, USA) as a calibration fluid in the jet, assuming it to have a constant surface tension. Two types of surfactants were chosen. A simple single-chain anionic surfactant