Micron-Scale Droplet Deposition on a Hydrophobic Surface Using a Retreating Syringe

Abstract

Droplet deposition onto a hydrophobic surface is studied experimentally and numerically. A wide range of droplet sizes can result from the same syringe, depending strongly on the needle retraction speed. Three regimes are identified according to the motion of the contact line. In Region I, at slow retraction speeds, the contact line expands and large droplets can be achieved. In Region II, at moderate needle speeds, a quasi-cylindrical liquid bridge forms resulting in drops approximately the size of the needle. Finally, at high speeds (Region III), the contact line retracts and droplets much smaller than the syringe diameter are observed. Scaling arguments are presented identifying the dominant mechanisms in each regime. Results from nonlinear numerical simulations agree well with the experiments, although the accuracy of the predictions is limited by inadequate models for the behavior of the dynamic contact angle. [5,6]. The process is, at first glance, straightforward and is initiated by the formation of a liquid bridge between the substrate and a dispensing syringe. As the syringe retreats, the liquid bridge stretches, grows and breaks, leaving a drop on the substrate. A seemingly simple question can be askedhow does the drop size depend on the syringe geometry, speed and the fluid properties? A comprehensive answer must consider the stability of the liquid bridge and the physics of the moving contact line at the liquid-air-solid interface -both difficult problems. Theoretical studies of liquid bridge stability date back to Rayleigh [7], and have been extended to include gravity and non-cylindrical geometries [8,9]. In addition, the nonlinear dynamics have been solved numerically, using both 2-D (axisymmetric) [10] and 1-D (slender-jet) [11,12] models. Previous work has concentrated on geometries in which the contact line is pinned at both ends of the liquid bridge [12,13], and there are only a few results that couple the liquid bridge with a moving contact line [14,15]. A possible reason for this is the difficulty in solving the flow near the contact line where the continuum equations are invalid [16,17] and a microscopic description must be imposed (e.g. [18]). In this letter, we focus on the physics of drop dispensing on a flat, smooth, hydrophobic substrate in which the contact line is free to move and is inherently coupled with the liquid bridge stability. Experiments and numerical simulations are used to identify a range of complex flow phenomena which enable the deposited drop size to vary by two orders of magnitude as the syringe retraction speed is changed.In our experiment, a stainless steel syringe (typical radius, R = 200µm) is mounted vertically on a computercontrolled stage. The syringe is connected by a small tube to a 10cc barrel mounted on the same stage. This configuration maintains a constant hydrostatic head, H, at the syringe tip (H ∼ 4cm). The fluid (a 85-15 mixture by volume of glycerol and water) has viscosity µ = 84 cP and surface tension γ = 0.063 N/m. The fluid exhibits a static co...

Liquid-bridge stability and breakup on surfaces with contact-angle hysteresis

“…However, at an unstable state away from its critical state, the instability margin amplifies the critical perturbation, leading to more dramatic dynamics, which could impact the dispensed-drop size. As previously stated, Qian et al 24 reported small drop sizes in a pressure-controlled deposition due to fast dynamics near the contact line. Here, achieving a fast-receding contact line is assisted by the withdrawal of the liquid near primary and satellite drops upon stability loss at the maximum-height stability limit 19 .…”

“…In the first two, U n ≪ u w , where u w is the capillary-wave speed; the contact line advances in the first and is stationary in the second with the drop size scaling as U −1/2 n ; the third corresponds to fast retraction speeds, U n /u w ∼ O(10 −2 ), where the dynamics dramatically change, and the drop size does not scale with U n as a simple power law. Here, the drop size is almost two orders of magnitude smaller than in the first two regimes, which Qian et al 24 attributed to a fast receding contact line with a speed approaching u w . However, in volume-controlled deposition, the dispensed-drop size did not exhibit the same sensitivity to the needle retraction speed in the parameter range studied by Qian and Breuer 25 .…”

“…Minimizing the dispensed-drop size relative to the needle diameter is central to surface patterning based on direct-write lithographic techniques 3,23 . Recent studies of contact-drop dispensing have shown that the deposited drop size is influenced by the needle retraction speed, needle-tip size, surface characteristics, and dispensing control parameters 24,25 . Interestingly, the deposited drop volume in pressure-controlled and volume-controlled dispensing behave differently with the needle retraction speed.…”

Mechanical vibrations of magnetically levitated viscoelastic droplets

“…Additives such as polymers and small particles can have a dramatic effect on the surface and rheological properties of small liquid droplets. These can, in turn, influence properties such as the wetting, spreading and dewetting behaviour of the fluids [3][4][5][6] . They also have a significant influence on their performance in applications such as droplet atomisation, ink jet printing, fuel injection 7 , microscale mixing/demixing 8,9 , and during drop impact and rebound phenomena 6 .…”

Catenoid Stability with a Free Contact Line

“…Early investigations were motivated by applications such as liquid-jet breakup [2,3], crystal growth in microgravity [4], oil recovery [5], and paper wet strength [6]. Recently, interests have grown into areas such as elastocapillarity [7][8][9][10], contact-drop dispensing [11] with applications to scanning-probe lithography [12] and micromachined fountain-pen techniques [13]. Molecular-resolution surface patterning provides new opportunities for advanced tissue engineering [14], DNA self-assembled nanoconstructs [15], and highly sensitive protein chips [16].…”