Generation of micro-droplet arrays by dip-coating of biphilic surfaces; the dependence of entrained droplet volume on withdrawal velocity

Droplet array chips were realized using an alignment-free fabrication process in silicon. The chips were textured with a homogeneous nano-scale surface roughness but were partially covered with a self-assembled monolayer of perfluorodecyltrichlorosilane (FDTS), resulting in a super-biphilic surface. When submerged in water and withdrawn again, microliter sized droplets are formed due to pinning of water on the hydrophilic spots. The entrained droplet volumes were investigated under variation of spot size and withdrawal velocity. Two regimes of droplet formation were revealed: at low speeds, the droplet volume achieved finite values even for vanishing speeds, while at higher speeds the volume was governed by fluid inertia. A simple 2D boundary layer model describes the behavior at high speeds well. Entrained droplet volume could be altered, post-fabrication, by more than a factor of 15, which opens up for more applications of the dip-coating technique due to the significant increase in versatility of the micro-droplet array platform.

Withdrawal experiments with speed and angle variation were also conducted for the 5 mm array. The sample was prepared with 70-90-8 nanograss. The data are presented in Figure S1 and the Blasius model is plotted along with it. A dependence of withdrawal is apparent for low speed but absent for high speed as it is the case for the 3 mm spots (see Figure 3b). For low speeds the withdrawal experiment was also conducted for various angles with the 70-50-8 nanograss. The results are shown in Figure S2 and are quantitatively similar to those with 70-90-8 surfaces in Figure S1. Figure S2: Investigation of the droplet size at low speeds. Connecting lines are added on the plot to guide the eye. The withdrawal was performed for 5 different angles and 6 different speeds in the interval from 1.1-4.5 cm/s. The spot size is 5 mm and the surface with 70-50-8 nanograss.

Pressure balance model
In Figure S3 the sketch used for the derivation of the volume-to-inclination relationship, for zerospeed, is shown. For superhydrophobic background materials the contact angle is defined to be above 150 o and the precision in its measurement decreases as compared to more moderate contact angles. To address possible effects of this uncertainty the developed model has been plotted for both 160 and 180 degrees apparent contact angles, 0 . The comparison is made in Figure S4. Some effect is observed but the overall trend does not change significantly. The slope decreases at smaller spot diameters. The deviation is considered small taking the crudeness of the model into account.

Array dimensions, mask design, and mask fabrication
The geometrical outline of the array is shown in Figure S6. Figure S6a includes the full mask design with all the alignment marks for mask printing, UV-exposure, and chip scribing. The array is a square array with a period of four times the hydrophilic spot diameter, . Figure S6(b-c) shows the array outline for the spot sizes of 3 mm and 7 mm. Figure S6: Droplet array dimensions on the mask used for the photolithographic definition of the hydrophilic spots. a) The complete mask overview for the = 5 mm case. The mask design includes 'print alignment marks' for quick determination of the alignment-quality for the three consecutive prints needed for total blocking of the UV-light. The square array period is 4d and the distance between the scribing marks, for defining the final array chip, is 58 mm. A flat alignment is added to ensure center-alignment of the array to achieve as good nanograss homogeneity as possible.

Preparation of photo mask
The photo mask was prepared by printing 3 times on top of each other on Premium Transparencies from Xerox with a Xerox 7502V_U printer using the by-pass feeder. An array of non-transparent circles/spots of diameter on the photomask defines the regions of hydrophilicity. The spots are organized in a square array (see Figure S6) aligned with respect to the direction of withdrawal.

Experimental setup
The experimental setup was built and assembled using CO 2 laser cut PMMA (to make the inclined slide and the sledge) and LEGO MINDSTORMS.The pull-chord is fishing line, and the reservoir is 6-8 L of DI water (Milli-Q). The setup is visualized in Figure S7.

Determination of withdrawal speed
Using a high speed camera (PLAYSTATION Eye) oriented normal to the sledge, the displacement of the sledge was tracked for different motor power settings (see Figure S8). L refers to low gearing and H to high gearing. The number, e.g., 20 in L20, refers to the percentage of full motor capacity. The best estimates for the power-speed correlation were determined from the displacement graphs. It was approximated by a linear model as seen in Figure S9(left). The associated relative uncertainty was assumed to be constant, 17 %, justified by Figure S9(right). For speeds lower than 5 cm/s this is a large overestimate, but to favor the use of a single model for predicting the uncertainty, this has been prioritized. Figure S9: (Left) Best estimates for sledge speeds for the tested power and gearing settings. The best estimates are based on 2-5 measurements each and the uncertainty is the average internal variation in each measurement combined with the standard sample deviation between the 2-5 measurements. (Right) The associated uncertainty to each best estimate for the speed exhibits a positive correlation that justifies predicting the uncertainty using a proportionality model; hence, stating that the relative uncertainty is independent of the speed.