Fabrication and characterization of a scalable surface textured with pico-liter oil drops for mechanistic studies of bacteria-oil interactions

Texturing a large surface with oily micro-drops with controlled size, shape and volume provides an unprecedented capability in investigating complex interactions of bacteria, cells and interfaces. It has particular implications in understanding key microbial processes involved in remediation of environmental disasters, such as Deepwater Horizon oil spill. This work presents a development of scalable micro-transfer molding to functionalize a substrate with oily drop array to generate a microcosm mimicking bacteria encountering a rising droplet cloud. The volume of each drop within a large “printed” surface can be tuned by varying base geometry and area with characteristic scales from 5 to 50 μm. Contrary to macroscopic counterparts, drops with non-Laplacian shapes, i.e. sharp corners, that appears to violate Young-Laplacian relationship locally, are produced. Although the drop relaxes into a spherical cap with constant mean curvature, the contact line with sharp corners remains pinned. Relaxation times from initial to asymptotic shape require extraordinarily long time (>7 days). We demonstrate that non-Laplacian drops are the direct results of self-pinning of contact line by nanoparticles in the oil. This technique has been applied to study biofilm formation at the oil-water interface and can be readily extended to other colloidal fluids.

detachment, the surface tension of crude-air is approximately 21.75 mN/m that is much lower than that of 5% crude-hexadecane mixture. However, the two systems have similar initial surface tensions; the surface tension of 5% crude hexadecane mixture starts at 26.5 mN/m in comparison to that of crude at 27 mN/m. As time evolves, the surface tension of both liquids reduces exponentially. This trend can be attributed to the adsorption of oleophilic particles within crude onto interface that reduces surface energy. The decay rate decreases with the particle [ S2. Model for Self-pinning Drops by Particles at Contact Line S2.1 Brief description on model. When a particle is adsorbed at the contact line (in Fig. 9a and 2 ), a capillary force will be exerted on the liquid film to counteract the spreading of the drop (or the contact line). When the number of particles is sufficiently large, the capillary force is large enough to pin the contact line completely. This self-pinning by particles can be best elucidated graphically as Fig. 9a and described mathematically as where / is termed as the line packing fraction, a dimensionless number indicating the fraction of the contact line with equivalent radius of occupied by solid particles of mean radius of . Here is the total number of particles at the contact line, is the initial spreading coefficient, and is the equilibrium surface tension between liquid and vapor. With a fixed line packing fraction, * , relation S1 predicts a maximum apparent contact angle, * . If the apparent contact angle of a drop exceeds * , the contact line will move; if the angle is less than * , the drop will be pinned.

S2.2 Relate line packing fraction, , at contact line to volume packing fraction,
The relation (Eqn. S1) can be rewritten in terms of volume packing fraction, , a dimensionless quantity representing the fraction of the total volume occupied by particles. One can define the volume packing fraction as , where is the volume of the drop, and is the number of particles contained within the drop. Substituting the above relation to Eqn. S1, we relate the with as Hence, the relation between apparent contact angle and line packing fraction can be obtained by substituting Eqn. S4 into Eqn. S1 as the following form or the more intuitive form: The relation (Eqn 6) show a power law dependency between the apparent contact angle, , and volume packing fraction, .

S2.3 Model for crude-hexadecane binary system
Since direct measurement of is difficult, we resort to using a crude-hexadecane binary system to vary the volume packing fraction, , by changing the volume concentration of crude in crudehexadecane mixture. The resultant, , , is where is the volume concentration of crude in mixture, , assuming simple volume addition to the mixture. Therefore, the model (Eqn. S6) can be expressed in terms of as .
Justified in the main text and section S1 above, the ratio between spreading coefficient, , and surface tension, , remains constant for mixtures at different concentration, i.e. / , . Thus the model for apparent contact angle with respect to is cos cos .
Note that the volume of a printed oil drop with a contact angle and a contact radius can be approximated as 2 3 cos cos / sin .

S3. Particle Size Distribution by Dynamic Light Scattering
The mean particle size distribution of crude-hexadecane mixture was averaged over five

S4. Compute local curvatures of AFM measurement.
Due to the non-axisymmetric base of the printed drops like squares, conventional means of topology characterization using cross-sectional profiles are inadequate. Instead, we characterize the 2D surface, , , directly by calculating the distribution of local principal radii of curvature, equation for micro/nano-colloidal particle contain the geometric term of (or 1/ , where is the equivalent radius of curvature), the proposed quantification is justified.
To estimate the local , we must first approximate the local principal radii, and . We apply least square fit of a second order polynomial surface, , ; ,  probes can also be observed in (Fig. S3b) but less pronounced in profile (Fig. S3A). More than 80% of the center portion of the drop has constant mean radius of curvature, 182.8

8.9
, while along the periphery (~20%), increases rapidly above 400 and transits to negative values. This trend is consistent regardless of the size and base shape (substantiated in §3.2) and suggests the oleophilic contact angle. Although due to the large measurement error near the periphery, the estimation of the contact angle and in this region is expected to be inaccurate, but it should provide us with qualitative information on drop shape. This trend can be further elucidated with radial profile in Fig. S3c (red line), which is averaged over the azimuthal direction at the interval of 5° and superimposed with that of a best fit sphere. Note that the radial profile of drop agrees well within an error of 0.46 or 0.5% with the profile of a sphere of an estimated radius, 96.7 . Recall that the of drop is ~1.89 in our measurement, while the of a sphere must maintain twice of in principle.