Imparting scalephobicity with rational microtexturing of soft materials

Crystallization fouling, a process where scale forms on surfaces, is widespread in nature and technology, negatively affecting energy and water industries. Despite the effort, rationally designed surfaces that are intrinsically resistant to it remain elusive, due in part to a lack of understanding of how microfoulants deposit and adhere in dynamic aqueous environments. Here, we show that rational tuning of coating compliance and wettability works synergistically with microtexture to enhance microfoulant repellency, characterized by low adhesion and high removal efficiency of numerous individual microparticles and tenacious crystallites in a flowing water environment. We study the microfoulant interfacial dynamics in situ using a micro-scanning fluid dynamic gauge system, elucidate the removal mechanisms, and rationalize the behavior with a shear adhesive moment model. We then demonstrate a rationally developed coating that can remove 98% of deposits under shear flow conditions, 66% better than rigid substrates.

The PDF file includes: Legends for movies S1 to S7 References Other Supplementary Material for this manuscript includes the following: Movies S1 to S7

Supplementary Materials
. Calcium carbonate crystallization fouling vs. particulate fouling.(A) Brightfield bottom-view image sequence showing a crystallite nucleating and growing on a glass substrate from an aqueous supersaturated calcium chloride-sodium bicarbonate solution (see Materials and Methods).(B) Microscopic crystallite settling and growing on a glass substrate from an aqueous supersaturated calcium chloride-sodium bicarbonate solution (see Materials and Methods).In both cases, the crystallites grow on the substrate producing scale deposits until we add deionized water, interrupting further growth (t > 600 s).(C) Image sequence showing a calcium carbonate particle settling on a glass substrate from a calcium carbonate particle-water dispersion, producing a particulate deposit.This dispersion was made by combining calcium carbonate powder with deionized water and sonicating (Materials and Methods).Here we do not observe any crystallite growth on the substrate.We measured the difference in adhesive behavior between the crystallites that settled on the surface compared to those that grew on the surface, using the µ-sFDG setup.show the modified theoretical analysis to account for the surface microtexture.From our SEM images we obtain that the particle tends to take a stable position between the texture ribs.Similar to previous research (61), we assume for r ≪ D/2 that the contact between the particle and the texture can be described by a contact of a small particle of radius r with a flat surface, in this case the particle.Also, the influence of the texture height e is negligible if the particle is considerably larger than the texture.For our anisotropic texture, the particle can either be removed along the rib texture or perpendicular.We model the latter case to account for the fact that only a small portion of the particles measured in our experimental design undergo removal aligned with the texture.The hydrodynamic moment can be described as  hyd = 0.7  hyd √( 2 ⁄ ) 2 − ( 2 ⁄ ) 2 and the adhesion moment as  adh = 3 adh  , which is a product of Fadh at one rib and the distance p between the ribs.Determining the drag coefficient CD: The drag coefficient of a spherical particle in the bulk of a fluid can be expressed as CD = 24/ReD, where ReD represents the particle Reynolds number given by ReD = ̅  ⁄ .In the case of a particle, or in our case a spherical foulant, which is attached to a surface a correction factor f = 1.7009 can be applied, to obtain CD = f 24/ReD (65).
It is important to note that this equation is only applicable when  D ≪ 1.In our study, we need to account for higher ReD especially for silicone coatings.Therefore, we use the following Therefore, we can determine  ̅ for z ∈ (0,  − ) across the foulant.

(
D) Volume flow  ̇ and gap height h vs. time, t.Image sequence showing the adhesive behavior of (E) scale deposits vs. (F) particulate deposits on glass substrates.The first image in (E), (F) indicates the reference state when the nozzle is far away (h = 2000 µm) from the glass-water interface, and the white lines indicate the inner and outer diameter of the µ-sFDG nozzle.Scale bars: (A)-(C) 10 µm; (E), (F) first image 200 µm; (E), (F) 100 µm.

Figure S2 .
Figure S2.Volume flow vs. time for crystallites removal experiments.Gray line represents the mean volume flow over time of 5 different experiments, black line is the fitted line.The region with the blue background represents the period from t = -10 s to -7 s, during which the channel gap is h = 2000 µm.In the subsequent period from t = -7 s to 0 s, indicated by the red background, the nozzle is brought close to the surface h = 80 µm.From t = 0 s to 10 s, denoted by the orange background, the volume flow ramps up.The green background represents the constant volume flow region between t = 10 s and 20 s.

Figure S3 .
Figure S3.Image postprocessing to obtain number of crystallites n on the surface and processing for image sequences.The image in (A) shows an unprocessed raw image.(B) nozzle detection using in-house MATLAB code to provide region where crystallites are counted (C) processed image after background subtraction, binarization, and non-local means denoising using ImageJ with overlayed nozzle position (D) object detection using in-house MATLAB code, orange circle represent detected crystallites.We obtain the number of crystallites n by counting the individual detected objects.(E) overlay of detected crystals with the raw image showing excellent detection quality.(F) Raw image with box to indicate the region which we crop for the image sequences in Figure 1.(G) Cropped raw image, rotated to obtain flow from top to bottom.(H) image after linear adjustments of brightness.Scale bars: (A)-(F) 200 µm; (G)-(H) 100 µm.

Figure S4 .
Figure S4.Water shear-driven microfoulant dynamics on compliant coated substrates.Bottom-view image sequence showing calcium carbonate crystallites on (A) CY52-276 and (B) PEG-DA 50 coated glass immersed in water and subjected to a shear flow (starting at t = 0 s, the flow rate increases from 7 to 103 mL/min in a channel of 80 µm height).Scale bar: 100 µm.

Figure S5 .
Figure S5.Microfoulant dynamics under shear-driven water flow on PDMS coated substrates: Bottom-view image sequence showing calcium carbonate crystallites on (A) PDMS 2:1 coated glass, (B) PDMS 30:1 coated glass and (C) PDMS 50:1 coated glass (coating thickness  ≈ 10 µm) immersed in water and subjected to a shear flow (starting at t = 0 s, the flow rate increases from 7 to 103 mL/min in a channel of 80 µm height, resulting in a bulk velocity, ̅ = 0.2 m s -1 to 6 m s -1 ).(D) Temporal evolution of n/n0 for the various PDMS coatings on glass substrates.Lines representing the mean values and shaded regions are the standard deviation for e ≥ 9 experiments on N = 3 independent samples.Scale bars: (A)-(C) 100 µm.

Figure S6 .
Figure S6.Schematic of the µ-sFDG setup.Schematics showing the developed and designed micro scanning fluid dynamic gauge system (µ-sFDG) inspired by previous work(42,82,83).The controllable pump, pump the water from the reservoir through a volume flow gauge system to the inlet of a glass capillary nozzle.The piezo stages allow the nanometer scale alignment of the nozzle parallel to the surface of the tested coating.The home-built holder, mounted on nanomicro piezo stages of a fluorescent inverted microscope (10x magnification, 50 FPS) can take up to six transparent samples.The peristaltic pump maintains a constant water level in the holder and pumps back the fluid to the temperature monitored reservoir.The data acquisition system controls and synchronizes all sensors, data acquisition, and triggering coupled to the Nikon microscope (see Materials and Methods for details on the used devices).

Figure S7 .
Figure S7.Influence of coating thickness on microfoulant removal.By knowing the flow condition in the channel and by observing the moment of foulant detachment the critical shear stress acting on the foulant can be approximated based on a radial laminar Poiseuille flow (83)as  * ≈ 3 ̇/(4(ℎ/2 − ) 2   ), where µ is the dynamic viscosity of the liquid, h the channel gap height, D the particle diameter, sr the microfoulant position below the nozzle and  ̇ the flow rate at the time of removal.Removal efficiency 1-n/n0 vs, critical shear stress  * acting on the microfoulant for varying coating thicknesses, square symbol δ ≈ 10 µm, circle δ ≈ 100 µm and triangle δ ≈ 1000 µm for (A) PDMS 10:1, (B) CY52-276 and (C) PEG-DA 10.For CY52-276 no removal occurred for δ ≈ 1000 µm.

Figure S8 .
Figure S8.Microscale roughness analysis of soft materials.White light interferometry (See Materials & Methods on details of the measurements) 3D micrograph of glass coated with (A) PDMS 10:1, RMS roughness 3.5 nm and (B) microtextured PDMS 10:1, RMS roughness 861.6 nm.(C) and (D) show extracted 2D line topography measurements for the samples shown in (A) and (B) at x=50µm.

Figure S9 .
FigureS9.Modification of moment analysis to account for surface microtexture.Schematics show the modified theoretical analysis to account for the surface microtexture.From our SEM images we obtain that the particle tends to take a stable position between the texture ribs.Similar to previous research (61), we assume for r ≪ D/2 that the contact between the particle and the texture can be described by a contact of a small particle of radius r with a flat surface, in this case the particle.Also, the influence of the texture height e is negligible if the particle is considerably larger than the texture.For our anisotropic texture, the particle can either be removed along the rib texture or perpendicular.We model the latter case to account for the fact that only a small portion of the particles measured in our experimental design undergo removal aligned with the texture.The hydrodynamic moment can be described as  hyd = 0.7  hyd √( 2 ⁄ ) 2 − ( 2 ⁄ ) 2 and the adhesion moment as  adh = 3 adh  , which is a product of Fadh at one rib and the distance p between the ribs.

Figure S10 .
Figure S10.Shear removal of microfoulants with D = 20 µm from PEG-DA 10 coating.Epifluorescent bottom view image sequence showing the position of the microfoulants beneath the nozzle (dashed circular lines) and the bulk flow velocities ̅ , imparted from the water flow to the surface at r = RI and RO, respectively, on PEG-DA 10 (δ ≈ 100 µm).The image at time-zero shows the projected (- plane at z = 0) trajectories of removed microfoulants in orange.Scale bar: 200 µm.

Figure S11 .
Figure S11.Influence of microtexture and flow orientation on critical removal shear stress.Critical removal shear stress  * versus flow angle of attack  for green smooth PDMS 10:1 and mint green microtextured (width w = 2 µm, height e = 2 µm, pitch p = 6 µm) PDMS 10:1.Lines represent moving mean value.The angle  is defined to be 90° if the flow is perpendicular to the orientation of the rib microtexture and 0° if the flow aligns with the microtexture.

Figure S12 .
Figure S12.Additional image sequences of crystallite removal from microtextured PEG-DA 50.Image sequence showing the removal of crystallites from microtextured (width w = 2 µm, height e = 2 µm, pitch p = 6 µm) PEG-DA 50 for three independent samples (A)-(C).Nozzle schematics indicate the nozzle position and the volume flow at specific times.Yellow rhombus markers represent already removed crystallites before the ramp up of the volume flow.Scale bars: (A)-(C) image sequence 100 µm.

Figure S13 .
Figure S13.Shear-driven crystallite removal from Glass in a parallel plate flow chamber.(A) Bottom view image sequence showing the removal of calcium carbonate crystallites from cleaned Glass by imposing a turbulent shear flow (Re =   / ≈ 6800; u ≈ 1.4 m s -1 ).(B) Magnified image sequence showing that most of the crystallites are not removed.Flow direction left to right.Scale bars: (A) 200 µm; (B) 20 µm.

Figure S14 .
Figure S14.Crystallite removal from microtextured PDMS 10:1.Image sequence showing the removal of crystallites from microtextured (width w = 2 µm, height e = 2 µm, pitch p = 6 µm) PDMS 10:1 for three independent samples (A)-(C).Nozzle schematics indicate the nozzle position and the volume flow at specific times.Yellow rhombus markers represent already removed crystallites before the ramp up of the volume flow.Scale bars: (A)-(C) image sequence 100 µm.
for 5 ≤  D < 250Determining the mean flow velocity near the foulant  ̅: The velocity profile in the channel can be described by radial laminar Poiseuille flow, for Regap=2 ̇/[(2  + ℎ)]< 1400 and a channel gap h, that is substantially less than the nozzle wall thickness,  o −  I .By knowing the radial position sr at the moment of detachment the velocity profile near the foulant can be described as(42):