Scaling of Anisotropic Wetting Behavior of Water Drop Configuration Arising from Parallel Groove-Textured Stainless Steel Surfaces

Understanding the wetting behavior of stainless steel surfaces can help in resolving many socio-economic challenges faced by modern day engineering developments. In this research paper, investigations have been carried out to understand the role of surface unidirectional microgrooves on the wetting behavior by the water drop liquid using the liquid drop shape configuration, captured in the view direction parallel and orthogonal to surface microgrooves. Because of the variation in wetting characteristics between these two directions, i.e., anisotropic wetting behavior, the liquid drop has attained ellipsoidal shape configuration in the microgroove-textured stainless steel surfaces. Detailed investigation has been carried out in understanding the role of microgroove geometrical sizes, i.e., width and depth and the spacing between the grooves on the wetting behavior in terms of contact diameter (D) and contact angle (θ). Overall, the wetting dynamics has been characterized by looking at the variation of eccentricity (ε, as a ratio between D in the direction parallel to microgroove and the spreading diameter in the direction orthogonal to microgroove) and wetting anisotropy (Δθ, as a difference in θ between the direction orthogonal and parallel to microgroove) with the microgroove depth parameter (ϕ as a ratio between the microgroove depth and width) and the groove spacing parameter (ξ as a ratio of the spacing between the grooves and the groove width). By and large, with increase in surface non-dimensional geometrical parameters, ϕ and ξ, the parameters quantifying eccentricity, ε and Δθ decrease, so the liquid drop shape configuration shifts towards spherical cap from ellipsoidal cap.


Introduction
Wettability of a solid surface has gained greater importance owing to many practical applications [1][2][3][4][5] involving control of the surface wettability. The wetting properties of the artificially designed smart surfaces find applications in different research areas ranging fluid physics, material science, and interfacial physics. Superhydrophobic surfaces with higher static contact angle and lower contact angle hysteresis play important role in the applications involving MEMS/NEMS, corrosion resistance, car windows, etc., because of its antisticking, anti-contaminating, and self-cleaning surface properties [6]. At the same time, applications like ink-jet printing [5], spray coating [9], etc., warrant the better adhesion and sticking properties along with higher spreading area. By enhancing non-wetting nature on the stainless steel surfaces through physical micro-and/or nano-structure and chemical coatings, the corrosion rate of such surfaces can be controlled by reducing the contact area between the liquid and solid surfaces. However, the textured arrangement of micro-or/and nano-asperities on the surfaces of solid offers better durability in establishing a non-wetting behavior when compared to chemical coating. Over the years, both experimental and analytical research works have been carried out in understanding the interaction between the solids and liquids with different physio-chemical behavior, and they are well summarized by the reviews presented by Fihri et al.  [12], Valipour et al. [13] and Quéré [14]. Larger attentions have been devoted towards the development of textured and chemically heterogeneous surfaces in understanding its role in modifying the wetting behavior by the liquids [7,8,[15][16][17][18][19][20][21][22][23][24][25][26].
Generally, the superhydrophobic states of rough surfaces are distinguished based on Cassie state [10] and Wenzel state [11]. The former represents a state of non-wetting liquid contact mode with a low hysteresis caused by the entrapped air between the liquid and solid interfaces, which makes the drop to roll off easily from the surface. The latter represents a liquid wetting contact mode where the pinning of the contact line leads to higher contact angle and contact angle hysteresis. In the recent past, natural and artificial phenomena have been widely discussed based on the classification of lotus effect [2,3] and petal effect [6] based on their adhesive force of the drop with solid surfaces. The self-cleaning property is achieved by the dual (micro-and nano-) rough surface on a low surface energy material, which in turn, promote a superhydrophobic property with both a high θ (greater than 150°) and a low sliding angle (less than 5°). This phenomenon is called as lotus effect [2,3,6] and is in the state of Cassie non-wetting. Other phenomenon, petal effect has a similar combination of micro-and nano-scale rough surface which exhibits a superhydrophobic property, but this superhydrophobic surface has high adhesion force and said to be in the state of Cassie impregnated wetting [16]. Following the understanding of surface roughness effect on the hydrophobicity of solid surface, much attentions are devoted on examining the behavior of liquid drop on isotropic patterned surfaces [8]; however, the anisotropic patterned surfaces can play a vital role in the dynamics of final shape of the sessile drop, thereby a better understanding about the influence of surface geometry can be obtained in characterizing its behavior of corrosion resistance. Most of the anisotropic studies involve groove-textured surfaces consist of periodic and parallel grooves due to its relatively easy fabrication technique and its simplicity in modeling to understand the wetting dynamics [19].
Comparing to the nearly spherical shape drop on an isotropic rough surface, the shape of the liquid drop is no longer spherical on the non-isotropic surface and also the apparent dynamic contact angle would not be uniform along the three-phase contact line (TPCL), i.e., there is a difference in apparent dynamic contact angle observed between the perpendicular and parallel to the grooves [8]. Anisotropic wetting is significant for the surfaces pertaining to be of two different wetting properties between the two mutually perpendicular directions caused by the physio-chemical nature of solid surfaces [16,[19][20][21][22][23][24]. The continuous, lengthy TPCL has a great influence in controlling the sliding behavior of the liquid drop [8]. The parallel groove-textured surface shows a short and continuous contact line along the channel direction than a longer and discontinuous contact line along the orthogonal to channel direction. Thus, the drop spreading occurs at lower sliding angle in the parallel to channel direction than the orthogonal to channel direction in the groove-textured surfaces [8,[19][20][21][22][23][24].
The present research focuses on understanding the role of surface microgrooves' geometrical parameters such as microgroove width, depth, and the spacing between the microgrooves in controlling the wetting behavior of the groove-textured stainless steel solid surfaces by the water drops.

Experimental Procedures
The surface pattern used in the present study consists of unidirectional parallel grooves in a regular pattern, giving rise to anisotropic wetting properties as represented in Fig. 1.
The surface "microgrooves" structures were fabricated using standard optical lithography technique. Smooth stainless steel surface was prepared in polishing machine using diamond paste and its arithmetical mean height, i.e., R a was measured as 0.13 μm using Vision32 optical profilometer. Using evaluation length of 200 µm, R a value was measured around 10 different locations of the surface and the average value was reported here. The unidirectional microgroovetextured stainless steel surface had been created in a SS304 plate with a dimension of 20 mm × 20 mm × 3 mm using photolithographic techniques and the process can be wellunderstood from the flowchart explained in Fig. 2a.
Before starting lithographic technique for generating surface unidirectional microgroove, the surface had been polished using diamond paste in the polishing machine and then the surfaces were cleaned from all organic impurities using acetone followed by distilled water. Initially, the photoresist PM230 had been coated on the plate by pressing the plastic film with photoresist and plate using two contrarotating rollers. Then this plate was heated in a furnace at 60 ℃ for 30 min to remove any moisture present over there. The photomask had been prepared using printing process for the required size of pillar and microgroove width as alternative dark and transparent stripes. Later, the photomask had been placed on the top of the plate coated with photoresist, and these arrangements had been placed in the rectangular transparent flexible chamber to remove any space that allowed light passage by creating vacuum in that. UV light was exposed on the top of these arrangements for 2 min. Then the substrate had been removed from these arrangements and plastic film had been removed. Later, the substrate had been washed with 5% NaOH for removing unexposed photoresist present on the surface where the pattern of the polymerized photoresist appeared as alternative light and dark patches on the stainless steel surface. Finally, this surface was kept in the tilting tray with 5% HCl and the exposure time had been changed according to the required depth of the microgroove. The surface microstructure had been examined using Scanning Electron Microscope (Quanta, FEI) and 2-D surface profile extracted from 3-D optical profilometer (NT9080 Optical Profilometer, Vecco), and the extracted images of groove-textured surfaces are shown in Fig. 2b, c. NT9080 is a three-dimensional optical profilometer which visualizes and also measures surface topographic features through non-destructive method. It helps in collecting the information regarding both nanometer and micrometer scale surface roughness and also helps in measuring the geometrical features of nano-and microlevel roughness asperities present on the surfaces. This optical profilometer system provides a precise XYZ topographic surface map of the sample which can be saved for subsequent analysis using Vision(R) software platform.
Magnification of objective can be varied from 1.5× to 50× for analayzing the wide varieties of samples with different surface sizes. A feature that has a vertical range between 0.1 and 10 mm can be examined with a resolution less than 0.12 nm. Using Vision(R) platform, the variation in vertical dimension of surface micro-feature of the unidirectional microgroove textured surfaces can be extracted with the help of line scan across the microgrooves. The microgrooves on surface structures are classified based on pillar width (b), i.e., the spacing between the surface microgroove, microgroove (hereafter, denoted as channel) width (w), and depth (d), and these parameters are measured in terms of micrometer (μm) using 2-D surface profile image obtained from NT9080 Vecco optical profilometer. The pillar width is varied from 60 to 190 μm, and the channel width is varied from 100 to 260 μm while keeping the channel depth ranging from 30 to 50 μm. The R a measured at the pillar top for all surfaces is in the range from The channel surface shows a little higher value of R a, i.e., from 0.8 to 1.2 μm due to its formation of roughness elements using chemical etching process.
The experiments had been carried out by forming the 2.51 mm in diameter liquid drop on the surfaces with negligible inertia to the drop using a 0.25 mm inner diameter and 0.36 mm outer diameter hypodermic needle using distilled water as the drop liquid. A drop volume of 8.18 µl was controlled with the help of micrometer actuated hypodermic syringe connected to the hypodermic needle for generating this drop. The drop formed at the bottom of the syringe needle and hung because of the forces arising due to surface tension. The drop deposition was achieved by very slow increase in the drop volume by controlling the micrometer for the movement of syringe piston to overcome the surface tension force holding the drop by the gravitational force. As soon as the deposited drop with negligible inertia contact with surface, the final static configuration of drop was reached within a minute. A shadowgraph image of the liquid drop shape configuration was captured using imaging system, consists of video microscope and high power LED white light source for backlight illumination [16,27]. Comparing to a spherical cap on an isotropic rough surface, the drop attains a configuration of non-spherical drop shape in the unidirectional groove-textured surface, and it is confirmed by the schematic diagram drawn based on the available literatures for the plane elevation view of drop shape configuration on the microgroove-textured solid surfaces as shown in Fig. 1. Figure 1 provides the self-illustration of θ and D of each drop configuration measurement using ImageJ software. The experiments were conducted for the surface orientation for both of the directions orthogonal and parallel to the microgroove. The identical experiments were repeated for more than ten times for each grooved surface to ensure the repeatability of experimental results. Before starting each experiment, the surfaces were cleaned first with the help of acetone followed by distilled water and high pressurized air for removing all organic impurities and water particles present in the surfaces.

Results and Discussion
Microgroove-textured stainless steel surfaces are categorized in such a way that each group has approximately constant channel depth but having different pillar and channel width. The wetting characteristics, i.e., in terms of θ and D of the microgroove textured stainless steel surface have been investigated for the two different surface microgroove geometrical parameters: where b is the spacing between the two successive surface microgrooves, w is the width of the microgroove, and d is the depth of the microgroove. the surface geometric parameters (d/w and b/w), the unidirectional groove-texture pattern on the surfaces induces anisotropic spreading properties, which in turn, leads to a difference in spreading behavior between the orthogonal and parallel to groove directions.

Variation in Contact Diameter
Figures 3 and 4 correlate qualitatively that the variation of surface structure parameters such as pillar width, channel width, and channel depth play a major role in the anisotropy, which is specific about the variation of wetting behavior between the parallel and orthogonal to the direction of the microgroove. A better quantitative understanding can be obtained by investigating the behavior of D ∥ and D ⊥ with different surface microgroove geometrical parameters. Figure 5 shows the variation of contact diameter with the geometrical parameters ξ = b/w for three different microgroove depths i.e., 30 μm, 40 μm, and 50 μm. The contact diameter, i.e., wetting liquid cap diameter decreases with increase in ξ in the direction parallel to groove for the three different microgroove depth under our investigations. At the same time, the variation of contact diameter is almost constant, even a slight increase is visible while increasing ξ for the wetting in the direction orthogonal to groove. Among the three different group of surfaces, the difference D ⊥ and D ∥ increases with depth of the microgroove present on the surfaces. Increasing ξ, i.e., the possibility of microgroove structure having higher pillar width than the microgroove width causes reduction in preferential wetting by squeezing of the drop liquid in the direction of microgroove. This results in higher level of wetting by the drop liquid in the direction of groove than the wetting by the drop liquid in the direction orthogonal to groove and also the wetting diameter in the direction of groove decreases with increase in ξ. In addition to that, pinning of the three-phase contact line of drop liquid at the edge of the pillar initially results constant variation of contact diameter with ξ and further increase in ξ, i.e., pillar width pushes the pinning location further in the direction orthogonal to the microgroove which is responsible for slight increase in contact diameter.
Other than the geometrical surface parameter ξ, the geometrical surface parameter, (ϕ = d/w) provides information regarding the relative variation between the microgroove width and its depth on wetting diameter of the drop liquid attained on the microgroove-textured solid surfaces. Figure 6 illustrates the variation of D both in the direction parallel and orthogonal to microgroove with ϕ for three different group of surfaces with constant depth. As ϕ increases, the wetting diameter shows an increasing trend initially until certain value and then decreases in the direction both parallel and orthogonal to microgroove for the surface group with the microgroove depth of 30 μm and 60 μm. Comparing the variation of D among the surface groups with three different groove depths, the contact diameter is marginally less in the direction orthogonal to groove and also the contact diameter in the direction orthogonal to groove shows slight less magnitude while increasing the groove depth for the almost close by values of ϕ. In line with the reported variation of difference in contact diameter variation between the orthogonal and parallel to grooves for the geometrical surface parameter ξ, the difference in contact diameter increases while increasing the depth of the microgroove present on the surfaces. The trend in the variation of D ⊥ and D ∥ with respect to ϕ and groove depth is mainly responsible to the pinning of TPCL by the edges of microgroove, followed by squeezing of the drop liquid flow into the microgrooves present in the surfaces.

Variation in Static Contact Angle
As illustrated in Fig. 1 about the schematic diagram of the liquid drop shape on the microgroove-textured solid surfaces, the variation of D is strongly connected with θ of liquid drop because the pinning of the three-phase contact point limits the variation of wetting of the drop liquid on the surfaces, which in turn, has detrimental effect on the θ of liquid drop. Figure 7 shows the variation of θ in the direction parallel to groove (θ ∥ ) and orthogonal to groove (θ ⊥ ) with surface groove spacing parameter, ξ for three different group of the surfaces with differences in groove depth. As ξ increases, θ ⊥ and θ ∥ increases until certain values and then show the decreasing trend for all three different group surfaces. Also, θ ∥ is lower than θ ⊥ for all the values of ξ. In addition to this, the difference in variation between θ ∥ and θ ⊥ increases with increase in the depth of the surface microgroove.
The variation in θ ∥ and θ ⊥ with groove depth parameter, ϕ is shown in Fig. 8 for three different group of surfaces considered for the investigations. With increase in ϕ, both θ ∥ and θ ⊥ decreases initially and then shows slight increasing trend and also θ ∥ is lower than θ ⊥ for all the surfaces with different values of ϕ. In line with the variation of θ ∥ and θ ⊥ with ξ, the difference between θ ∥ and θ ⊥ increases with increase in the depth of the microgroove. The variation in θ ∥ and θ ⊥ is governed by the pinning of TPCL by the edges of grooves in the direction orthogonal to groove and also preferential spreading along the passage of the microgroove.
Overall, an anomaly is visible in Figs. 5, 6, 7, and 8 while looking at the difference in variation between D ∥ and D ⊥ and also variation between θ ∥ and θ ⊥ , the same differences decrease with increase ξ and ϕ for the surface groups with a depth of 30 μm, 40 μm, and 50 μm. One such a possibility is that the differences might be tending towards zero while increasing ξ and ϕ even more, i.e., towards an isotropic liquid drop shape configuration.

Anisotropic Behavior of Liquid Drop Configuration
The variation of D ⊥ , D ∥ , θ ∥ and θ ⊥ with surface microgroove parameters ξ and ϕ clearly indicate that the drop shape is clearly deviated from the spherical cap, i.e., approximately the shape of ellipsoidal cap. The geometrical shape variation of liquid drop shape configuration on the microgroove-textured solid surfaces can be characterized using anisotropic nature of the liquid drop shape configuration. The anisotropy in contact diameter is quantified using and its associated difference in θ between the orthogonal and parallel to the groove direction is expressed using Figure 9a illustrate the variation of eccentricity (ε) with ξ and ϕ for three different group of surfaces with difference in Wetting Anisotropy Δ = ⊥ − ∥ groove depth. The magnitude of ε, that represents the shape of ellipsoidal cap formed by the drop liquid on the microgroove -textured surfaces decreases with increase in surface groove spacing parameter, ξ for the surface groups categorized with different microgroove depths. The magnitude of ε seems to be increasing while increasing the depth of microgroove present on the surfaces. Similarly, ε decreases its magnitude close to a level of drop shape configuration attained on the smooth surface while increasing the surface groove geometrical spacing parameter, ϕ. Also, the increase in depth of the microgroove results in higher value of ε. The variation in ε with respect to the surface microgroove parameters such as ϕ and ξ clearly indicates that the wetting by the drop liquid is dictated by the geometrical parameters of the microgroove such as microgroove width and depth and also spacing between the microgrooves. There is a strong link between the wetting area formed by the drop liquid and its static contact angle of liquid-vapor interface with solid-liquid interface. Already the effect of surface microgroove geometrical parameters on the spreading diameter of the drop liquid has been discussed in detail in the preceding sections. At the same time, the θ of the liquid drop formed on the surface both in the direction orthogonal and parallel to the grooves have strongly been influenced by the surface groove geometrical parameters as shown in Figs. 7 and 8. Another anisotropic wetting behavior, wetting anisotropy (Δθ) (i.e., the difference in θ between the direction orthogonal and parallel to surface microgrooves) can be used to look at characteristic of wetting by the drop liquid on the groovetextured stainless steel surfaces. Figure 9b explains the variation of Δθ with ϕ and ξ. When ϕ and ξ increases, the value of Δθ increases for the three different categories of surfaces with varying microgroove depth. Out of these three groups of surfaces, the surface group with higher microgroove depth attains the same value of Δθ that achieved by the surface group with lower microgroove depth at relatively higher value of ϕ. Overall, these phenomena have been occurred due to the preferential spreading of the drop liquid in the direction of groove by the squeezing effect induced through decrease in groove width and also the pinning of TPCL of the wetting liquid on the edges of pillar.

Conclusion
The experimental investigation has been carried out in understanding the role of surface microgrooves' geometrical parameters and the spacing between the surface microgrooves on the wetting characteristics by the drop liquid both in the direction parallel and orthogonal to grooves for three different group of microgroove-textured surfaces with difference in groove depth. Because of the structured arrangements of unidirectional microgrooves, the liquid drop attains a shape of an ellipsoidal cap. The ellipsoidal cap has been caused due to higher D with lower θ and lower D with higher θ for liquid drop shape view in the direction parallel and orthogonal to microgrooves, respectively. With increase in surface geometric parameters such as, ϕ (as a ratio between the groove depth and width) and ξ (as a ratio of the spacing between the grooves and the groove width), the θ and D shows a definitive trend in variation and also, the appreciable difference in wetting parameters between the direction parallel and orthogonal to microgrooves is visible. The difference in wetting parameter is further quantified using eccentricity (ε, as a ratio between the D in the direction parallel to microgroove and the D in the direction orthogonal to microgroove) and wetting anisotropy (Δθ, as a difference in θ between the direction orthogonal and parallel to microgroove). While increasing the surface non-dimensional geometric parameters i.e., ϕ and ξ, the magnitude of ε and Δθ decrease; so, the liquid drop shape configuration shifts towards spherical cap from ellipsoidal cap. Behavior of such a shift is happened because of pinning of TPCL in the direction orthogonal to groove and also preferential slip in the TPCL in the direction parallel to groove.