Morphology of Evaporating Sessile Microdroplets on Lyophilic

Jan 9, 2019 - In the corresponding numerical simulations, we minimize the interfacial free energy of the droplet, employing Surface Evolver. The numer...
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Morphology of Evaporating Sessile Microdroplets on Lyophilic Elliptical Patches José Manuel Encarnación Escobar, Diana Garcia-Gonzalez, Ivan Devic, Xuehua Zhang, and Detlef Lohse Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b03393 • Publication Date (Web): 09 Jan 2019 Downloaded from http://pubs.acs.org on January 10, 2019

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Morphology of Evaporating Sessile Microdroplets on Lyophilic Elliptical Patches Jos´e M. Encarnaci´on Escobar,†,k Diana Garc´ıa-Gonz´alez ,†,‡,k Ivan Devi´c ,† Xuehua Zhang,∗,¶ and Detlef Lohse∗,† †Department of Physics of Fluids, University of Twente, Enschede, The Netherlands ‡Max Planck Institute for Polymer Research, Mainz, Germany ¶Department of Chemical & Materials Engineering, University of Alberta, Edmonton, Alberta, Canada §Max Plank Institute for Dynamics and Self-Organization, G¨ottingen, Germany kBoth authors contributed equally to this work E-mail: [email protected]; [email protected]

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Abstract

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The evaporation of droplets occurs in a large variety of natural and technolog-

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ical processes such as medical diagnostics, agriculture, food industry, printing, and

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catalytic reactions. We study the different droplet morphologies adopted by an evapo-

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rating droplet on a surface with an elliptical patch with a different contact angle. We

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perform experiments to observe these morphologies and use numerical calculations to

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predict the effect of the patched surfaces. We observe that tuning the geometry of

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the patches offers control over the shape of the droplet. In the experiments, the drops

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of various volumes are placed on elliptical chemical patches of different aspect ratios

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and imaged in 3D using laser scanning confocal microscopy, extracting the droplet’s

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shape. In the corresponding numerical simulations, we minimize the interfacial free

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energy of the droplet, employing Surface Evolver. The numerical results are in good

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qualitative agreement with our experimental data and can be used for the design of

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micro-patterned structures, potentially suggesting or excluding certain morphologies

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for particular applications. However, the experimental results show the effects of pin-

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ning and contact angle hysteresis, which are obviously absent in the numerical energy

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minimization. The work culminates with a morphology diagram in the aspect ratio vs

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relative volume parameter space, comparing the predictions with the measurements.

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Introduction

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The use of patterned surfaces to control the behavior of liquid drops is not only a re-

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current phenomenon in nature, but it is also useful in various industrial and scientific

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applications. For instance, the observation of nature inspired the use of patterned sur-

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faces for water harvesting applications 1 as well as the fabrication of anti-fogging 2 and

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self-cleaning materials 3 . The geometry of droplets and the substrates in which they lay

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can affect their adhesion, as can their evaporation and other important properties 4–6 .

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The interest in wetting motivated by applications covers a wide range of scales and

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backgrounds from microfluidics 7–9 to catalytic reactors 10 , including advanced printing

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techniques 11,12 ; improved heat transfer 13,14 ; nano-architecture 15–17 ; droplet-based di-

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agnostics 18 or anti-wetting surfaces 19–21 . Aside from all the practical significance, we

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have to add the interest on wetting fundamentals 22 , including contact angle hystere-

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sis and dynamics 23–25 ; contact line dynamics 26 ; nanobubbles and nanodroplets 27–29 ;

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spreading dynamics 30,31 ; and complex surfaces 32,33 .

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Due to the complexity of the field, most previous studies have restricted themselves

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to considering geometries with constant curvature as straight stripes or constant cur-

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vature geometries, namely circumferences. In this work we will study the behavior

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of evaporating drops on lyophobized substrates that have lyophilic elliptical patches.

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The elliptical shape for the patches is chosen as a transitional case between a circular

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patch 34 and a single stripe 35–38 , having the uniqueness of a perimeter with non-constant

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curvature. When a drop is placed on a homogeneous substrate, the minimization of

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surface energy leads to a spherical cap shape. This is traditionally described by the

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Young-Laplace, Wenzel, or, for pillars or patterns with length scales much smaller

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than the drop, Cassie-Baxter relations 39–42 , which reasonably apply to homogeneous

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substrates or substrates with sufficiently small and homogeneously distributed hetero-

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geneities 43–45 , which are not the focus of this study.

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Our previous work (Devi´c et al. 46 ) based on Surface Evolver and Monte Carlo cal-

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culations showed that, when a droplet rests on an elliptical patch, four distinguishable

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morphologies are found, depending on the volume of the drop and the aspect ratio of

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the patch. These morphologies were termed 46 A, B, C and D, see figure 1. When a

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large enough droplet evaporates on an elliptical patch, the first morphology found is D.

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In this case, the droplet completely wets the ellipse with a part of its contact line out-

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side the ellipse and the rest pinned to the contour of the patch. After a certain volume

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loss, the droplet adopts either morphology B or C - depending on the geometry of the

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patch. In morphology B, a part of the droplet’s contact line remains outside the patch

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while the rest is already inside the patch. In contrast, the contact line of a droplet

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adopting morphology C follows the perimeter of the ellipse. The final morphology to

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be found for evaporating drops is morphology A, characterized by a part of its contact

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line following the perimeter of the ellipse and the rest of the contact line laying inside

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it.

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Methods

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In this paper we perform corresponding experiments and numerical simulations, per-

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formed again with Surface Evolver using the experimental parameters. Both the ex-

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periments and the calculations are performed for Bond numbers below unity to avoid

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the effects of gravity. Moreover, the experiments are performed at room temperature

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with a relative humidity of 38±2% in a closed and controlled environment, ensuring

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Figure 1: Scheme of the morphologies of a droplet as seen from the top as expected from the calculations by Devi´c et al. 46

Figure 2: Left: Coordinate system employed in this paper. θ1 and θ2 are, respectively, the Young’s angles of the lyophobic (white) and lyophilic (red) regions. R(φ) is the distance from the center of the ellipse to the contact line of the droplet (blue), and a and b are the major and minor axis respectively. S indicates the vertical section. Right: Experimental results: Top view images taken during the evaporation of various droplets on ellipses with different sizes and aspect ratios, the red contours represent the elliptical patches on the surface. A) Morphology A, droplet on an ellipse of aspect ratio b/a=0.61 and semi-major axis a=512±16µm. B) Morphology B, droplet on an ellipse of aspect ratio b/a=0.43 and semi-major axis a=392±20µm. C) Morphology C, droplet on an ellipse of aspect ratio b/a=0.98 and semi-major axis a=410±20µm. D) Morphology D, droplet on an ellipse of aspect ratio b/a=0.69 and semi-major axis a=411±20µm.

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that the evaporation driven volume change is slow enough so that the droplets evolve

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in quasi-static equilibrium. The effects of humidity, evaporative cooling, and evapo-

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ration driven flows do not have any important effects. However, for heated or cooled

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substrates or more volatile liquids this situation may change. Unlike the gravitational

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and evaporative effects, the effects of the inhomogeneities of the substrate —like pin-

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ning and contact angle hysteresis— are unavoidable in our experiments while they are

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absent from the Surface Evolver calculations.

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Preparation of substrates with lyophilic elliptical patches

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The patched substrates were prepared via photolithography followed by chemical va-

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por deposition (CVD) of a mono layer of trimethylchlorosilane (TMCS). The 100 x

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100 mm2 chromium on glass photo-mask used was designed with an array of ellipses

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of aspect ratios varying from 0.3 to 1 and sizes varying from a=320µm to b=2500µm,

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see figure 3 (a), and fabricated in the MESA+ Institute clean room facilities of the

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University of Twente, using laser writing technology. The substrates were glass slides

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(20 × 60 mm2 ) of 170 µm thickness, which is optimal for confocal microscopy. The

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photolithography steps of the fabrication, outlined in figure 3 (b), were performed in

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a cleanroom environment. First, the substrates were pre-cleaned in a nitric acid bath

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(NOH3 , purity 99%) followed by water rinsing and nitrogen drying. Subsequently,

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we dehydrated the substrate (120◦ C, 5 min). After dehydration, we spin-coated the

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photoresist (Olin OiR, 17 µm), pre-baked it (95◦ C, 90 s) and proceeded with the align-

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ment of the photomask and UV irradiation (4 s, 12 mW/cm2 ). Once the photoresist

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was cured, we developed and post-baked it (120◦ C, 10 min). Finally, the substrates

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were taken outside the clean-room environment for the CVD ( 2 h, 0.1 MPa) of a

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TMCS monolayer (Sigma Aldrich, purity ≥ 99%) to lyophobize the exterior of the el-

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lipses. The photoresist was later stripped away by rinsing the substrates with acetone,

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cleaned with isopropanol and dried using pressurized nitrogen.

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a) Design Photomask

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b) 1

Pre-cleaning with NOH3 Developement photoresist Glass Substrate 4 Spin-coating photoresist

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Photoresist

CVD deposition of TMCS 5 TMCS

UV light through photomask

5 mm

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TMCS elliptical patches TMCS

Figure 3: a) Array of ellipses of aspect ratios varying from 0.3 to 1 and sizes varying from a=320 µm to b=2500 µm fabricated on the photomask. b) Simplified steps of the substrates’ fabrication in the order indicated by the numbers. 92

Experimental data acquisition and analysis

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For all the measurements, we used droplets of ultrapure (Milli-Q) water dyed with

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Rhodamine 6G at a concentration of 0.2 µg/ml. The droplet was deposited cover-

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ing the lyophilic patch and imaged by laser scanning confocal microscopy (LSCM) in

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three dimensions during the evaporation process. After deposition of the droplet, the

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substrate was covered to avoid external perturbations.

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In figure 4, we show four examples of three-dimensional reconstructions of a stack

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of scans with increasing heights taken under LSCM. For each scan, we detected the

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surface of the drop using a threshold algorithm, allowing for the three-dimensional

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reconstruction of the drop. Using this data we calculate the local contact angle at

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every point detected on the contact line. For the measurement of the contact angle θ,

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we extract the height profile along the contact line. This can be achieved, as sketched

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in figure 2, by identifying the tangent to each point of the contact line at an angle

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φ and finding the points belonging simultaneously to its normal plane S and to the

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surface of the droplet.

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We extracted three-dimensional images of evaporating water droplets using LSCM.

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From the three-dimensional data we measured the local contact angle along the three-

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phase contact line through the azimuthal angle φ. Figure 2, right, shows top views

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of various evaporating droplets as examples of each of the morphologies introduced

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previously. The lyophilic elliptical islands of the substrate are highlighted by red curves.

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We adopted a cylindrical coordinate system with its origin at the center of the

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ellipse. The polar axis was fixed to be in the direction of one of the major semi-axes a as

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shown in figure 2 (left). We set the large semi-axis (a) of the ellipse as the characteristic

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length scale for this system and the aspect ratio of the ellipses b/a to characterize the

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geometry of the patch. The relative volume of the droplets is normalized as V /a3 .

Figure 4: Three-dimensional reconstruction of the shape extracted from the LSCM data collected for four different droplets adopting morphologies A, B, C and D respectively as performed for the extraction of the contact angle along the contact line with the shape of the elliptical patch, highlighted in red lines. Repeatability is subjected to the initial position of the droplet and pinning of the contact line which can affect the symmetry of the shape as well as delay the transition between phases as compared to the predictions. In figure 6 all the morphologies observed during the experiments are shown.

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Calculations

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We compute the surface energy minimization using Surface Evolver, a free software

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package used for minimization of the interfacial free energy developed by Brakke 47 , to

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extract the droplet’s shape and local contact angle as in the previous work by Devi´c

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et al. 46 . An initial shape of the droplet and the characteristic interfacial tensions of

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the surfaces are given to Surface Evolver as an input. The software minimizes the

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surface energy by an energy gradient descent method. Since hysteresis is not captured

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by our simulations, we compared each group of experimental results with two different

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calculations: one considering the receding contact angles for the two regions, and the

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other considering the advancing contact angle for the lyophilic part.

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To perform the calculations, we measured the contact angles of both the lyophilic

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and lyophobic parts of our patches. To do this, we treated two separated substrates ho-

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mogeneously in the same manner as in these two regions. We measured the advancing

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and receding contact angles on both substrates. Respectively for the lyophobic (sub-

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script 1) and lyophilic surfaces (subscript 2), the advancing contact angles measured

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were θa1 = 85±3◦ and θa2 = 33±4◦ , and the receding contact angles were θr1 = 49±3◦

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and θr2 = 15 ± 4◦ . During the experiments, we observed variations between 5% and

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10% of the contact angle due to occasional pinning events.

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Results

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In this section, we present the results of our experiments and the Surface Evolver cal-

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culations for each of the observed morphologies. In Figure 5, each row presents one

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of the morphologies shown previously in Figure 4. For each morphology, we show

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the normalized footprint radii R/a next to the local contact angles θ, both along the

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azimuthal coordinate φ. In each of the plots we overlay experimental and computa-

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tional results. The red and blue markers represent the calculations done considering

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the lyophilic contact angle θ2 = 33◦ and θ2 = 15◦ , respectively. In the plots of the

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normalized footprint radii we plot the position of the patch contour (black curve).

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To follow the chronological sequence of our evaporating experiments, we present

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the results starting from morphology D (largest droplet volume) and finishing with

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morphology A (smallest droplet volume). Finally, in figure 6 we present the morphology

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diagrams predicted by the Surface Evolver calculations (colored areas) and compare

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those with the results of all our experiments (colored markers).

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Morphology type D

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In figure 5 (a and b), we can see an example of an experiment in which morphology

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D was found. The normalized footprint radius R/a and the contact angle are plotted

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along the azimuthal coordinate. From the figure, we observe reasonable agreement

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between Surface Evolver calculations and experiments. However, the existence of inho-

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mogeneities introduces pinning and hence, a delay in the movement of the contact line.

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This delay translates into an experimental radius larger than that predicted by the

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Surface Evolver calculations. Despite this mismatch of the contact line, consequence

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of individual pinning events of the contact line, we obtain reasonable agreement with

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the contact angle calculations.

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Morphology type C

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Morphology C appeared for ellipses of higher aspect ratio b/a as compared to morphol-

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ogy B. Additionally, when evaporating, the drop reaches morphology C always through

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morphology D, implying that any pinning event of the contact line outside the ellipse

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prevents morphology C. Indeed, the transition from morphology D to C was always

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found in a later stage of evaporation than predicted by theory, i.e., for lower volumes

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(see figure 6 (b)).

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In figure 5 (c and d), we show a droplet of volume V /a3 =0.37 placed on a high

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aspect ratio ellipse (b/a=0.98). The results of the calculations predict morphology C

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and contact angles between the receding and the advancing ones. The contact angle

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and the contact line show always good agreement with the Surface Evolver calculations.

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This is expected as it is the closer case to the trivial spherical cap shape.

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Morphology type B

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The experimental data shown in figure 5 e and f, are particularly interesting as this

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case presents a strong asymmetry in the radius caused by a sharp pinning point which

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can be identified at φ ≈ 120◦ (indicated by an arrow in figure 5 e). Unlike the radius,

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the contact angle shows a symmetric behavior. We found that pinning leads to an

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asymmetric behavior in this morphology for all our experiments but, besides the asym-

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metry forced by pinning, the experiments agree with the Surface Evolver calculations.

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The good match for the angle can be explained considering that the contact angle at

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every point of the contact line –far enough from the ellipse contour– is dictated by the

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chemistry of the surrounding substrate.

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Morphology type A

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The experimental results showed morphology type A as predicted by the calculations

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for θ2 = 15◦ , with a part of the contact line pinned at the boundaries of the ellipse and

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the rest of the contact line inside the ellipse. Note that, in the calculations for the higher

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receding contact angle (θ2 = 33◦ ), the results predict a spherical cap shape with radius

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R < b. However, our results for the contact angle were not in good agreement with

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either of the Surface Evolver calculations, but rather an intermediate state between

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them, subjected to the irregularities of the edge (see figure 5 g and h. This can be

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due to imperfections of the coating in the edges of the ellipse. The high portion of

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the contact line that remains pinned at the boundary between the lyophilic and the

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lyophobic parts appeared to be very sensitive to the quality of the patch rim.

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Figure 5: Normalized footprint radius R/a and contact angle θ along the azimuthal coordinate φ (as defined in figure 2). Experimental results for the four different morphologies (green). From top to bottom; morphology D (V /a3 = 0.40, b/a = 0.69, and a = 411±20µm); morphology C (V /a3 = 0.37, b/a = 0.98, and a = 410 ± 20 µm); morphology B (V /a3 = 0.30, b/a = 0.43, and a = 392 ± 20 µm); and morphology A (V /a3 = 0.08, b/a = 0.60, and a = 512 ± 16 µm). Results of the numerical simulations considering the lyophilic contact angles θ2 = 15◦ (blue) and θ2 = 33◦ (red). The black curve in the radius plot shows the contour of the elliptical patch. 11

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Morphology Diagrams

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Figure 6 presents two morphology diagrams showing all the morphological regions

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and transitions predicted by the Surface Evolver calculations (as color shaded areas),

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together with the experimental results (colored markers). In this figure, morphology

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E is added, to illustrate the transition to the case in which the ellipse does not have

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an effect, as in that case the droplet is smaller than the ellipse minor axis. Using

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the receding contact angle for the calculations (see figure 6(a)) is, in principle, the

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most logical method for calculating the shape of evaporating droplets. However, the

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experimental results show a behavior that falls between the results calculated for both

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limits of contact angle hysteresis.

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In fact, for the first transitions (from morphology D to B and to C), the calculations

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done considering the hysteresis limits θr1 = 49 ± 4◦ and θa2 = 33 ± 4◦ show better

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qualitative agreement with our experiments than those done considering both receding

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angles. For these morphologies, in which part of the contact line lays on the lyophobic

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area, the overall angle of the drop is kept higher by the influence of the high contact

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angle of the lyophobic area θ1 = θr1 = 49 ± 4◦ , bringing it to the maximum angle

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possible for the lyophilic patch θ2 = θa2 = 33 ± 4◦ . For the same reason, the transitions

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from morphologies B and C to morphology A, in which the contact line has to travel

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along the lyophilic patch, show better agreement with the calculations performed for

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θ2 = θr2 = 15 ± 4◦ . The experiments also show that the transitions occur for smaller

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droplet volumes as compared to those predicted. This delay can be observed if, for

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a fixed aspect ratio b/a, we follow down the vertical line in the decreasing volume

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direction. This effect is forced by pinning, which acts to favor larger radii morphologies.

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Moreover, during the calculations we found that, for certain lyophilicity differences,

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we can exclude morphologies from the diagram. In our case, the calculations that

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were computed considering θ2 = θr2 = 15◦ (see figure 6(a)) predict the absence of

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morphology B.

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Figure 6: Morphology diagrams in aspect ratio b/a vs relative volume V /a3 phase space showing the morphologies A, B, C, D and E. (a) Experimental results displayed together with the computational results considering θ2 = θr2 = 15◦ (b) Experimental results displayed with the computational results considering θ2 = θa2 = 33◦ . The main features for A-D are indicated in figure 4, while E shows the case in which the droplet is small enough to adopt the trivial spherical cap shape inside the patch. The color shadowed regions represent the morphologies obtained with our calculations. Green, yellow, dark blue, red and light blue regions represent respectively the regions where morphologies D,C, B, A and E where found in our calculations and the colored markers show the experimental points specified in the legend.

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Conclusions

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We have performed experiments to validate the Surface Evolver calculations, and these

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showed good agreement. We observe how the effect of substrate heterogeneities, in-

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cluding pinning and contact angle hysteresis, can affect the accuracy of our surface

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minimization calculations. These heterogeneities seem mostly to affect the symmetry

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and the transitions in the morphology diagrams. With this study, we show the ro-

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bustness of the contact angle predictions which contrast with the sensitivity that radii

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predictions have to pinning. The reason is that the radius depends on the mobility of

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the contact line and therefore on pinning, even when a different morphology would be

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energetically more efficient, while the contact angle is forced by the chemistry of the

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substrate in the vicinity of the contact line, making it more robust.

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According to our results, we conclude that the knowledge of the hysteresis limits can

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be used for improving the predictions of Surface Evolver calculations. In general, the

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morphologies found experimentally show good repeatability However, the morphologies

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adopted by the droplets are always subjected to the effect of pinning, which influences

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the droplet’s symmetry and delays its transition to the next morphology. This effect

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shifts the experimental transitions to smaller volumes than those predicted by our

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calculations, as shown in the morphology diagram. We expect this effect to be opposite

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for growing droplets but that remains an open question and it is beyond the scope of

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the present study, as it would require a different experimental setup. Finally, the

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exploration of lyophilicity differences between the patches and the surroundings have

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shown the feasibility of excluding morphologies from the phase diagram, which is an

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interesting result with bearing on the design of micro-patterned structures for various

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applications.

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(46) Devi´c, I.; Soligno, G.; Dijkstra, M.; Roij, R. v.; Zhang, X.; Lohse, D. Sessile

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Nanodroplets on Elliptical Patches of Enhanced Lyophilicity. Langmuir 2017,

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(47) Brakke, K. A. The surface evolver. Experiment. Math. 1992, 1, 141–165.

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Morphology of Evaporating Sessile Microdroplets on Lyophilic Elliptical Patches Jos´e M. Encarnaci´on Escobar,†,k Diana Garc´ıa-Gonz´alez ,†,‡,k Ivan Devi´c ,† Xuehua Zhang,⇤,¶ and Detlef Lohse⇤,† †Department of Physics of Fluids, University of Twente, Enschede, The Netherlands ‡Max Planck Institute for Polymer Research, Mainz, Germany ¶Department of Chemical & Materials Engineering, University of Alberta, Edmonton, Alberta, Canada §Max Plank Institute for Dynamics and Self-Organization, G¨ottingen, Germany kBoth authors contributed equally to this work E-mail: [email protected]; [email protected]

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Abstract

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The evaporation of droplets occurs in a large variety of natural and technolog-

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ical processes such as medical diagnostics, agriculture, food industry, printing, and

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catalytic reactions. We study the di↵erent droplet morphologies adopted by an evapo-

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rating droplet on a surface with an elliptical patch with a di↵erent contact angle. We

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perform experiments to observe these morphologies and use numerical calculations to

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predict the e↵ect of the patched surfaces. We observe that tuning the geometry of

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the patches o↵ers control over the shape of the droplet. In the experiments, the drops

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of various volumes are placed on elliptical chemical patches of di↵erent aspect ratios

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and imaged in 3D using laser scanning confocal microscopy, extracting the droplet’s

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shape. In the corresponding numerical simulations, we minimize the interfacial free

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energy of the droplet, employing Surface Evolver. The numerical results are in good

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qualitative agreement with our experimental data and can be used for the design of

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micro-patterned structures, potentially suggesting or excluding certain morphologies

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for particular applications. However, the experimental results show the e↵ects of pin-

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ning and contact angle hysteresis, which are obviously absent in the numerical energy

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minimization. The work culminates with a morphology diagram in the aspect ratio vs

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relative volume parameter space, comparing the predictions with the measurements.

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Introduction

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The use of patterned surfaces to control the behavior of liquid drops is not only a re-

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current phenomenon in nature, but it is also useful in various industrial and scientific

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applications. For instance, the observation of nature inspired the use of patterned sur-

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faces for water harvesting applications 1 as well as the fabrication of anti-fogging 2 and

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self-cleaning materials 3 . The geometry of droplets and the substrates in which they lay

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can a↵ect their adhesion, as can their evaporation and other important properties 4–6 .

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The interest in wetting motivated by applications covers a wide range of scales and

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backgrounds from microfluidics 7–9 to catalytic reactors 10 , including advanced printing

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techniques 11,12 ; improved heat transfer 13,14 ; nano-architecture 15–17 ; droplet-based di-

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agnostics 18 or anti-wetting surfaces 19–21 . Aside from all the practical significance, we

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have to add the interest on wetting fundamentals 22 , including contact angle hystere-

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sis and dynamics 23–25 ; contact line dynamics 26 ; nanobubbles and nanodroplets 27–29 ;

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spreading dynamics 30,31 ; and complex surfaces 32,33 .

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Due to the complexity of the field, most previous studies have restricted themselves

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to considering geometries with constant curvature as straight stripes or constant cur-

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vature geometries, namely circumferences. In this work we will study the behavior

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of evaporating drops on lyophobized substrates that have lyophilic elliptical patches.

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The elliptical shape for the patches is chosen as a transitional case between a circular

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patch 34 and a single stripe 35–38 , having the uniqueness of a perimeter with non-constant

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curvature. When a drop is placed on a homogeneous substrate, the minimization of

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surface energy leads to a spherical cap shape. This is traditionally described by the

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Young-Laplace, Wenzel, or, for pillars or patterns with length scales much smaller

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than the drop, Cassie-Baxter relations 39–42 , which reasonably apply to homogeneous

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substrates or substrates with sufficiently small and homogeneously distributed hetero-

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geneities 43–45 , which are not the focus of this study.

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Our previous work (Devi´c et al. 46 ) based on Surface Evolver and Monte Carlo cal-

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culations showed that, when a droplet rests on an elliptical patch, four distinguishable

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morphologies are found, depending on the volume of the drop and the aspect ratio of

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the patch. These morphologies were termed 46 A, B, C and D, see figure 1. When a

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large enough droplet evaporates on an elliptical patch, the first morphology found is D.

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In this case, the droplet completely wets the ellipse with a part of its contact line out-

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side the ellipse and the rest pinned to the contour of the patch. After a certain volume

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loss, the droplet adopts either morphology B or C - depending on the geometry of the

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patch. In morphology B, a part of the droplet’s contact line remains outside the patch

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while the rest is already inside the patch. In contrast, the contact line of a droplet

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adopting morphology C follows the perimeter of the ellipse. The final morphology to

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be found for evaporating drops is morphology A, characterized by a part of its contact

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line following the perimeter of the ellipse and the rest of the contact line laying inside

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it.

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Methods

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In this paper we perform corresponding experiments and numerical simulations, per-

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formed again with Surface Evolver using the experimental parameters. Both the ex-

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periments and the calculations are performed for Bond numbers below unity to avoid

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the e↵ects of gravity. Moreover, the experiments are performed at room temperature

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with a relative humidity of 38±2% in a closed and controlled environment, ensuring

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Figure 1: Scheme of the morphologies of a droplet as seen from the top as expected from the calculations by Devi´c et al. 46

Figure 2: Left: Coordinate system employed in this paper. ✓1 and ✓2 are, respectively, the Young’s angles of the lyophobic (white) and lyophilic (red) regions. R( ) is the distance from the center of the ellipse to the contact line of the droplet (blue), and a and b are the major and minor axis respectively. S indicates the vertical section. Right: Experimental results: Top view images taken during the evaporation of various droplets on ellipses with di↵erent sizes and aspect ratios, the red contours represent the elliptical patches on the surface. A) Morphology A, droplet on an ellipse of aspect ratio b/a=0.61 and semi-major axis a=512±16µm. B) Morphology B, droplet on an ellipse of aspect ratio b/a=0.43 and semi-major axis a=392±20µm. C) Morphology C, droplet on an ellipse of aspect ratio b/a=0.98 and semi-major axis a=410±20µm. D) Morphology D, droplet on an ellipse of aspect ratio b/a=0.69 and semi-major axis a=411±20µm.

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that the evaporation driven volume change is slow enough so that the droplets evolve

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in quasi-static equilibrium. The e↵ects of humidity, evaporative cooling, and evapo-

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ration driven flows do not have any important e↵ects. However, for heated or cooled

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substrates or more volatile liquids this situation may change. Unlike the gravitational

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and evaporative e↵ects, the e↵ects of the inhomogeneities of the substrate —like pin-

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ning and contact angle hysteresis— are unavoidable in our experiments while they are

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absent from the Surface Evolver calculations.

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Preparation of substrates with lyophilic elliptical patches

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The patched substrates were prepared via photolithography followed by chemical va-

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por deposition (CVD) of a mono layer of trimethylchlorosilane (TMCS). The 100 x

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100 mm2 chromium on glass photo-mask used was designed with an array of ellipses

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of aspect ratios varying from 0.3 to 1 and sizes varying from a=320µm to b=2500µm,

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see figure 3 (a), and fabricated in the MESA+ Institute clean room facilities of the

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University of Twente, using laser writing technology. The substrates were glass slides

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(20 ⇥ 60 mm2 ) of 170 µm thickness, which is optimal for confocal microscopy. The

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photolithography steps of the fabrication, outlined in figure 3 (b), were performed in

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a cleanroom environment. First, the substrates were pre-cleaned in a nitric acid bath

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(NOH3 , purity 99%) followed by water rinsing and nitrogen drying. Subsequently,

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we dehydrated the substrate (120 C, 5 min). After dehydration, we spin-coated the

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photoresist (Olin OiR, 17 µm), pre-baked it (95 C, 90 s) and proceeded with the align-

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ment of the photomask and UV irradiation (4 s, 12 mW/cm2 ). Once the photoresist

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was cured, we developed and post-baked it (120 C, 10 min). Finally, the substrates

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were taken outside the clean-room environment for the CVD ( 2 h, 0.1 MPa) of a

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TMCS monolayer (Sigma Aldrich, purity

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lipses. The photoresist was later stripped away by rinsing the substrates with acetone,

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cleaned with isopropanol and dried using pressurized nitrogen.

99%) to lyophobize the exterior of the el-

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a) Design Photomask

b) 1

Pre-cleaning with NOH3 Developement photoresist Glass Substrate 4 Spin-coating photoresist

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Photoresist

CVD deposition of TMCS 5 TMCS

UV light through photomask

5 mm

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TMCS elliptical patches TMCS

Figure 3: a) Array of ellipses of aspect ratios varying from 0.3 to 1 and sizes varying from a=320 µm to b=2500 µm fabricated on the photomask. b) Simplified steps of the substrates’ fabrication in the order indicated by the numbers. 92

Experimental data acquisition and analysis

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For all the measurements, we used droplets of ultrapure (Milli-Q) water dyed with

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Rhodamine 6G at a concentration of 0.2 µg/ml. The droplet was deposited cover-

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ing the lyophilic patch and imaged by laser scanning confocal microscopy (LSCM) in

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three dimensions during the evaporation process. After deposition of the droplet, the

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substrate was covered to avoid external perturbations.

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In figure 4, we show four examples of three-dimensional reconstructions of a stack

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of scans with increasing heights taken under LSCM. For each scan, we detected the

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surface of the drop using a threshold algorithm, allowing for the three-dimensional

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reconstruction of the drop. Using this data we calculate the local contact angle at

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every point detected on the contact line. For the measurement of the contact angle ✓,

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we extract the height profile along the contact line. This can be achieved, as sketched

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in figure 2, by identifying the tangent to each point of the contact line at an angle

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and finding the points belonging simultaneously to its normal plane S and to the

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surface of the droplet.

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We extracted three-dimensional images of evaporating water droplets using LSCM.

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From the three-dimensional data we measured the local contact angle along the three-

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phase contact line through the azimuthal angle

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of various evaporating droplets as examples of each of the morphologies introduced

6

. Figure 2, right, shows top views

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previously. The lyophilic elliptical islands of the substrate are highlighted by red curves.

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We adopted a cylindrical coordinate system with its origin at the center of the

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ellipse. The polar axis was fixed to be in the direction of one of the major semi-axes a as

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shown in figure 2 (left). We set the large semi-axis (a) of the ellipse as the characteristic

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length scale for this system and the aspect ratio of the ellipses b/a to characterize the

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geometry of the patch. The relative volume of the droplets is normalized as V /a3 .

Figure 4: Three-dimensional reconstruction of the shape extracted from the LSCM data collected for four di↵erent droplets adopting morphologies A, B, C and D respectively as performed for the extraction of the contact angle along the contact line with the shape of the elliptical patch, highlighted in red lines. Repeatability is subjected to the initial position of the droplet and pinning of the contact line which can a↵ect the symmetry of the shape as well as delay the transition between phases as compared to the predictions. In figure 6 all the morphologies observed during the experiments are shown.

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Calculations

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We compute the surface energy minimization using Surface Evolver, a free software

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package used for minimization of the interfacial free energy developed by Brakke 47 , to

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extract the droplet’s shape and local contact angle as in the previous work by Devi´c

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et al. 46 . An initial shape of the droplet and the characteristic interfacial tensions of

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the surfaces are given to Surface Evolver as an input. The software minimizes the

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surface energy by an energy gradient descent method. Since hysteresis is not captured

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by our simulations, we compared each group of experimental results with two di↵erent

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calculations: one considering the receding contact angles for the two regions, and the

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other considering the advancing contact angle for the lyophilic part.

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To perform the calculations, we measured the contact angles of both the lyophilic

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and lyophobic parts of our patches. To do this, we treated two separated substrates ho-

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mogeneously in the same manner as in these two regions. We measured the advancing

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and receding contact angles on both substrates. Respectively for the lyophobic (sub-

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script 1) and lyophilic surfaces (subscript 2), the advancing contact angles measured

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were ✓a1 = 85±3 and ✓a2 = 33±4 , and the receding contact angles were ✓r1 = 49±3

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and ✓r2 = 15 ± 4 . During the experiments, we observed variations between 5% and

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10% of the contact angle due to occasional pinning events.

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Results

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In this section, we present the results of our experiments and the Surface Evolver cal-

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culations for each of the observed morphologies. In Figure 5, each row presents one

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of the morphologies shown previously in Figure 4. For each morphology, we show

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the normalized footprint radii R/a next to the local contact angles ✓, both along the

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azimuthal coordinate . In each of the plots we overlay experimental and computa-

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tional results. The red and blue markers represent the calculations done considering

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the lyophilic contact angle ✓2 = 33 and ✓2 = 15 , respectively. In the plots of the

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normalized footprint radii we plot the position of the patch contour (black curve).

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To follow the chronological sequence of our evaporating experiments, we present

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the results starting from morphology D (largest droplet volume) and finishing with

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morphology A (smallest droplet volume). Finally, in figure 6 we present the morphology

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diagrams predicted by the Surface Evolver calculations (colored areas) and compare

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those with the results of all our experiments (colored markers).

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Morphology type D

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In figure 5 (a and b), we can see an example of an experiment in which morphology

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D was found. The normalized footprint radius R/a and the contact angle are plotted

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along the azimuthal coordinate. From the figure, we observe reasonable agreement

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between Surface Evolver calculations and experiments. However, the existence of inho-

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mogeneities introduces pinning and hence, a delay in the movement of the contact line.

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This delay translates into an experimental radius larger than that predicted by the

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Surface Evolver calculations. Despite this mismatch of the contact line, consequence

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of individual pinning events of the contact line, we obtain reasonable agreement with

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the contact angle calculations.

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Morphology type C

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Morphology C appeared for ellipses of higher aspect ratio b/a as compared to morphol-

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ogy B. Additionally, when evaporating, the drop reaches morphology C always through

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morphology D, implying that any pinning event of the contact line outside the ellipse

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prevents morphology C. Indeed, the transition from morphology D to C was always

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found in a later stage of evaporation than predicted by theory, i.e., for lower volumes

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(see figure 6 (b)).

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In figure 5 (c and d), we show a droplet of volume V /a3 =0.37 placed on a high

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aspect ratio ellipse (b/a=0.98). The results of the calculations predict morphology C

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and contact angles between the receding and the advancing ones. The contact angle

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and the contact line show always good agreement with the Surface Evolver calculations.

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This is expected as it is the closer case to the trivial spherical cap shape.

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Morphology type B

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The experimental data shown in figure 5 e and f, are particularly interesting as this

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case presents a strong asymmetry in the radius caused by a sharp pinning point which

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can be identified at

⇡ 120 (indicated by an arrow in figure 5 e). Unlike the radius,

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the contact angle shows a symmetric behavior. We found that pinning leads to an

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asymmetric behavior in this morphology for all our experiments but, besides the asym-

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metry forced by pinning, the experiments agree with the Surface Evolver calculations.

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The good match for the angle can be explained considering that the contact angle at

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every point of the contact line –far enough from the ellipse contour– is dictated by the

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chemistry of the surrounding substrate.

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Morphology type A

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The experimental results showed morphology type A as predicted by the calculations

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for ✓2 = 15 , with a part of the contact line pinned at the boundaries of the ellipse and

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the rest of the contact line inside the ellipse. Note that, in the calculations for the higher

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receding contact angle (✓2 = 33 ), the results predict a spherical cap shape with radius

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R < b. However, our results for the contact angle were not in good agreement with

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either of the Surface Evolver calculations, but rather an intermediate state between

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them, subjected to the irregularities of the edge (see figure 5 g and h. This can be

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due to imperfections of the coating in the edges of the ellipse. The high portion of

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the contact line that remains pinned at the boundary between the lyophilic and the

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lyophobic parts appeared to be very sensitive to the quality of the patch rim.

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Figure 5: Normalized footprint radius R/a and contact angle ✓ along the azimuthal coordinate (as defined in figure 2). Experimental results for the four di↵erent morphologies (green). From top to bottom; morphology D (V /a3 = 0.40, b/a = 0.69, and a = 411±20µm); morphology C (V /a3 = 0.37, b/a = 0.98, and a = 410 ± 20 µm); morphology B (V /a3 = 0.30, b/a = 0.43, and a = 392 ± 20 µm); and morphology A (V /a3 = 0.08, b/a = 0.60, and a = 512 ± 16 µm). Results of the numerical simulations considering the lyophilic contact angles ✓2 = 15 (blue) and ✓2 = 33 (red). The black curve in the radius plot shows the contour of the elliptical patch. 11

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Morphology Diagrams

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Figure 6 presents two morphology diagrams showing all the morphological regions

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and transitions predicted by the Surface Evolver calculations (as color shaded areas),

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together with the experimental results (colored markers). In this figure, morphology

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E is added, to illustrate the transition to the case in which the ellipse does not have

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an e↵ect, as in that case the droplet is smaller than the ellipse minor axis. Using

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the receding contact angle for the calculations (see figure 6(a)) is, in principle, the

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most logical method for calculating the shape of evaporating droplets. However, the

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experimental results show a behavior that falls between the results calculated for both

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limits of contact angle hysteresis.

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In fact, for the first transitions (from morphology D to B and to C), the calculations

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done considering the hysteresis limits ✓r1 = 49 ± 4 and ✓a2 = 33 ± 4 show better

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qualitative agreement with our experiments than those done considering both receding

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angles. For these morphologies, in which part of the contact line lays on the lyophobic

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area, the overall angle of the drop is kept higher by the influence of the high contact

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angle of the lyophobic area ✓1 = ✓r1 = 49 ± 4 , bringing it to the maximum angle

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possible for the lyophilic patch ✓2 = ✓a2 = 33 ± 4 . For the same reason, the transitions

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from morphologies B and C to morphology A, in which the contact line has to travel

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along the lyophilic patch, show better agreement with the calculations performed for

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✓2 = ✓r2 = 15 ± 4 . The experiments also show that the transitions occur for smaller

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droplet volumes as compared to those predicted. This delay can be observed if, for

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a fixed aspect ratio b/a, we follow down the vertical line in the decreasing volume

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direction. This e↵ect is forced by pinning, which acts to favor larger radii morphologies.

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Moreover, during the calculations we found that, for certain lyophilicity di↵erences,

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we can exclude morphologies from the diagram. In our case, the calculations that

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were computed considering ✓2 = ✓r2 = 15 (see figure 6(a)) predict the absence of

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morphology B.

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Figure 6: Morphology diagrams in aspect ratio b/a vs relative volume V /a3 phase space showing the morphologies A, B, C, D and E. (a) Experimental results displayed together with the computational results considering ✓2 = ✓r2 = 15 (b) Experimental results displayed with the computational results considering ✓2 = ✓a2 = 33 . The main features for A-D are indicated in figure 4, while E shows the case in which the droplet is small enough to adopt the trivial spherical cap shape inside the patch. The color shadowed regions represent the morphologies obtained with our calculations. Green, yellow, dark blue, red and light blue regions represent respectively the regions where morphologies D,C, B, A and E where found in our calculations and the colored markers show the experimental points specified in the legend.

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Conclusions

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We have performed experiments to validate the Surface Evolver calculations, and these

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showed good agreement. We observe how the e↵ect of substrate heterogeneities, in-

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cluding pinning and contact angle hysteresis, can a↵ect the accuracy of our surface

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minimization calculations. These heterogeneities seem mostly to a↵ect the symmetry

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and the transitions in the morphology diagrams. With this study, we show the ro-

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bustness of the contact angle predictions which contrast with the sensitivity that radii

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predictions have to pinning. The reason is that the radius depends on the mobility of

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the contact line and therefore on pinning, even when a di↵erent morphology would be

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energetically more efficient, while the contact angle is forced by the chemistry of the

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substrate in the vicinity of the contact line, making it more robust.

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According to our results, we conclude that the knowledge of the hysteresis limits can

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be used for improving the predictions of Surface Evolver calculations. In general, the

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morphologies found experimentally show good repeatability However, the morphologies

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adopted by the droplets are always subjected to the e↵ect of pinning, which influences

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the droplet’s symmetry and delays its transition to the next morphology. This e↵ect

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shifts the experimental transitions to smaller volumes than those predicted by our

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calculations, as shown in the morphology diagram. We expect this e↵ect to be opposite

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for growing droplets but that remains an open question and it is beyond the scope of

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the present study, as it would require a di↵erent experimental setup. Finally, the

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exploration of lyophilicity di↵erences between the patches and the surroundings have

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shown the feasibility of excluding morphologies from the phase diagram, which is an

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interesting result with bearing on the design of micro-patterned structures for various

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applications.

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Acknowledgments

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This work was supported by the Netherlands Center for Multiscale Catalytic En-

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ergy Conversion (MCEC), an NWO Gravitation program funded by the Ministry of

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Education, Culture and Science of the government of the Netherlands. DL also ac-

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knowledges an ERC Advanced grant. We acknowledge the support of the Natural

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Sciences and Engineering Research Council of Canada (NSERC).

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