Estimation of size and contact angle of evaporating sessile liquid

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Estimation of size and contact angle of evaporating sessile liquid drops using texture analysis Chonghua Xue, Jared T Lott, and Vijaya Kolachalama Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b04043 • Publication Date (Web): 01 Feb 2019 Downloaded from http://pubs.acs.org on February 3, 2019

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Estimation of size and contact angle of evaporating sessile liquid drops using texture analysis

Chonghua Xue1, Jared T. Lott2, Vijaya B. Kolachalama1, 3, 4, *

1Section

of Computational Biomedicine, Department of Medicine, Boston University School of Medicine, Boston, MA, USA - 02118 2College

3Whitaker

of Engineering, Boston University, Boston, MA, USA – 02215

Cardiovascular Institute, Boston University School of Medicine, Boston, MA, USA – 02118

4Hariri

Institute for Computing and Computational Science and Engineering, Boston University, Boston, MA, USA – 02215

*Corresponding author: Vijaya B. Kolachalama, PhD Assistant Professor of Medicine 72 E. Concord Street, Evans 636, Boston, MA, USA – 02118 Phone: 1-617-358-7253 Email: [email protected]

ACS Paragon Plus Environment

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Abstract Size and contact angle of liquid drops are fundamental parameters in interfacial science. Accurate estimation of these parameters can provide objective information regarding several properties of the contacting surface. We leveraged principles of texture analysis to estimate the contact angle and the drop diameter from videos of evaporating sessile liquid drops deposited on solid surfaces. Specifically, we used a Harris corner detector to locate the corners and dynamically estimate the changing size and a Gabor wavelet-based approach to estimate the varying contact angle of the evaporating sessile drop. We demonstrated the ability of our approach to accurately estimate size and contact angles of drops deposited on a hydrophilic glass slide and on a paraffin film representing a hydrophobic surface. We also estimated contact angle and size of drops deposited on horizontal and tilted surfaces to generate symmetric and asymmetric drop shapes, respectively. A software application that has the ability to analyze videos of sessile liquid drops as inputs is provided, and this tool can generate plots of estimated contact angle and the drop diameter as a function of frame number.


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Introduction Surface wetting is an important phenomenon with several chemical, physical and biological applications.1-8 Wetting is characterized using the contact angle of a liquid drop deposited on a solid surface,9-10 defined as the angle between the solid surface and liquid–air interface on the side of the liquid phase.11 In addition, wetting behavior is linked with drop size and its characteristic evaporation and condensation kinetics.12-13 Accurate estimation of the contact angle and the drop size is therefore of fundamental importance. Sessile drop evaporation is defined by relating contact angle and contact diameter dynamics throughout the process. A drop is defined in one of the three evaporation states:13-17 Constant contact radius (CCR), when the edges are pinned as contact angle decreases, constant contact angle (CCA), when the contact angle is fixed as the diameter recedes, or mixed which constitutes some combination of the two aforementioned states. To accurately define such states of evaporation, it is critical that both contact angle and diameter are measured concurrently. These states can be analyzed to gain information about the dynamic evaporation processes of a liquidsolid interface, such as water drops evaporating on silicon surfaces.18-19 Several techniques exist that can estimate the contact angle and the size of liquid drops but most use edge fitting or direct image processing methods.20-25 In the case of edge fitting methods, information is extracted from the raw image to define a drop profile. One type of edge fitting method is called axisymmetric drop shape analysis (ADSA), which uses analytical functions to define a drop edge. In contrast, direct image processing uses techniques that are applied on the images to generate information that can be used for further processing. Methods such as ‘local contour analysis’ apply masks to the image and implement algorithms on the extracted information to determine a local contour of the drop and subsequently the contact angle and drop


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diameter. It is important to understand that edge fitting and direct image processing methods differ in functionality when measuring contact angle and diameter of sessile drops. Contact angles are estimated from the side view of drop images that are generated by placing the drop on a solid surface. Of these, ADSA methods are widely used due to their simplicity.21-23 An advantage of using ADSA methods is their ability to compute contact angles concomitantly with volume and surface area of the drops. Typically, the ADSA methods for contact angle estimation involve quantifying the liquid-solid interaction force and relating it to the contact angle using the Young-Laplace (YL) equation. In this case, a solution of the YL equation is fitted to the drop shape by performing error minimization between the observed and theoretical drop boundaries. It is important to note that most of the ADSA methods assume a symmetric drop shape, thus making them unsuitable for asymmetric drop shape analysis. As many of these ADSA methods show shortcomings in versatility for accurately measuring contact angle of sessile drops, the same holds true for measuring the diameter. One method for measuring diameter of a sessile drop is to use an analytical fit to locate the contact points representing the liquid-solid interface.24-25 The diameter then gets estimated from the points of intersection between the reference line and the analytical fit. While the ADSA methods have analytical solutions for simple cases, there are many optical methods available that involve direct image processing to estimate the apparent contact angle.20 These methods are less sensitive to image resolution and allow for analysis on left and right angles to be individually executed. Also, these methods are sensitive in the manner that over processing will lead to contour smoothing which can cause inaccurate measurements. Moreover, direct image processing methods focused on measuring contact angle do not necessarily focus on tracking and measuring the diameter of a sessile drop. Few methods that do allow for tracking


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drop diameter use the drop reflection as a way to locate the endpoint. There may be limitations in these methods as the drop reflection is dependent on the video generation technique and is hard to standardize. In engineering our approach, we recognized the wider range of capabilities which direct image processing offers compared to edge fitting methods. For this reason, we chose to use direct image processing as a means to execute sessile liquid drop analysis. We sought to address some of the common limitations of previous sessile liquid drop analysis methods. In this process, we aimed to develop a single framework based on image textural analysis to concomitantly estimate the drop diameter and contact angle of symmetric and asymmetric drops. While the mathematical formulations were borrowed mostly from the literature, the novelty in this work lies in our ability to tailor these methods to accurately estimate drop diameter and contact angle of liquid drops, respectively. In addition, our goal was to provide a free, downloadable software that can be utilized as a user-friendly tool for shape analysis of sessile liquid drops.


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Methods Drop preparation A 500 μL glass syringe was filled with distilled water. The liquid was allowed to flow from the syringe by a dispensing mechanism that uses a screw adjusted plunger (Figure 1). The syringe was lowered until its tip was just above the substrate. At this point, the plunger was tightened until a liquid drop formed at the opening of the syringe tip and the syringe was then gently lowered until contact with the substrate was made. The syringe was then lifted carefully as the drop was transferred from the syringe to the substrate. Due to the continuous nature of the screwing mechanism, it was not possible to standardize an exact drop volume, but for the experiment, drops were visually inspected and estimated to be of the same scale.

Data generation Drop evaporation was captured using a drop shape analyzer (DSA100, Krüss GmbH, Germany) (Figure 1, Element A), which allowed us to record high resolution and high-speed videos captured with a digital camera (Figure 1, Element B). To create a clear and defined drop profile, the machine uses a diffused high power monochromatic LED backlight (Figure 1, Element C). The backlight allows for a shadow to be cast over the drop, creating high contrast between the drop and its surroundings. The substrate was placed on a 3-axis translating stage that allowed for minor adjustments of the drop location (Figure 1, Element D). In order to generate images with best possible resolution, the translating stage was used to move the drop to the closest focal point of the camera. A test trial to pre-determine the optimized zoom and focus of the camera that yielded clear results was run before the experimental trials. Once these parameters were set, the syringe dispensing mechanism (Figure 1, Element E) was


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used to create the drop. The location of the syringe was not within this optimized zoom and focal point, so the translating stage was used to bring the drop into this optimized region. For the set of experiments, recording was performed such that all cases were captured within 5000 frames. Trials that dried faster were recorded at higher framerate, while longer drying trials were forced to use a lower framerate. Videos were exported in AVI format directly after recording (Figure 1, Element F). In order to fully demonstrate the ability of our approach to analyze a range of liquid drops, we considered the deposition of the drop on 2 different substrates (a hydrophilic glass surface and a paraffin film, representing a hydrophobic surface) (Figures 2A-2L). Distilled water on glass produces a sessile drop with contact angle less than 90°, whereas distilled water on paraffin produces a contact angle greater than 90°. Most methods that can perform drop shape analysis of sessile liquid drops assume a symmetric drop shape. Indeed, due to the complex nature of sessile drop formation and evaporation, the drop may never be truly symmetrical, even in controlled environments. We aimed to demonstrate the ability of our approach to measure left and right angles independently, and hence designed cases with liquid drop on flat and tilted glass slides as well as paraffin sheets, respectively (Figures 2A-L). To demonstrate consistency, we performed multiple experiments simulating similar conditions followed by drop shape analysis. Before each trial, the glass slides were cleaned by washing the slide in 70% ethanol and wiped down to remove any surface heterogeneities. The paraffin sheets were cut to dimensions larger than the glass slide and carefully placed over the slide. To ensure a flat profile, the edges of the paraffin sheet were wrapped around the glass slide, and smoothed out to remove any air bubbles between the paraffin sheet and glass base. To standardize video generation, the lighting set up of the room was kept consistent between trials. Also, the diffused backlight setup was unchanged between


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trials. Each experiment was conducted in the same room with stable humidity levels and temperature around 20-23℃. For each case, the same technique was used to generate the videos.

Drop diameter measurement The diameter of a sessile drop (Figure 3A) was estimated using a 2-step sequence consisting of applying the well-known Harris corner detection (HCD) (Figure 3B), followed by a Gaussian prior application on the HCD response (Figure 3C). HCD measures and classifies the intensity differences along an image.26 Using these detected intensity differences, the type of surface (edge, corner or flat) can be distinguished. Differences in local intensity are defined as 𝐸[𝑢,𝑣] = ∑ 𝑤[𝑥,𝑦](𝐼[𝑢 + 𝑥, 𝑣 + 𝑦] ― 𝐼[𝑥,𝑦])2, (1) 𝑥,𝑦

where 𝑤[𝑥,𝑦] is a shifting window function that weighs the set of pixels based upon Gaussian distribution. The term 𝐼[𝑥,𝑦] signifies the intensity value of the original point [𝑥,𝑦], and 𝐼[𝑥 + 𝑢,𝑦 + 𝑣] represents the intensity value of the point shifted from [𝑥,𝑦] by [𝑢,𝑣]. Using Taylor expansion on Equation 1, the expression can be simplified to

[]

𝑢 𝐸[𝑢,𝑣] ≈ [𝑢 𝑣]𝑀 𝑣 .(2) Here M is described as

[

]

𝐼𝑥𝐼𝑥 𝐼𝑥𝐼𝑦 𝑀 = ∑ 𝑤[𝑥,𝑦] 𝐼 𝐼 𝐼 𝐼 ,(3) 𝑥 𝑦 𝑦 𝑦 𝑥,𝑦 where 𝐼𝑥 , 𝐼𝑦 are the derivatives for the image intensity with respect to x and y, and they can be estimated by a Sobel filter. Using this, we compute a descriptor 𝑅𝐻𝐶𝐷 defined as 𝑅𝐻𝐶𝐷 = det (𝑀) ― 𝑘(𝑡𝑟𝑎𝑐𝑒(𝑀))2,(4) where k is a free parameter of the HCD. Using R, each pixel of the image can be classified in one of the following three categories: (a) a flat region when |R| is small, (b) an edge if R < 0, and (c)


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a corner if R is large. Depending on the HCD response, this method can detect all possible pixels as part of edges and corners within an image. Therefore, the two endpoints of the drop would exist in a set of many points which stimulate a response (Figure 3B). We therefore applied a Gaussian prior on the points generated from the HCD response to filter all unrelated stimuli. The prior is defined as 𝑝[𝑥,𝑦] =

1 2𝜋 |𝛴|

𝜇 𝑥 𝛴 ― [ ] [ ] [ ] [ ])).(5) ( ) ( 𝑦 𝜇 (

exp ―

1 𝑥 𝜇𝑥 ― 𝜇 𝑦 𝑦 2

T

―1

𝑥

𝑦

Here Σ = σI is the covariance matrix, σ represents the standard deviation of the generated Gaussian prior, and [μx,μy]T, refers to the mean of the Gaussian prior coordinates which correspond to the drop corner region of interest (See Supplement for more information). Subsequently, when the Gaussian prior was used in conjunction with the HCD response, the filtered endpoints are defined as follows (Figure 3D):

[𝑦𝑥 ] = argmax 𝑅 ∗

∗

𝑥,𝑦

𝐻𝐶𝐷[𝑥,𝑦]

∙ 𝑝[𝑥,𝑦].(6)

Edge crossing Despite the ability of the HCD-Gaussian method to detect endpoints, the framework is limited by the fact that for instances where the contact angle approaches 90, the generated HCD-Gaussian response no longer results as a clearly defined bright spot (Figure 3B). Therefore, we added another processing step to measure the change in intensity values on the surface line, and the endpoints were determined as the locations where the surface line ‘crosses’ the drop edge (Figure 3D). This edge-crossing technique allowed us to estimate drop size for various scenarios, where the endpoints of the drop were calculated only once. Specifically, we used the combined HCD-Gaussian method to determine the endpoints of the drop for the first


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measurable frame of the video (Figure 3D). Once the two initial endpoints were calculated, we assumed the line which intersects these two points to be the surface line for all points of the video. An equation for the surface line was then determined. For each frame, the pixel coordinates of the end points were recorded, and the drop diameter was measured as the Euclidean distance between these points.

Gabor wavelets to measure contact angle A Gabor wavelet-based approach was developed to estimate the contact angle of the evaporating sessile liquid drop.27 Gabor wavelets are typically implemented in order to perform texture analysis on images.28-30 For our problem, the drop’s edge is characteristically black and surrounded by white background (Figure 2). Due to this characteristic texture of the drop, we hypothesized that applying the correct Gabor wavelet can be highly effective in defining the location of the drop edge, and subsequently determining the contact angle. The Gabor wavelet is defined as the function ―

𝐺[𝑥,𝑦;𝜎,𝜃,𝜆,𝜓,𝛾] = 𝑒

(

)𝑒 (

𝑥′2 + 𝛾𝑦′2 2𝜎

2

𝑖

),(7)

2𝜋𝑥′ +𝜓 𝜆

where (𝜎,𝜃,𝜆,𝜓,𝛾) are the parameters and 𝑥′ = 𝑥cos 𝜃 +𝑦𝑠𝑖𝑛𝜃 and 𝑦′ = ―𝑥𝑠𝑖𝑛 𝜃 + 𝑦𝑐𝑜𝑠𝜃. Here 𝜎 controls the standard deviation of the Gaussian envelope. It may vary depending on the resolution of input images as well as the linearity of the drop edge. Also, 𝜆 determines the sinusoidal wavelength and 𝜓 refers to the phase shift of the sinusoidal function. For example, a phase shift of ¼ octave makes the sinusoidal function odd to detect an edge feature. The ratio of the eigenvalues of the Gaussian enveloped is defined using 𝛾, where tuning a smaller value makes the envelope ‘thinner’. Finally, 𝜃 represents the orientation of the Gabor wavelet. The


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( sinusoidal wave 𝑒 𝑖

2𝜋𝑥′ 𝜆

) is composed of both real and imaginary components which have a

+𝜓

phase difference of ¼ of an octave. One component typically is sensitive to asymmetric features such as edges, while the other is sensitive to symmetric features such as lines. For our purposes, only edge features are relevant, and therefore we discarded the imaginary component of the sinusoidal wave. To improve function, we implemented another method that merges displacement into the Gabor wavelet definition. In this way, we can adjust the formula for determining 𝜃 ∗ (contact angle) to simplify the calculation. The displaced filter is defined by the same expression with two added parameters (𝑑,𝒗), where d is the magnitude of the Gabor wavelet shift and 𝒗 is a constant unit vector that denotes the directional shift of (𝑑) (Figure 4A). The unit vector (𝒗) is approximately orthogonal to the drop edge. By allowing these parameters to be variable, the wavelet can be applied to the drop edge with more flexibility to choose between various combinations of positions and orientation parameters. As the drop profile is changing, the allowance of these parameters to be variable gives further validation that the calculated 𝜃 ∗ is optimal for each set drop profile. With these added parameters, the Gabor wavelet is now described as ―

𝐺𝜃,𝑑[𝑥, 𝑦] = 𝐺[𝑥,𝑦;𝜎,𝜃,𝜆,𝜓,𝛾,𝑑,𝒗] = ― 𝑒

(

)sin

𝑥′2 + 𝛾𝑦′2 2𝜎2

( )

2𝜋𝑥′ ,(8) 𝜆

where 𝑥′ = (𝑥 ― 𝑑𝑥)cos 𝜃 + (𝑦 ― 𝑑𝑦)𝑠𝑖𝑛𝜃, 𝑦′ = ― (𝑥 ― 𝑑𝑥)𝑠𝑖𝑛 𝜃 + (𝑦 ― 𝑑𝑦)𝑐𝑜𝑠𝜃, 𝑑𝑥 = 𝒗 ∙ [𝑑, 0]𝑇, and 𝑑𝑦 = 𝒗 ∙ [0, 𝑑]𝑇. Measuring the orientation of the drop edge near the endpoint is fundamental for contact angle measurement. To find this orientation, we must find the optimum in a family of Gabor wavelets (ℱ) that has different orientations and displacements. The parameters defining ℱ provide a much wider framework than what is required for estimating the


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contact angle. In practice, this translated to keeping all the parameters except 𝜃 and d as π

constants. For our work, we assigned 𝜎 = 4 (pixels), 𝜆 = 20 (pixels), 𝜓 = 2 (radians) and 𝛾 = 0.2 (non-dimensional). For each case, the drop edge can exist within an unknown range of angles. For this reason, we allow the filter orientation parameter 𝜃 to be free to rotate, where 𝜃 ∈ (0, 2π) so that the wavelet can be applicable for drop profiles of various angles. The image resolution for our generated videos was 768 pixels wide and 576 pixels high. Note that the wavelet parameters can be scaled accordingly for various datasets. The Gabor wavelet family is then denoted as ℱ = {𝐺𝜃,𝑑[𝑥, 𝑦] | 𝜃 ∈ (0, 2𝜋), 𝑑 ∈ ℝ}#(9) where the length of the Gabor wavelet displacement is controlled directionally by the unit vector, 𝒗. Using this method, we can determine the optimal angle and optimal Gabor wavelet shift by finding only one extremum described as 𝜃∗, 𝑑∗ =

argmax 𝜃 ∈ (0, 2𝜋),𝑑 ∈ ℝ

∑∑𝐺

𝜃,𝑑[𝑥,𝑦]

𝑥

∙ 𝐼[𝑥,𝑦].#(10)

𝑦

The optimization routines used to iteratively estimate 𝜃 ∗ , 𝑑 ∗ are described in the Supplement. For a visualization of the optimization, see Figure 4B.

Eliminating instrument related variability Drop shape analyzers that are allowed to track sessile liquid drop evaporation generate profiles that create a reflection to be cast on the substrate (Figure 3A), leading to true and reflected profiles (Figure 5A). While the Gabor wavelet aims to exclusively estimate the angle of the true edge, the placement of the wavelet gets influenced by the reflected profile, thus leading to biased estimation. The reflected edge induces error that is described as the deviation


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between measured contact angle (𝜃 ∗ ) and the true contact angle. We noticed that this error was highest when the sum of the true and reflected angles approached 0 or 180 (Figure 5B). In contrast, when the sum of the true and reflected angles approaches 90, the Gabor wavelet was best able to differentiate the true profile from the reflected profile (Figure 5B). We devised an image processing step that aimed to exploit the error minimizing quality of the 90 case through the implementation of color masks (Figures 5A, 5B & S1). The first mask was defined to mimic the white background and another mask was defined to mimic the drop profile. The masks are controlled by 3 vectors. Among these vectors, the surface vector and surface normal vector were determined using HCD and remained constant. The edge normal vector, however, is not constant. To estimate the edge normal vector, we assigned it the Gabor wavelet displacement vector 𝒗, which is approximately perpendicular to the true edge. With these three known vectors, the masks can be efficiently generated by leveraging the handedness of vector cross product combined with a proper sequence of logical operations. Theoretical analysis on the impact of the reflection is presented in the Supplement. A combination of the ‘background color mask’ and the ‘drop profile color mask’ were used in conjunction to maintain the sum of true and reflected angles at 90°.

GUI development We have packaged these methodologies into a user-friendly GUI (MATLAB, Mathworks, Natick, MA). The GUI allows for the entire framework to be executable in a logical sequence. By uploading a video of sessile drop evaporation and initializing a few parameters, the program will generate live results which can be saved and analyzed. More information can be found in the Supplement (Figure S2).


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Results and discussion Our experimental framework using a drop shape analyzer allowed us to simulate a series of scenarios representing common evaporation kinetics, which ranged from smooth evaporation on a flat, hydrophilic surface to inconsistent evaporation on a tilted, hydrophobic surface. For the purposes of our experiment, we used distilled water as the candidate liquid but varied the surface parameters to simulate various scenarios. This strategy allowed us to demonstrate a proof-ofconcept that image-based texture analysis can be applied to estimate contact angle and drop diameter, which can then be easily extended to other liquid drops as well. While the experiments are not fully exhaustive, they still cover a major set of common scenarios encountered when liquid drops are subjected to interact with surfaces. A liquid drop placed on a horizontal, hydrophilic surface resulted in an evaporation kinetic profile that exhibited a smoothly changing contact angle, whereas a drop placed on an inclined, hydrophobic surface led to more inconsistent kinetics (Figure 6). For example, when glass was used as the substrate, decreasing angle was a more observable dynamic than decreasing diameter for a large portion of the evaporation process (Figures 6A & 6B). On the other hand, when paraffin film was used, we noticed a combination of the three states of evaporation (CCA, CCR and mixed)14-17 (Figures 6C & 6D). For approximately equal volume drops, those placed on paraffin experienced much longer evaporation time compared to a glass substrate, requiring a lower framerate for video generation. For drops placed on a hydrophilic glass surface, the drop was more spread, which was characterized by a slightly larger diameter (Figures 2A & 2G). However, on paraffin, the initial drop profile was more representative of a tight spherical cap (Figures 2D & 2J). The hydrophilic surface allowed for increased surface area, i.e. larger area where evaporation can occur relative to the hydrophobic surface. For visualization of the


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dynamic estimation of contact angle and drop diameter, refer to Figure S3. Although distilled water was the only liquid used, we were able to encompass a wide spectrum of drop profiles and corresponding evaporation kinetics. To visualize results from additional experiments for flat substrates, refer to Figure S4 and Figure S5.

Corner point detection We hypothesized that a texture analysis method (HCD), which can systematically quantify local intensity differences can be applied to videos of evaporating sessile drops to estimate the coordinates of the drop endpoints. When we applied the HCD algorithm on each image frame, it resulted in a set of responses that corresponded to many corners and edges within the image, including the desired endpoints (Figure 3B). Interestingly, we observed that the corners corresponding to the endpoints produced the highest response (Figure 3B). However, the HCD also resulted in responses representing features in other areas of the drop. A Gaussian prior which was then applied on the HCD output resulted in a secondary response that filtered unwanted pixels and identified the endpoints representing the corners of the drop (Figures 3C & 3D), thus confirming our hypothesis. Once the endpoint locations were identified on the first measurable frame of the video, a surface line was defined by connecting the two endpoints. The edge-crossing method subsequently used this line to locate the endpoints for all the other frames in the video. The edge-crossing method (See Supplement) proved to be robust for both wetting and nonwetting cases, as well as flat and inclined substrates (Figure 2). However, it is important to recognize that the edge crossing method is dependent on two variables. First, the camera and substrate must be held still throughout the data collection process. Secondly, we assume the color


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of the drop face to be distinct from the background of the image. By considering these nuances, we were able to utilize a technique that can accurately estimate the diameter of sessile liquid drops during evaporation.

Contact angle estimation The application of a Gabor wavelet for contact angle estimation proved to be effective for measuring contact angle of liquid drops evaporating under different settings. The experiment was designed so that tilted substrates allowed for nuances between left and right angles to be measured. Interestingly, our method showed that even for flat substrate cases, there still exists some deviation for left and right contact angles (Figures 6A & 6C). As expected, differences in left and right angles for a tilted substrate were measured for both wetting and non-wetting cases (Figures 6B & 6D). Another aspect of this designed experiment was to show the wide range of angles for which this approach was applicable. Also, the method was successful in dynamically tracking contact angle as the drop transitioned from a state of non-wetting to wetting (Figures 6C & 6D). Specifically, generating results for small contact angles is of great significance as many common edge fitting methods are unable to produce such results. As seen in Figures 6A & 6B, the capabilities of our modified Gabor wavelet allow for estimation of contact angles less than 10. However, when contact angle of drops are nearing 3-4, they become too small for analysis as the resolution of the image cannot define a clear, dark profile. For such instances, the drop appears as a small group of grey pixels with little to no definition. For this reason, the method is unable to accurately measure angles less than 3-4. We believe that if the image resolution was greater and the drop edge was more well defined, our proposed framework would be able to


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measure such angles. Unfortunately, we were unable to test such cases with the resources available for this experiment. However, for angles less than 10, the YL fit is not applicable. For such angles, we used a visual qualitative check to ensure the results were significant. To generate consistent and meaningful contact angle results, it is important to understand that the Gabor wavelet functionality is dependent on implementation of the parameters (𝑑,𝒗) (Figure 4A). Without these parameters added, the Gabor wavelet is only applied on the detected endpoint. Applying the wavelet at one point causes a dependence on the accuracy of the corner detection for contact angle measurement and is susceptible to an amplification of error. What this means is that a small deviation in the detected endpoint (~1-2 pixels) for subsequent frames could amount to a large change in contact angle. Allowing for the wavelet to be translated according to (𝑑,𝒗) corrects the dependency between contact angle measurement and corner point detection. Gabor wavelet functionality was also dependent on the sum of true and reflected angles. With the implementation of the color masks, we were able to minimize the error of the applied Gabor wavelet for cases where the sum of the angles neared 0° and 180°. Through these modifications, we were able to improve the functionality of Gabor wavelet application for sessile drop analysis.

Method validation To verify quantitatively that our method produced meaningful results, we used the wellknown YL method for comparison. Note that the data for the YL fit in Figure 7 was obtained directly from the software (DSA100). In drop shape analysis, the YL method assumes an axisymmetric drop and fits a curve around the profile of the drop. In assuming an axisymmetric drop, left angle and right angle cannot be measured independently, but rather one overall angle is


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determined. This aspect was evident when the YL method was used to measure the contact angle for the case of the distilled water drop evaporating on a horizontal glass slide (Figure 7A). Since our method could measure both angles independently, we observed two distinct curves following the same trend as the YL model (Figure 7A). It is also important to notice that when the YL fit approached small angles, it was unable to generate a measurement. Our proposed method was able to estimate contact angle for over 300 more frames than the YL fit (Figure 7A). The performance of the YL fit was even more suboptimal for the case when the droplet was placed on an inclined surface (Figure 7B). When our method was applied, we observed two distinct curves following a similar trend as the YL fit (Figure 7B). The YL fit was also applied to the hydrophobic drop cases (Figures 7C & 7D). For such cases the YL fit proves to be highly variable, especially for the tilted substrate case (Figure 7D), whereas our measurements were much smoother. We hypothesize that the YL equation fluctuates mainly due to the fact that the YL method assumes the drop to be axisymmetric. As no drop will be truly symmetric, the YL method can lead to some error as asymmetry occurs in every drop. We also hypothesize that small light changes which are standard to the video taking procedure may throw off the YL algorithm. Our hope with using the YL method for comparison was to present the limitations in industry standard methods as well as highlight how our method attempts to overcome them. In summary, our method had three key distinctions relative to the YL fit. First, our method could produce contact angle estimates for both left and right angles independently. Second, our method generated smoother trendlines and finally, our method was able to estimate small contact angles.

Study limitations


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Our study has few limitations. The modified HCD method tends to fail when the contact angle of the drop approaches 90, which results in a suboptimal surface line estimation. Also, the effectiveness of the Gabor wavelet application is dependent on the variables that describe the filter. After careful experimentation, we identified the set of Gabor wavelet parameters that produced successful results for each of the four experimental cases. Despite this success, we cannot assume that these parameters would result in correct estimation of contact angle for all cases.


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Conclusion Texture analysis based on Harris corner detection and Gabor wavelets can dynamically estimate the diameter and contact angle of evaporating sessile liquid drops deposited on solid surfaces, respectively. The two-step corner detecting sequence that we proposed can accurately estimate drop corners for all processed frames while requiring input from only one reference frame. In addition, a rigorous analysis on the functional aspects of Gabor wavelets demonstrated that our method is versatile for contact angle estimation. As a result, the software tool that we developed based on our proposed framework can accurately estimate the drop size and contact angle for symmetric and asymmetric drops generated on various surfaces. When compared with the traditional Young-Laplace fit, our method demonstrated better performance for contact angle measurement for a wide range of drop profiles and environments. Adoption of our method can expedite contact angle and diameter estimation, and serve as a first step towards more comprehensive automated analysis.


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Supporting information GUI development, Optimization methods (Gradient ascent/descent algorithm, Other optimization methods, Theoretical and numerical analysis to minimize instrument dependent variability), Analysis of reflection generated error (Problem formulation, Simulation on synthetic images), and GUI manual.

Funding This work was supported by the American Heart Association through a Scientist Development Grant [17SDG33670323 to V.B.K]; the Hariri Institute for Computing and Computational Science & Engineering at Boston University through a Research Award to V.B.K; the National Center for Advancing Translational Sciences, National Institutes of Health, through BU-CTSI Grant [1UL1TR001430 to V.B.K]; the Whitaker Cardiovascular Institute at Boston University School of Medicine through a pilot grant award to V.B.K; Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the NIH.

Disclosure The authors declare no competing interests.


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References 1. Salaun, F.; Devaux, E.; Bourbigot, S.; Rumeau, P., Application of Contact Angle Measurement to the Manufacture of Textiles Containing Microcapsules. Text Res J 2009, 79 (13), 1202-1212. 2. Zhang, X.; Shi, F.; Niu, J.; Jiang, Y. G.; Wang, Z. Q., Superhydrophobic surfaces: from structural control to functional application. J Mater Chem 2008, 18 (6), 621-633. 3. Whitesides, G. M.; Laibinis, P. E., Wet Chemical Approaches to the Characterization of Organic-Surfaces - Self-Assembled Monolayers, Wetting, and the Physical Organic-Chemistry of the Solid Liquid Interface. Langmuir 1990, 6 (1), 87-96. 4. Zhou, F.; Huck, W. T. S., Three-stage switching of surface wetting using phosphatebearing polymer brushes. Chem Commun 2005, (48), 5999-6001. 5. Bico, J.; Thiele, U.; Quere, D., Wetting of textured surfaces. Colloid Surface A 2002, 206 (1-3), 41-46. 6. Yao, X.; Song, Y. L.; Jiang, L., Applications of Bio-Inspired Special Wettable Surfaces. Adv Mater 2011, 23 (6), 719-734. 7. Wen, L. P.; Tian, Y.; Jiang, L., Bioinspired Super-Wettability from Fundamental Research to Practical Applications. Angew Chem Int Edit 2015, 54 (11), 3387-3399. 8. Chung, D. W.; Lim, J. C., Study on the effect of structure of polydimethylsiloxane grafted with polyethyleneoxide on surface activities. Colloid Surface A 2009, 336 (1-3), 35-40. 9. Degennes, P. G., Wetting - Statics and Dynamics. Rev Mod Phys 1985, 57 (3), 827-863. 10. Jung, Y. C.; Bhushan, B., Wetting Behavior of Water and Oil Droplets in Three-Phase Interfaces for Hydrophobicity/philicity and Oleophobicity/philicity. Langmuir 2009, 25 (24), 14165-14173. 11. Adamson, A. W., The physical chemistry of surfaces. Abstr Pap Am Chem S 2001, 221, U320-U320. 12. Nguyen, T. A. H.; Nguyen, A. V., Increased Evaporation Kinetics of Sessile Droplets by Using Nanoparticles. Langmuir 2012, 28 (49), 16725-16728. 13. Xu, W.; Leeladhar, R.; Kang, Y. T.; Choi, C. H., Evaporation Kinetics of Sessile Water Droplets on Micropillared Superhydrophobic Surfaces. Langmuir 2013, 29 (20), 6032-6041. 14. Wang, F. C.; Wu, H. A., Pinning and depinning mechanism of the contact line during evaporation of nano-droplets sessile on textured surfaces. Soft Matter 2013, 9 (24), 5703-5709. 15. Lopes, M. C.; Bonaccurso, E., Evaporation control of sessile water drops by soft viscoelastic surfaces. Soft Matter 2012, 8 (30), 7875-7881. 16. Yu, Y. S.; Wang, Z. Q.; Zhao, Y. P., Experimental study of evaporation of sessile water droplet on PDMS surfaces. Acta Mech Sinica-Prc 2013, 29 (6), 799-805. 17. Gleason, K.; Voota, H.; Putnam, S. A., Steady-state droplet evaporation: Contact angle influence on the evaporation efficiency. Int J Heat Mass Tran 2016, 101, 418-426. 18. Golovko, D. S.; Butt, H. J.; Bonaccurso, E., Transition in the evaporation kinetics of water microdrops on hydrophilic surfaces. Langmuir 2009, 25 (1), 75-8. 19. Dietrich, E.; Kooij, E. S.; Zhang, X.; Zandvliet, H. J.; Lohse, D., Stick-jump mode in surface droplet dissolution. Langmuir 2015, 31 (16), 4696-703. 20. Biole, D.; Wang, M.; Bertola, V., Assessment of direct image processing methods to measure the apparent contact angle of liquid drops. Exp Therm Fluid Sci 2016, 76, 296-305.


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21. del Rio, O. I.; Neumann, A. W., Axisymmetric drop shape analysis: Computational methods for the measurement of interfacial properties from the shape and dimensions of pendant and sessile drops. J Colloid Interf Sci 1997, 196 (2), 136-147. 22. Hoorfar, M.; Neumann, A. W., Recent progress in Axisymmetric Drop Shape Analysis (ADSA). Adv Colloid Interfac 2006, 121 (1-3), 25-49. 23. Saad, S. M. I.; Neumann, A. W., Axisymmetric Drop Shape Analysis (ADSA): An Outline. Adv Colloid Interfac 2016, 238, 62-87. 24. Skinner, F. K.; Rotenberg, Y.; Neumann, A. W., Contact-Angle Measurements from the Contact Diameter of Sessile Drops by Means of a Modified Axisymmetric Drop Shape-Analysis. J Colloid Interf Sci 1989, 130 (1), 25-34. 25. Stalder, A. F.; Melchior, T.; Muller, M.; Sage, D.; Blu, T.; Unser, M., Low-bond axisymmetric drop shape analysis for surface tension and contact angle measurements of sessile drops. Colloid Surface A 2010, 364 (1-3), 72-81. 26. Harris, C.; Stephens, M. J. In A combined corner and edge detector, Alvey Vision Conference, Alvey Vision Club, Taylor, C. J., Ed. Alvey Vision Club, 1988; pp 23.1-23.6. 27. Kamarainen, J. K.; Kyrki, V.; Kalviainen, H., Invariance properties of Gabor filter-based features - Overview and applications. Ieee T Image Process 2006, 15 (5), 1088-1099. 28. Chen, C. C.; Chen, D. C., Multi-resolutional gabor filter in texture analysis. Pattern Recogn Lett 1996, 17 (10), 1069-1076. 29. Daugman, J., How iris recognition works. Ieee T Circ Syst Vid 2004, 14 (1), 21-30. 30. Grigorescu, S. E.; Petkov, N.; Kruizinga, P., Comparison of texture features based on Gabor filters. Ieee T Image Process 2002, 11 (10), 1160-1167.


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Figure captions

Figure 1: Schematic of the Kruss DSA100 goniometer used for generating sessile liquid drop evaporation videos. (A) Kruss DSA100 Frame. (B) High speed video camera. (C) Diffused backlight, used to cast a shadow which creates the drop profile. (D) Translating stage with the liquid drop. (E) Liquid dispensing syringe. (F) Live-feed video monitoring of the drop evaporation process. The Kruss DSA100 software was used for live monitoring.

Figure 2: Drop cases with generated surface and tangent lines, depicted as yellow and orange lines, respectively. (A-C) Distilled water placed on a horizontal glass substrate. (D-F) Distilled water placed on a horizontal paraffin substrate. (G-H) Distilled water placed on an inclined glass substrate. (J-L) Distilled water placed on an inclined paraffin substrate.

Figure 3: Modified Harris corner detection scheme. (A) Image of the evaporating sessile liquid drop. (B) Intensity map of the Harris corner detector response. (C) Gaussian prior applied on the response for identifying left and right endpoints. (D) Intensity map of the two detected endpoints.

Figure 4: Gabor wavelet optimization. (A) Representation of the Gabor wavelet applied on the sessile drop edge. The arrows denoting 𝛥𝑑 and 𝛥𝜃 demonstrate the translation of the wavelet in the direction 𝑑 and rotation by the angle 𝜃, respectively. (B) Contour map of the applied wavelet responses. The contour map is used for optimization of the two free parameters, 𝜃 and 𝑑. Figure 5: (A) Color mask visualization to improve Gabor wavelet functionality for sum of angles near 180°. Numbering scheme correspond as follows: (1) Background color mask, hashed


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texture, (2) Surface normal vector, (3) True edge, (4) Surface vector, (5) Drop color mask, crosshatched texture, (6) Edge normal vector, and (7) Reflected edge. (B) Representation of the relationship between Gabor wavelet error and sum of true and reflected angles for four different Gabor wavelet parameters. The default trendline refers to the parameter set defined in the Methods section. For other trendlines, the figure legend distinguishes the altered variable.

Figure 6: Results for dynamic measurement of drop diameter and individual contact angles. (A) Distilled water on flat glass. (B) Distilled water on tilted glass. (C) Distilled water on a flat paraffin surface. (D) Distilled water on a tilted paraffin surface. The insets illustrate the drop profile for the first measured frame.

Figure 7: Comparison of the Gabor wavelet method with the Young-Laplace fit. (A) Method comparison for distilled water on flat glass. (B) Method comparison for distilled water on inclined glass. (C) Method comparison for distilled water on flat paraffin surface. (D) Method comparison for distilled water on inclined paraffin surface.

Figure S1: Color mask visualization for to improve Gabor wavelet functionality. (A) Sum of angles less than 90° (D) Sum of angles greater than 90°. (1) Background color mask, hashed texture, (2) Surface normal vector, (3) True edge, (4) Surface vector, (5) Drop color mask, crosshatched texture, (6) Edge normal vector, and (7) Reflected edge.

Figure S2: Screenshots of the GUI-based software for drop shape analysis. (A) Video preview tab with slider function that scrolls through each frame of the video. Slider function is used to


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determine the first and last measurable frames. (B) Surface line detection tab. Five figure windows show (from top left – bottom right), raw image, intensity plot of Gaussian prior, detected surface line overlaid on the raw image, detected endpoints overlaid on the raw image, intensity plot of the detected endpoints. Using this tab, the user finds a reference frame where the surface line can be clearly defined. After the user inputs relative locations for left and right endpoints, the surface line can be visualized. (C) Gabor wavelet tab. Allows user to adjust the Gabor wavelet parameters to suit their needs. The tab shows the left and right applied Gabor wavelets as well as the edge which they correspond to. The user must alter the parameters so that the wavelet mimics the drop edge. (D) Optimization tab. Used to select the method of optimization, as well as any error checking implemented features. Four windows are displayed. One window illustrates the detected tangent line for the left angle, and a second window shows the contour map used to validate optimization. Two more windows highlight the same features, however for the right tangent line. (E) Run Tab. The user will input the last measurable frame and run the program within this tab. When the program is running, two real-time updating windows are displayed. The left window shows the real-time tangent lines and endpoints detected on each measured frame. The right window illustrates an updating graph of left angle,

Figure S3: Dynamic estimation of contact angle and drop diameter with generated surface and tangent lines, depicted as yellow and orange lines, respectively. (A-D) Distilled water on flat glass. (E-H) Distilled water on a flat paraffin surface. (I-L) Distilled water on tilted glass. (M-P) Distilled water on a tilted paraffin surface. Each row signifies a different time point in the drying process. From the top row to the bottom row, the intervals are 20%, 40%, 60% and 80% normalized drying time.


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Figure S4: Additional trials demonstrating dynamic estimation of contact angle and drop diameter with generated surface and tangent lines, depicted as yellow and orange lines, respectively. (A-D) and (E-H) Distilled water on flat glass. (I-L) and (M-P) Distilled water on a flat paraffin surface. Each row signifies a different time point in the drying process. From the top row to the bottom row, the intervals are 20%, 40%, 60% and 80% normalized drying time.

Figure S5: Additional trial results for dynamic measurement of drop diameter and individual contact angles. (A, C) Distilled water on flat glass. (B, D) Distilled water on a flat paraffin surface.

Figure S6: Visualization of the synthetic drop profile. Here α determines the rotation of the reflected edge, 𝛺𝐷 is the area of the drop profile and 𝛺𝐵 is the area of the background. The Gabor wavelet is shown to be parallel to the y-axis.


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Gabor wavelet application Sessile drop video generation

Individual contact angle and drop diameter estimation Corner detection


Estimation of size and contact angle of evaporating sessile liquid

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